JIMMA UNIVERSITY

COLLAGE OF BUSINESS AND ECONOMICS

DEPARTMENT OF ECONOMICS

MACROECONOMICS II (ECON 312)

LECTURE NOTE

ByWondaferahu Mulugeta1

June 2009 Jimma

Ethiopia

1 The author is lecturer of economics, collage of business and economics, department of economics, Jimma University

CHAPTER ONE SECTORAL DEMAND THEORIES AND FUNCTIONS

Introduction: How do households decide how much to consume today and in future? We care about this decision because consumption is the largest component of aggregate demand and saving is one of the determinants of growth. Thus, knowledge about how do households arrive at this decision and what factors affect their decision making is critical.

1.1 Theories of Consumption and consumption expenditure 1.1.1 Keynesian Consumption theory: The absolute income hypothesis (AIH)

Keynes postulates three complementary propositions/assumptions:1. Consumption will rise as disposable income rises. In other words, income is the

most important determinant of consumption. That is the higher the income of a household the higher will be consumption.

2. The MPC is positive and less than 1. This is to mean the increase in consumption will be smaller that the increase in disposable income. \in other words households spend less that their total income

3. APC ( ) is greater than the MPC but assumed to fall as income rises. The implication is that on average the rich spend less of their income than (or saves more than) the poor.

Algebraically, Keynes’s short-run consumption function is given by

---------------------------------------------------------------- (1)

Where is autonomous consumption and is or the MPC and is greater than 1 (by the

first proposition). Graphically, the function is shown in Figure 1.1, which plots consumption expenditure ( ), against real income ( ). This function indicates the observation that as income increase people tend to spend a decreasing percentage of income, or conversely tend to save an increasing percentage of income(by the second proposition). The slope of the line from the origin to a point on the consumption function gives the average propensity to consume (APC) or the ratio at that point.

The slope of the function itself is the Marginal Propensity to Consume (MPC). From the graph it is clear that the MPC is less that APC. If the ratio of falls as income rises, the ratio of increment in ( ) to the increment in ( ), or (MPC), must be smaller than . Keynes saw this as the behavior of consumer expenditure in the short-run- over the duration of a business cycle- reasoning that as income falls relative to the recent levels, people will protect consumption standards by not cutting consumption proportionally to the drop in income, and conversely as income rises, consumption will not rise proportionally.

2

B A

Figure 1.1: Keynes Consumption Function (absolute income hypothesis)

The line is the line along which all income is consumed. At income level , consumption is given by , while savings are given by and represent that amount of income not spent. The average propensity to consume ( ) is represented by the slope of line . The figure also represents APC declines as income increases. Suppose now that income increased from to . The APC is now given by the slope of the line , which is less than the slope of and hence APC has declined.

The acceptance of the theory that ; so that as income rises falls led to the formulation of stagflation thesis around 1940. It was observed that if consumption follows this pattern, the ratio of consumption demand to income would decrease as income rises. The problem for fiscal policy that the stagflation thesis poses can be seen as follows. If

or ------------------------------------- (2)

is the condition for equilibrium growth of real output ( ), and there is no reason to assume that the ratio of private investment to income ( ) will rise as economy grows, then government expenditure to income ( ) must rise to balance the consumer expenditure to income ( ) drops to maintain full-employment demand as grows.

In 1946, Simon Kuznets published the first long-run time-series data for the USA for the period 1869 -1929 a study on consumption and saving behavior dating back to the Civil War (1865). Kuznets’ data pointed out two important things about consumption behavior. First, it appeared that on average over the long-run the ratio of consumer expenditure to income ( ) or APC, showed no downward trend, so the MPC equaled the APC as income grew along trend. This meant that along trend the function was a straight line passing through the origin as shown in Figure 1.2

3

Long-run function:

Short-run function:

Figure 1.2: Long-run and short-run consumption functions

Second, Kuznets’ study suggest that years when the ratio was below the long-run average occurred during boom periods, and with ratio above the average occurred during periods economic slump (recession). This meant that the ratio varied inversely with income during cyclical fluctuation, so that for the short period corresponding to a business cycle empirical studies would show consumption as a function of income to have a slope like that of the short-run functions of Figure 1.2 rather than the long-run functions. Thus, by the late 1940s it was clear that there were three observed phenomena, which the consumption function must account for

1. Cross-section budget studies show increasing as rises, so that in cross-section of the population

2. Business cycle, or short-run data show that the ratio is smaller than average during boom periods and greater than average during slumps, and hence in the short-run, as income fluctuates,

3. Long-run trend data show no tendency for the to change over the long-run, so that as income grows along trend,

In addition, the theory of consumption should be able to explain the apparent effect of liquid assets on consumption. Therefore, the failure of Keynesian consumption function to explain long-run behavior of consumption in cross-section studies and the effect of liquid assets on consumption has motivated to the emergence of alternative consumption theories in 1950s. Unlike Keynes, the theories that were developed by Fisher, Ando-Modigliani, and Friedman have basic foundation in the microeconomics theory of consumer intertemporal choice to explain these phenomena. In particular, Modigliani and Friedman begin with the explicit common assumption that observed consumer behavior is the result of an attempt by rational consumers to maximize utility by allocating a lifetime stream of earning to an optimum lifetime pattern of consumption. Thus, we begin the discussion of these three theories at their common points of departure in the theory of consumer behavior and follow them individually as they diverge.

1.1.2 Irving Fisher’s model of consumption (the intertemporal choice)

4

Consumption is assumed to be the purpose of all economic activities. However, though consumption theories before Fisher introduced some dynamics into consumption behavior, they do not have sound micro foundation.

Fisher assumes that household’s utility depends upon its lifetime profile of consumption. Hence, he began his explanation with a single rational consumer utility maximization behavior as

--------------------------------------------- (1)

Where, lifetime utility is a function of the individual’s real consumption in all time period up to , the instance before he/she dies. The consumer will try to maximize his/her utility, that is obtain the highest level of utility, subject to the constraint that the present value ( ) of his/her total consumption cannot exceed the of his/her total income in life. That is

------------------------------------------- (2)

Where, is the individual’s expected lifetime. The constraint says that the individual can allocate his/her income stream to a consumption stream by borrowing or lending, but the present value of consumption is limited by the present value of income. We thus have an individual with an expected stream of lifetime income who will want to spread that income over a consumption pattern in an optimum way. We might imagine that his/her expected income stream begins and ends low, with a rise in the middle, and he wants to smooth it out into a more even consumption pattern.

To keep the analysis as simple as possible and formulate the problem in a workable manner he assumed that the individual lives only for two periods: today; period zero and tomorrow; period 1 (intertemporal choice). The two-period case utility of the household for is thus given as:

------------------------------------------------ (3)

Second, the household is assumed to maximize lifetime utility subject to the borrowing-lending constraint imposed by its real wealth, where wealth is defined as the present value of all future income streams. In a two-period model this is simply:

-------------------------------------------- (4)

Where, represents the household’s expected real wealth measured in terms of current period (period 0); is this period’s real income; and is next period income discounted by the real rate of interest, .

5

Third, it is also assumed that the agent knows with certainty the expected future rate of interest and that capital market is perfectly competitive. This means that the household can either lend or borrow money as much as it wants at the going rate of interest without affecting the rate. Forth, transaction cost is also assumed to be zero. Since this is a two-period model and consumption is the sole determinant of economic growth (GDP), it follows that lifetime wealth will be the constraint of lifetime consumption. Thus at equilibrium, equation (4) can be

---------------------------------------- (5)

Figure 1.3 shows the structure of intertemporal model. The vertical axis measures income and consumption in period 1 while the horizontal axis measures income and consumption in the current period (or period zero).

Period 1

Period 0

Figure 1.3: Two-period consumption case: utility maximization added

The budget constraint (BC) in the above graph indicates the maximum amount of lifetime consumption. If the household is to consume its entire lifetime income stream in period zero by borrowing against period 1, then the maximum amount that can be consumed can

be , which is the intercept of the budget line in period zero axis, point .

Conversely, if the household decides to consume nothing in period zero, delaying or postponing all consumptions until period 1, then the maximum it can consume in period 1 is , which is given by point on period 1 axis. The slope of the budget

6

constraint (line) is given by differentiating the wealth constraint for a given level of interest rate, which is

------------------------------------------------- (6)

Point in figure 1.3 shows that the amount of income the household will earn in period zero, and the amount of income he/she will earn in period 1, . The household has also indifference map, representing preference for consumption in both periods and given by lines and . The subscripts of denote increasing level of utility.

The optimal consumption position for the household is thus given by indifference curve labeled . From point it is clear that the household saves in period zero for and dissaves in period 1 as . That is the unspent income (saving) in period 0:

Money lent --------------------------------- (7)

By lending this amount, the individual will receive in period 1 an amount equal to , so that his/her consumption in period 1 can exceed his/her income by that

amount, which is his/her period 1 dissaving, ------------------------------------- (8)

Since the slope of the indifference curve (IC), is equal to the slope of the budget line at point , the marginal utility of consumption (MUC) in period 0, to that in period, 1 , is exactly equal to . That is the between consumption in period 0 and consumption in period 1 is .

Furthermore, if the indifference curves (ICs) are homogenous of degree zero, then the slope of all ICs are identical along the straight line passing through the origin. This implies that the of and depends only on the ratio of and not on the absolute size of and .

This assumption has an important implication that if consumption is not an inferior good, one with negative income/wealth effect, then whenever a consumer received an extra Birr worth of resource he/she would allocate it between and in exactly the same proportion as he/she allocated his/her original resource.

1.1.3 The Ando-Modigliani approach: The Life-cycle Hypothesis of consumption

7

In order to explain the three observed consumption function relationships discussed earlier under 1.1.1, Ando and Modigliani postulate a life-cycle hypothesis. According to this hypothesis:

The typical individual has different income streams in his/her lifetime. It is relatively low at the beginning and end of his/her life, when his/her productivity is low and high during the middle of his/her life. This “typical” income stream is shown as the curve in figure 1.5, where is expected lifetime

$ Adult = Average income Youth Old Time

Figure 1.4: The ‘life-cycle’ hypothesis of consumption

On the other hand, the individuals might be expected to maintain a more or less constant/smooth or perhaps slightly increasing level of consumption that maximizes his/her utility, shown as the line in Figure 1.4 throughout his life.

The model suggests that in the early years of a person’s life, the first shaded portion of Figure 1.4, the individual is a net borrower. In the middle years (when adult) he/she saves to repay debt and provide for retirement. In the late years, the second shaded portion of Figure 1.4, the individual dissaves. This is to say that their consumption level does not vary with their income but with and .

Hence if the life-cycle hypothesis is correct then the high-income groups would contain a higher-average proportion of persons who are high-income levels because they are in the middle years of life, and thus have a relatively low ( ) ratio. Similarly, the low-income groups would include relatively more persons whose incomes are low because they are at the end of the age distribution, and thus have high ( ). Thus, if the life-cycle hypothesis is true, a cross section study would show ( ) falling as income rises, explaining the cross section studies showing Therefore, it seems reasonable to assume that in the absence of any particular reason (say holiday, unforeseen events/contingencies like hospitalization, rise in payment bills, car repairs, and the like) to favor consumption in any one period over any other, for representative consumer ( ) if rises, all his/her consumption in period ( ) rises more or less proportionally. In other words, the Ando-Modigliani life-cycle hypothesis of consumption for the consumer can be written algebraically, as

; ------------------------------------------ (1)

8

Where, is consumption; represents an individual; is time (in year); and implies present value. On the other hand, is a constant, which is assigned overtime to indicate that an individual will spend certain proportion of his/her income and asset values on consumption of goods and services. Here , the fraction of consumer he/she wants to consume in period , would depend on the shape of the indifference curve and the interest rate.

Equation (1) says that if an increase in any income entry, present or expected, rises the consumer’s estimate of , he/she will consume the fraction of the increase in the current period.

If the population distribution by age and income are constant, and tests between the present and future consumption (that is the average shape of indifference curves) are stable through time, we can add up all the individual consumption functions (1) and obtain a stable aggregate function2:

--------------------------------------------------------- (2)

The next step is to develop an operational consumption function from (2) is to relate theterm measurable economic variables3. The Ando-Modigliani began to make the

tem operational by noting that income can be divided into income from labour ( ) and income from asset or property ( ). That is,

------------------------------------- (3)

Where, time zero is the current period and changes from zero to the remaining years of life of life expectancy of an individual ( ), which is highly unpredictable.

Now, if capital markets are reasonably efficient, we can assume that the of income form an assets is equal to the value of the asset itself, measured at the beginning of the current period. That is,

------------------------------------------------------ (4)

Where, is real household net worth at the beginning of the period. Furthermore, we

can separate the known current labour income ( ) from the unknown (future or

(expected) labour income ( ). Then substituting (4) into equation (3) we get

2 Branson (1998) noted that the gradual change in age and income distribution in the U.S. since World War II certainly meet the Ando-Modigliani assumption.

3 This is the crucial step in empirical investigation of the consumption function, as it is in almost any empirical study in economics. The theory involves consumption as a function of expected income, which of course cannot be measured.

9

---------------------------------------- (5)

In equation (5), current labour income ( ) and the value of current wealth or assets ( ) are known. But, the expected or future stream of labour income that flow overtime during

the lifetime ( ) is unknown. The next step is this sequence is thus determining

how the expected labour income ( ) might be related to the current observable variables. First, let as assume that there is an average expected labour income in time zero, such that:

------------------------------------------ (6)4

Where, is the remaining life expectancy of the population up to retirement, which is

37 (19 to 55 years) for an Ethiopian who joins the labour force at the age of 18 and

averages the present value of the future stream of labour income over years. Then the expected labour income term in expression 5 can be written as:

----------------------------------------- (7)

Substituting, the term in the left hand side of equation (7) into equation (5) we get------------------------------------- (8)

Equation (8) has only one remaining variable that is not measured - average expected labour income; that is . We now need a final hypothesis linking average expected labour income to a current variable – current labour income.

The simplest assumption Ando and Modigliani considered was that the expected average income is just a multiple of present labour income; that is and . This assumes that if current income rises, people adjust their expectation of future incomes up to that rises by the fraction of the increase in . We might note here that this assumption assigns great importance to movements in current income as a determinant of current consumption. Thus, substituting for in expression (8) we obtain:

------------------------------------------ (9)

4 In equation (3.6), 1 indicates the first year an individual is entitled legally to be employed in formal sectors. For instance, the constitution indicates that the minimum age for an Ethiopia to apply for a vacancy and be employed in formal sectors is the age of 18. In Sweden an individual who has celebrated his/her 16th birthday is permitted to engage in formal sector.

10

Where, is a constant which represents the discount rate or by how much the future stream of labour income will be discounted? Equation (3.9) is an operational expression for in that both and can be measured statistically. Finally, substituting, equation (9) into equation (2) for consumption we obtain a statistically measurable form of the Ando-Modigliani lifecycle consumption function as:

---------------------------------------- (10)

For instance, the coefficients of and in equation (10); that is the marginal propensity to consume out of labour income and marginal propensity to consume out of asset, were measured by Ando and Modigliani using annual U.S. date and obtained

------------------------------------------------ (11)

The econometric result of Ando and Modigliani indicates that a $1 billion (or 1%) increase in real labour income will raise real consumption by about $0.72 billion or the marginal propensity to consume out of labour income by 72%. Similarly, the marginal propensity to consume out of assets is 0.06 billion for an increase of households net worth by $1 billion.

Comparing the estimates of the coefficients in (11) with the derived coefficients in (8), we can see from the coefficient of in equation 11, that is is 0.06. This suggests, from equation (2) that on aggregate, households consume about 6% of their net worth in a year. Using this value for equal to 0.06 and 45 years as a rough estimate of average remaining lifetime ( ), we can obtain the value of (discount rate) from equation (10) that is implicit in the estimate of the coefficient in (11):

This suggests that when current labour income ( ) goes by $100, in the aggregate, the

average expected labour income ( ) rise by $25. Put differently, when current income doubles (increases by 100%), then the expected labour income will rise by 25%.

The Ando-Modigliani lifecycle consumption function of equation (10) is shown in Figure 1.5 below, which graphs consumption against labour income. The intercept of the consumption-income function is set by the level of assets; that is . The slope of the function – the marginal propensity to consume out of labour income – is the coefficient of in the Ando-Modigliani consumption function. In short-run, cyclical fluctuations with assets remaining fairly constant, consumption and income will vary along a single

11

consumption-income function. Over the longer run, as saving causes assets to rise the consumption-income function shifts up as increases.

0

Figure 1.5: Estimated consumption function: Ando and Modigliani

Thus, overtime we may observe a set of points such as those along the line in Figure 1.5, which shows constant consumption – income ratio along trend as the economy grows. This constancy of the ratio can be derived from the Ando-Modigliani consumption as follows. We can divided all the terms in equation (11) by total real income to obtain

----------------------------------------------- (12)

If the ratio given by this equation is constant as income grows along trend, then the line , which gives the average propensity to consume , will go through the origin in Figure 1.5. The will be constant if the - the labour share in total income – and

- the ratio of assets or capital to total output/income – are roughly constant as the economy grows along the trend5.

Ando and Modigliani noted that the observed data for the U.S. confirm that both the labour share of income and the ratio of assets to income terms were fairly constant around 76% and 300% (or simply 3) respectively. Substituting, these typical values into equation (12), for the or ratio we obtain

5 Ando-Modigliani noted that the observed data for the U.S. confirm that both these terms were fairly

constant. Overtime, the labour share of income has remained around 75 percent with a slight tendency to

drift up, and the ratio of assets to income has been roughly constant at about 3 percent with a slight

tendency to drift downward overtime.

12

Thus, the average propensity to consume out of total income ( ) is constant at about 0.72, which implies that the line in Figure 1.5 is a straight line passing through the origin with the slope of 0.72.

Merits of the life-cycle hypothesis1) The Ando-Modigliani model of consumption behavior

explains all three of the observed consumption phenomena. That is(A) It explains the result of cross-section budget studies by the life-cycle

hypothesis.(B) It provides an explanation for the cyclical behavior of consumption with the

consumption-income ratio inversely related to income along a short-run function (see Figure 1.3) and

(C) It also explains the long-run constancy of the average propensity to consume out of total income ( ratio).

2) In addition, it explicitly includes assets as an explanatory variable in the consumption function, a role which was observed in the post-World War II inflation.

Limitations of the life-cycle hypothesis1) There remains a question concerning the role of current income in explaining

current consumption whether

1.1.4 The Friedman approach: Permanent Income Hypothesis Freidman also begins with the assumption of individual consumer utility maximization which gives the relationship between an individual’s consumption and of future streams of income. That is

--------------------------------------------------------- (1)

Where, the change in consumption with respect to or . Friedman differs from Ando-Modigliani beginning with his treatment of the . Multiplying expression (1) by the rate of return on assets ( ) gives us Friedman’s permanent income.

---------------------------------------------------------- (2)

Where, and are permanent income and interest rate respectively. Equation (2) is the permanent income from the consumer present value, which includes his/her human capita- the of his/her future labour income stream, that is included in in equation (2) and his/her wealth ( ).

---------------------------------------------------------- (3)

Like Ando-Modigliani, Friedman also assumes that an individual consumer wants to smooth his/her actual income stream into a more or less flat/uniform consumption

13

pattern. This assumption gives a level of individual’s permanent consumption ( ), which

is proportional to his/her permanent income ( ):

---------------------------------------------------------- (4)

The individual’s permanent consumption to permanent income ratio ( ) mainly depends on the interest rate -the return on saving and individual tests shaping the indifference curves, and the variability of expected income. That is,

------------------------------------------------------- (5)

Thus, if there is no reason to expect these factors to be associated with the level of income, we can assume that the average for all income classes will be the same; equal

to the population average . If we classify the population by income strata, we would

expect that the average permanent consumption in each income class (using subscripts

for income class as opposed superscripts to denote individuals) would be times the

average permanent income.

for all income class ------------------------------ (6)

Equation (6) states that permanent consumption of any income class (group) , be it the high or lower than average-income group, is a certain proportion of the group’s permanent. According to Friedman, total income of an individual is composed of two components: permanent income ( ), which the individual has imputed for himself, plus a random transitory/random income ( ), which can be positive, negative, or zero, and really represents income deviations from permanent income. That is, measured income is the sum of permanent and transitory income.

-------------------------------------------------------- (7)

In equation (7) the subscript refers to “transitory” not time. Permanent income is therefore, that part of income which the household regards as normal or expected, while transitory income is the difference between measured and permanent income, which arises due to unexpected or unforeseen occurrences or chances (such as a win in lottery). Similarly, total consumption in any period is the sum of permanent consumption ( )

and a random transitory-consumption6 component ( Tic ), which can be positive, negative, or zero, and represents deviations from the “normal” or permanent level of consumption. Thus, measured consumption is the sum of permanent and transitory consumption.

------------------------------------------------------- (8)

6 It is important to note that, at any period, transitory consumption can also be planned in advance or

unplanned at all. Whether planned or unplanned, random expenditures will be made only for a very short

period of time. Examples include expenditure on weeding, in case of condolence, hospitalization, inviting

a friend (s), etc.

14

In order to give the model some predictable power Friedman makes three further assumptions concerning the relationship between permanent and transitory income, permanent and transitory consumption, and transitory income and consumption. The assumptions concerning these relationships give the explanation in the Friedman theory of the cross-section result that

First, Friedman assumes that there is no symmetric relationship or correlation between permanent income and transitory income; in other words, is just a random disturbance (fluctuation) around . So the covariance of and across individuals; i.e., the

This assumption has the following implication for cross-section budget study results. Suppose we draw a sample of families from a roughly normal income distribution and then sort them out by income classes. Since and are not related, the income class that centers on the population

average income will have an average transitory-income component equal to zero

(i.e., ) and for that income class observed income will be equal to permanent

income (or ).

As we go up from the average income strata, we will find for each income class, more people in that income group because they had unusually high incomes that year, that is than people who were in that class because they had unusually low incomes that year. This happened because in a normal distribution, for any income class above the average, there are more people with permanent income below that class who can come up into it because in any one period than there are people above that class who can fall down due to . Thus, for income

classes above the population mean transitory income is positive ( ) and hence

observed income will be greater than permanent income ( ).

Similarly, below the average-income level, for any income class, there are more people who can fall into it due to having bad year so that than people who come up to it by having good year so that . Thus, for the population in the below average- income class transitory income is negative ( ). As a result,

observed income will be less than permanent income ( ).

This result, that when sorted by measured income, groups above the population mean

have and groups below the population mean have is important for Friedman’s

analysis, as we will see shortly.

15

Second, he assumes that there is no correlation or symmetric relationship between permanent consumption and transitory consumption. In other word, is just a random disturbance (fluctuation) around , which implies the .

Finally, he assumes that there is no symmetric relationship or correlation between transitory consumption and transitory income. In other words, a sudden increase in income due to transitory fluctuation will not contribute immediately to an individual’s consumption. Thus, he concluded that the .

The last assumption is intuitively less obvious or is highly debatable than the previous two, suggesting a lottery win does not increase transitory consumption. But it seems fairly reasonable since we are dealing with consumption as opposed to consumer expenditure. Freidman justifies this by arguing that in the face of a transitory rise in income individuals usually stick to the consumption plan and just opt to increase their savings. An alternative explanation is that his definition of consumption includes only the flow of service from durable goods and not expenditure on durable goods. If transitory income is spent on durable goods, then this can be classified as unplanned saving rather than unplanned consumption. In this sense the assumption looks much more credible.

The last two assumptions, that transitory consumption is not correlated with either permanent consumption or transitory income, mean that when we sample the population and classify the sample by income levels, for each income class the transitory variation in

consumption will cancel out so that for each income class and average permanent

consumption is the population average, ; for all income class .

We can now bring this series assumptions together into an explanation of the cross-section result that even when the basic hypothesis of the theory is that the

ratio of permanent consumption to permanent income is a constant .

1.1.4.1 Cross-section consumption functionConsider a randomly selected sample of population classified by income levels. For simplicity, let us denote income group above and below the population average by different letters as the above average population income group by and the below average population income group by . On the other hand, the average population income refers to national income/output divided by total population, which is most

popularly known as the Per Capita Income (PCI). In figure 1.6 it is designated by

in the horizontal axis.

A group with average observed income above the average population income will

have a positive average transitory-income component . Then for this above-average

16

group, observed average income will be greater than average permanent income; that is

(see to the right of the mid point of the horizontal axis in Figure 1.6).

Observe that average consumption, both measured and permanent for group is given by

multiplying permanent income by to obtain permanent consumption along the solid

line in figure 1.7. That is, first all income groups will have average permanent

consumption equal to (or ) along the line. Since transitory consumption

of income group ( ) is not related to either to its permanent consumption ( ) or

transitory income ( ); by assumption 1, all groups, including the above-average income

group will have zero average transitory-consumption component. Moreover, measured

average consumption of income group (i.e., ) is equal to its permanent consumption (

) or . Linking these two consumption conditions gives us

----------------------------------------------------- (8)

From equation (8), we know that . The solid line represents the relationship

between permanent consumption and permanent income. The point is the population

average measured income and if the sample is taken in “normal” year when measured

average income is on trend or along line, then average transitory income will be zero;

so that measured average and permanent income will be equal (i.e., ). On the other

hand, the point is the population average measured consumption and permanent

consumption.

However, though the above-average income group have average measured consumption (

) equal to permanent consumption ( ), its average measured income ( ) is greater

than permanent income ( ) as shown by point . As a result, an above-average

income group’s measured consumption to income ratio ( ) will be less than

. A similar story follows for the below-average income group ( ). For this

group, the average observed income is below average population income as shown by

17

point and hence measured consumption to income ratio ( or ) is greater

than . These results are illustrated in Figure 1.6.

First, consider sample group with average income above the population average

(i.e., ). This group has positive average transitory income component ( ), which

is greater than the population average permanent income (i.e., ), as shown in the

horizontal axis of Figure 1.6. Nevertheless, neither measured consumption nor the permanent consumption of the above average income group does not increase

proportional to the increase in transitory income; so that in the upper part of the

vertical axis. In order to locate both the measured and permanent average consumption

for group we multiply permanent income ( ) by to obtain along the line.

Thus, for an above-average income group ( ) we observe and ate at point ,

which lies below the permanent consumption line .

A

B

Figure 1.6: Friedman’s permanent income hypothesis consumption function

Next, observing lower than-average income group ( ), we see in the horizontal axis that

the average income of the group ( ) is less than the national average income ( ) or

18

. This is because, the average transitory income of the below-average sample group

( ) is less than zero. Nevertheless, average observed consumption (i.e., ) does not

decrease from that of the permanent consumption of income group. Furthermore, we

observe that and know that it is equal to and or along the

line. The location of and gives us point , lying above the line.

Therefore, connecting the points A and B, we obtain the cross-section consumption function that connects observed average income-consumption points. Since, this function has smaller slope than the underlying permanent function, it implies that in the cross-section budget studies we expect to see that marginal propensity to consume ( is less than average propensity to consume or if (but only if) the Friedman permanent hypothesis is correct (holds).

1.1.4.2. Time series dataThe permanent income hypothesis can also be used to explain the time series data. In

Figure 1.7, the long run permanent consumption function is again given by . Overtime,

as the economy and the national average permanent income grows along trend. What we observe in a long-run time series data are thus movements of the national average

consumption and income along the line ; giving a constant ratio. As the economy

cycles along its trend growth path, the average point will move above and below the

long-run line . During boom year, say period 1, when is above the trend, the average

transitory income of the population will be positive as measured by the distance

and hence average income will be greater than permanent income (or ). But

average transitory consumption will be zero; implying . Thus, when is above

trend, will be less than .

Similarly, in times of economic slump or when is below the trend as in year 2, will

be negative; ; and the ratio will be greater than . The cyclical movement is

depicted in Figure 1.7. Again joining point A and B gives the short-run time-series consumption function, where again the short run is less than the long run and

, but in the long-run .

19

Note that the difference between figure 1.6 and 1.7 is that in figure 1.6 the variation in income and consumption is in a cross-section in any one time, while in figure 1.7 the variation is in average income and consumption over the business cycle.

A

B

Figure 1.7: Friedman’s consumption function: cyclical movements

2.2.3 Distinguishing features of the lifecycle and permanent income hypothesesSimilarities

I. The two models are similar in the starting point of the analysis in the consumption-present value relationship given in equation 2.1. In other words, both hypotheses have micro foundation. Thus, they argued that an individual have different income stream of income in life and smooth out consumption overtime

II. Both concentrate on the structural relationship between expected lifetime income and current consumption.

III. Both the LCH and PIH treated the wealth effect on consumption.

Differences: The two theories differ in the empirical implementation of the theoryI. The LCH model exhibit smaller MPC than PIH because the former also includes a

wealth variable whereas in the latter the wealth effect is included in permanent income.

II. Friedman’s consumption model/function is somewhat less satisfactory than Modigliani in that assets are only implicitly taken into account as determinants of permanent income. In short, he did not clearly distinguishes between permanent income and (which is considered as a shift factor) as did by Ando-Modigliani , and

20

SR Consumption functions

III. Friedman relies on the unobservable concepts of income (i.e., permanent income and transitory incomes) while Ando-Modigliani relies on the observable income (i.e., income from labour and income from assets/property or the value of assets)

Applicability of the consumption theories to LDCsHow consumption theories discussed so far are relevant to LDCs such as a typical African economy?1) Both the LCH and PIH emphasize on households consumption smoothing or have

uniform consumption pattern (intertemporal consumption) due to their assumption of absence of borrowing and lending (liquidity) constraints to households. However, these assumptions are unrealistic in explaining the actual situation of African economies where households have excessive borrowing and lending constraints.

This is because we know that financial sectors are underdeveloped in almost all African economies. Due to this the majority of households do not have easy access to financial sectors. As a result, households in Africa, particularly those living in rural areas, are forced to relay mostly on individual creditors or usurers for borrowing. Even when there are financial intermediaries they have acute shortage of loanable fund due to high propensity to consume /or low propensity to save/ by the population due to high dependency ratio and in part due to commercial banks weak capacity to mobilize savings. Moreover, protracted loan application screening and disbursement processes; high collateral requirements of banks than most households can afford; and high lending interest rates are also some of the major constraints. For instance lending rate of commercial banks in Ethiopia is greater than 10% compared to only 1.5% in England.

In some cases, there are preferential treatments of financial intermediaries to public sectors borrowing than private firms and/or individuals in LDCs. This biased policy can be either due to political reasons; credit ceilings; or poor loan repayment enforcement mechanism to defaulters. The later has to do mostly with the underdevelopment of legal and judiciary system in LDCs.

2) The notion of the present value of future income streams in both the LCH and PIH models implies that consumers or economic agents have long planning horizon. Nevertheless, this assumption is irrelevant for a typical LDC even though there is no borrowing and lending constraints.

The reason is that, the planning horizon in LDCs is different than developed countries due to uncertainty in terms of what will happen next, which in turn influence peoples’ preferences for investment (which is more of short term than long term planning horizon); perception of life, and control over assets.

3) Parallel to the second limitation of the models, the assumption of perfect capital markets in both the LCH and PIH and hence income from assets at any time is equal to the value of asset itself are also irrelevant to LDCs or African economies. This is because markets in LDCs are more of imperfect and hence getting information about the value of assets is costly.

21

4) The argument of the LCH that individuals will save when income is high during adult for retirement does not also explain much LDC economies that have different demographic structure compared to developed countries. This is because LDCs have more young population, large family size, and high population growth7 compared to developed countries due to high birth rate.

High population growth and the type and composition of family in LDCs (extended family compared to nuclear family in developed countries) have in turn lead to high dependency ratio. Thus if resources are shared between workers and the dependents, the need for hump or saving when adult for retirement as the LCH argued is not necessary.

5) Income derived from agriculture is not considered explicitly in the models. In a typical African household economy, there is high uncertainty of income due to the erratic behavior of agricultural output or its vulnerability to weather change and macroeconomic instabilities such as fluctuation of price and exchange rate fueled by internal and external shocks. Hence, the subsistence income level derived from agriculture possesses a real threat to consumption level of households, a threat that is likely to exert powerful influence on the way in which income is spend and saved. Thus, in such a context the standard model in which permanent consumption is equal to permanent income cannot be derived from the utility maximization of an individual.

In general, the implication of the above limitations of the models is that in most LDCs. Therefore, the direct applicability of the models in explaining the subsistence economy of a typical LDCs or African economies is less compared to that of developed countries.

Exercise 1.1: 1)Distinguish between consumption of durable goods and consumer purchase of durable

goods. Why is this distinction important?2)Use the two period intertemporal model of consumption to show the effect of the

following(A)an decrease in income in period 1(B)supposing an individual faces a borrowing constraint in period zero and

period 1 3) In the context of the permanent income hypothesis what happen to consumption when

(A)There is charismas bonus(B)There is temporary tax increase(C)There is a major house repair required

4) Assume that you have established an empirical consumption function of

Where, and are real consumption, real income, and real wealth. What would you estimate to be

7 For instance the average size and population growth in Ethiopia are 6 and 2.5% respectively. With this growth rate, the WB (2004) has forecasted that Ethiopia will be the 9th populated country in the world by the year 2050.

22

(A) The short-run MPC?(B) The long run MPC?(C) The short run APC?

1.2 INVESTMENT DEMAND HYPOTHESESInvestment is the accumulation of physical capital by firms’ overtime. There are three different types of real capital goods: fixed capital, items such as plant, machinery, and building; working capital, which consists of stock of raw materials, manufactured input, and final goods awaiting for sale; and residual investment, which include new houses for purchase or rent. Of these components of investment, fixed capital is the most important and is commonly referred as gross domestic capital formation.

Investment is much smaller than consumption, but it is the most volatile component of aggregate demand. Despite its size, investment is very important for the macro economy, since it is by investing in plant and machinery that the economy can produce goods for consumption in the future. Thus investment is an inherently dynamic process, whereby consumption is sacrificed today in order to enhance production and consumption in the future. Investment is therefore an element of economic growth.

From a theoretical point of view a stationary economy one where the capital stock is constant and the level of investment is exactly equal to the rate of depreciation of the existing capital stock. So although existing machineries are replaced as they wear out, there are no new additions to the capital stock, thus net investment, is zero. In this case, total or gross investment, is exactly equal to replacement investment- . This can be represented by a simple identity

--------------------------------------------------- (1)In the following sections four principal alternative theories of investment will be considered: Keynes theory of investment; the neoclassical theory of investment; the accelerator theory; and the Tobin’s Q model of investment.

1.2.1 Keynesian Explanation of investmentThere are two distinctive components in the Keynes’ theory of investment. First, he emphasizes on the role of expectations in deriving investment demand and second, he explicitly refers to the supply of capital goods which is related to the marginal efficiency of capital (MEC). In modern project analysis, the two components of Keynes’ theory of investment are called discounting measures of project worth or investment assessment criteria

1.2.1.1 Net Present Value (NPV)For Keynes the value of the owners unit of capital equipment was the flow of income, it would yield over its life in excess of the purchase cost. The flow can be thought as the net present value of income (NPV) or the demand price, , of the machine. Thus, the discounted net lifetime income of the machine is given as:

--- (2)

23

Where, is the rate of interest and is the life of the asset. Thus, if NPV or the demand price is greater than zero the investment project is profitable, in that the expected future revenue exceeds cost. As progressively more marginal projects are added the demand price of new capital declines until NPV becomes equal to zero, after which the additional project yields negative returns (profit).

0 Figure 1.8: The demand price of capital

Figure 1.9 shows that the demand schedule for capital good, which rises as the demand price falls, for a given market rate of interest and stream of expected returns.

A project’s net benefits have to be measured against the benefits that could have been gained by investing the equivalent sum for alternative uses. This is termed as the opportunity cost of capital achieved by using Discounted Cash Flow (DCF) measures of project worth. In investment project analysis discounting is normally used to work out the Present Value (PV) of a set of several Future Values (FVs). In its simplest form equation (2) can be expressed as:

--------------------------------------------------------------- (3)

Where, is the discounted rate expressed as a fraction or percentage and is year. The value in the bracket is called discounted factor (DF) for each year.

The NPV is defined as the difference between the present values of the future benefits and costs. It is the simplest of all the four methods and is essentially a measure of the present value of aggregate surplus generated by the project over its expected operating life. It is calculated by subtracting the present values of costs (PVC)8 from the present values of benefits (PVB). This implies that NPV represents the net benefit over and above the compensation for time and risk. This involves two steps of calculations as expressed by the formula.

--------------------------------------------------- (3a)

Or

--------------------------------------------- (3b)

8 Total cost is the sum of investment costs, incremental working capital (incremental stocks plus net incremental receivables, account receivable less account payable), and operating cost.

24

Where, is the life of a project

Decision Rule:a. Accept the project if the NPV is positive, which implies that the net

benefits will be created after allowing for the required rate of return fixed principally to cover the cost of capital in financing or opportunity cost of a sacrificed investment.

b. If the NPV is zero, is a marginal case and hence the decision may need to be informed by other criteria particularly for public sector projects. NPV equal to zero means the project will return the capital utilized, but it will not generate any surplus.

c. Reject the project if the NPV is less than zero or negative because the project will not recover its cost at the specified rate of discount.

1.2.1.2 Marginal efficiency of capital (MEC) or Internal Rate of Return (IRR)In addition to the concept of the demand price of capital goods Keynes also introduced the concept of the marginal efficiency of capital (MEC). The marginal efficiency of capital is defined as the rate of discount, , which would make the present value of expected returns from the capital asset during the project life to just equal to zero or the supply price, ; that is;

------------------------------------------------ (4)

Where, is the supply price of capital asset, which would just induce a manufacturer to produce new additional unit of such assets. That is the supply price is the replacement cost of new machine and not the cost of the purchase of second-hand machine, which of course does not add to the stock of capital in the economy as a whole. Thus the MEC or, is drawn for a given capital stream of expected returns and the supply price of capital. Indeed if , new capital equipment would be profitable to acquire, since only then will the MEC exceed the market interest rate, which denotes the return on alternative asses. In equilibrium, Keynes argued that the MEC in general is equal to the rate of interest; that is

.

In sum the PV ranking depends on the market interest rate-the rate at which earning can be reinvested-while the MEC of investment is not related to the market rate. So the PV rankings can be different from rankings. The best way to see this is to look at an example which can be easily generalized.

Example 1: Suppose we have two investment projects, both with initial cost one million. Both projects have zero return in period/year 1, when they are built. Project I returns 0 in period 1, and 4 in period 2. Project II on the other hand, returns 2 million in period 1 and 1 million in period 2. The costs and returns of two projects are summarized in the table below.

Year Project I Project IICost Return Cost Return

0 1 0 1 0

25

1 0 22 4 1

Given the information given in the table above1) Calculate the NPV of the two projects at market interest rate equal to 5% and 10%2) In which project should an investor invest when market interest rate are 5% and

10%? Why?3) If financial constraint dictates the investor to invest in one of the projects which

one should be chosen at the lowest interest rate? Why?4) Calculate the MEC ( ) for the two projects5) If the two projects are competing which of the two projects is better according to

the MEC criterion? Why?6) If the projects are not competing should we select and invest in both projects

according to the MEC criterion? Why or why not?

SOLUTION:1) The NPV of the two projects at interest rate equal to 5% and 10%. To

calculate the NPV we follow the following three steps

First: Find the net benefit of the two projects by subtracting the return of the projects in each year. The net benefits of project I and II are shown in column 2 and 3 respectively.Second: Find the discount factor at 5% and 10% from year zero to year two. This can

be obtained by using the formula; .It is shown in the 3rd and 4th

column in the table below.Third: Multiply the net benefit of project I and II in each year by the corresponding discount factors to get the NPV of the projects in each year. Summing up the NPV of the projects in each year gives the overall NPV as shown from column 6 to column 9.

Table 1.1: Net Present Value (NPV) and Marginal efficiency of capital (MEC)Net benefit (Return – Cost) Discount Factors NPV Project I NPV Project II

1.Year 2.Project I 3.Project II 4.r=0% 5. r=1% 6.(1*3) 7.(1*4) 8.(2*3) 9.(2*4)0 -1 -1 1 1 -1 -1 -1 -11 0 2 0.9524 0.9091 0 0 1.9048 1.81822 4 1 0.9070 0.8264 3.625 3.3056 0.9070 0.8264

SUM 0.9804 0.9612 2.6281 2.3056 1.8118 1.6446

2) Based on the overall NPV of the two projects as shown in the last row of column 6 to column 9 an investor should invest in both projects. This is because the overall NPV of the projects at 5% and 10% are greater than zero. However, the NPV of both projects is higher at 5% than at 10%.

3) If an investor has financial constraint to invest in the two projects, he/she should decide to invest in project II than in project I both at 5% and 10% market interest rate for it yields higher NPV; that is as can be seen in the last row of table 1.1 above 2.6281 is greater than 1.8118 when the market interest rate is 5% and 2.3058 is greater than 1.6446 at 10%. However, not that if the NPV of projects

26

vary as the market interest rate changes the criterion does not help to make such a conclusion. The reason is that if we compare two projects, the one which has larger return in the distant future (e.g. project I in year 2) will have higher NPV at some low interest rate than the second project that yields smaller return in future (e.g. in year 2) and will have a higher NPV at some higher market interest rate that pushes down the PV of the distant returns of the first project. For instance, calculate and determine which project is better according to the NPV criterion when market interest rate is zero and 100%.

4) The marginal efficiency of capital (MEC) or IRR using the NPV formula but looking for the interest rate that makes the NPV equal to zero for each projects.

MEC of Project 1:

Solving this equation for , we have

. This implies that the NPV of project I will be equal to zero when the rate of discount, ,is 100%.

MEC of Project 2:

Moving to the other side of the equation and multiplying both sides by gives

. Factorizing the left hand side we get. Subtracting from both sides we have

. This implies that the rate of discount ( ) that

makes the NPV of the second project zero is 141.4%.

Thus, since the MEC of the two projects is greater than the market interest rate both investment projects should be chosen. The MEC investment criterion or IRR indicates that project II is unequivocally better than project I, because or . The implication is that project I will have higher NPV at market interest rate lower than the equilibrium interest rate that makes the NPV of the two projects equal and the NPV of project II will be at higher at interest rate higher than the equilibrium rate.

27

In reference to this conclusion someone may raise the following questions. What is equilibrium interest rate that makes the NPV of the two projects equal? How can we calculate it? How can we show it graphically? We follow the steps below to answer these questions for projects with two years life.

First: Find the NPV of the two projects when interest rate is zero. Following the same procedure in example 1, we will get the NPV of project I equal to 3 and that of project II is 2 when the market interest rate is zero or there is no market interest rate to be charged on funds obtained from borrowing. Second: Find the equilibrium interest rate that makes the NPV of the two projects equal. This can be determined by equating the NPV of the two projects as

. Dropping from both sides and

multiplying through by gives us

. This implies that the NPV of the two projects will be equal when interest rate is 50%. In short, the equilibrium interest rate is half of the lower discount rate; that is .

At or 50% the NPV of both projects is 0.78. You can verify this using the NPV criterion we have applied in example 1 while computing the NPV of the projects at 5% and 10%. Therefore, if the two projects are competing the investor should choose project I if the market interest rate is below 50% and project II if the market interest rate is above 50%.

Third: We depict the NPV of the projects in the first and second steps as well as at the rate of discount ( ) graphically as follows.

3.0

2.0

1.0 0.78 E

0.2 0.4 0.6 0.8 1 1.4 II 2

IFigure 1.9: Present value and the market interest

Decision rule for MEC:

28

Accept the project if the MEC or IRR is greater than the market interest rate. For competing projects choose the one with the higher IRR.

If MEC or IRR is equal to the market interest rate, it indicates the project has no net return but will recover the cost to be incurred. In other word the project is marginal.

Reject the project with MEC or IRR less than the market interest rate because it will not recover its cost after allowing for the cost of capital.

Exercise 1.2: Given information on the costs and returns for investment project X and Y answer the following questions.

1) Find the sum of the net benefit streams of the projects and discus the implication2) Calculate the NPV of the two projects at the market interest rate of 5%. Which of

the two investment project is better according to the NPV criterion? Why?3) Calculate the MEC of the projects. Which one is better according to the MEC?

Why?4) What is the equilibrium market interest rate? What will be the NPV of the projects

at that interest rate? In witch should we invest if market interest rate is below the equilibrium rate?

Evaluation of NPV:The NPV as one of the discounting criteria of measuring project worth has the following advantages.a. It takes into account the value of resources overtime.b. It considers the net benefit stream in its entirety.c. The NPV of various projects, measured as they are in

today’s Birr can be added. The additive property of NPV ensures that a poor project (one which has a negative NPV) will not be accepted, just because it is combined with a good project, which has positive NPV.

d. The concept is clear and the solution is always determined.

Despite the above advantages, the NPV has its opponents towards some limitations.a. The application and dimension of NPV, seems to be

constrained in ranking investment or projects, is influenced by the discount rate.b. The NPV is expressed by in absolute terms rather

than relative terms and hence does not factor in the scale of investment. For example, project A may have a NPV of 5000 while project B has a NPV of 2500, but project A requires an investment of Birr 50,000 whereas project B may require an investment of 10,000. Advocators of NPV argue that what matters is the surplus value (rate of returns) irrespective of what is invested. However, opponents argue that for the NPV is an absolute measure of value it does not show the efficiency of a project in using capital. Out of the two projects B is efficient than A for its investment capital generates a 25% return than as compared to 10% of A.

c. The NPV rule does not consider the life of the project. Hence, when mutually exclusive projects are with different lives are considered the NPV is rule is biased in favour of the longer-term projects.

29

Evaluation of MEC or IRR:The use of MEC or IRR as a measure of project worth has the following advantages.a. It is more familiar concept and better understood by most

peopleb. It takes into account the value of resources overtime.c. It considers the net benefit stream in its entirety.d. It provides a measure of efficiency of the project in using

capital.The limitations of MEC or IRR include:a. Table 1.1 illustrates on of the deficiency of the MEC for ranking

investment projects. That is the MEC criterion makes no reference to the market interest rate, which measures the opportunity cost of capital.

b. It does not distinguish between large and small investment and it does not tell anything about the timing of the net benefits of the project. Therefore, it is not very useful for deciding between two or more mutually exclusive projects.

c. It is also possible that if the net benefit stream of a project changes or has more than one sign, there may be more than one IRR.

Exercise 1.3: (1) Calculate the NPV for the hypothetical X and Y projects at

10%. The cost and benefit streams are given in the table below (All figures in million)

Year 1.Total cost

2.Total Revenues/Benefits

0 140 0.01 65 1002 95 1503 95 2004 75 1505 55 100

(2) Given the cash flow for 2 projects calculate the NPV of the two projects at 10% interest rate

Year

Project 1 Cash flow

Project 2 Cash flow

0 (1,000,000) (1,000,000)1 65,000 35,0002 55,000 45,0003 45,000 55,0004 35,000 65,000

1.2.2 The Flexible Accelerator (inventory) model The relationship between the growth rate of output and the level of net investment implied in the previous section is called the accelerator principle since it suggests that an increase in the growth rate of output or acceleration is needed to increase the level of investment. The PV criterion suggests that this relationship between output growth and net investment is not a fixed one. However, an increase in interest rate should reduce the

30

level of net investment associated with a given growth rate of output. This variable relationship between the growth rate of output and the level of net investment is frequently known as the flexible accelerator model.

Equilibrium capital stock: we begin with the general production function

; ------------------------------------------- (2.1)

Here, is output pre unit of time; is human power input per unit of time; and is the capital stock.-plant and equipment. Implicitly we assume here a constant rate of utilization of capital stock so that there is a one-to-one relationship between capital stock and machine hour input. Thus a firm will expand its plan size until the marginal product of capita equals the real user cost of capital.

----------------------------------------------------------- (2.2)

Where, is the real user cost of capital. Equation (2.2) can be seen in another way. The increase in revenue which a competitive firm will obtain by adding another unit of capital , given its labour input is price of output times the increment to output produced by the increase in .

The increased cost to the firm of adding another unit of capital is simply the user cost of that unit

As long as the increase in revenue is greater than the increase in cost from another unit of capital the competitive firm will add capital. Equilibrium will be reached when

and , which is the same condition as equation (2.2).

This marginal condition (2.2) determines the equilibrium capital stock of the firm. Let’s take the following Cobb-Douglas production function as an example.

This production function has the property that the exponent of the capital and labour inputs add up to one, which gives constant return to scale. If capital and labour inputs are doubled, output will also double. The marginal product of capital in the Cobb-Douglas function is given by

--------------------------------------------------- (2.3)

This can also be written as

, substituting back into .

31

Thus with the Cobb-Douglas function, in equilibrium

----------------------------------------------------- (2.4)

The right hand side of equation (2.4) can be solved for the equilibrium level of capital stock in the Cobb-Douglas function

-------------------------------------------------- (2.5)

The equilibrium capital stock rises with an increase in and falls with an increase in the real user cost of capital. Equation (2.5) gives the expression for a particular production function. We can generalize this by writing as a function of and .

------------------------------------------------ (2.6)

In equation (2.6), and are positive and is negative. With equation (2.6) as a general expression for the determinants of , we can now develop the investment demand function relating realized investment to .

Investment demand and output growth: Total or gross investment is given as the sum of net investment ( ) and replacement investment ( ).

------------------------------------------------------- (2.7)

Net investment is that part of gross investment that increases the level of capital stock. On the other hand, replacement investment is part of gross investment needed to keep the capital stock at a constant level and is equal to economic depreciation of the stock in any one period. Replacement investment will simply be the depreciation of the capital stock

----------------------------------------------------------- (2.8)

Where, is the depreciation rate; a number like one-tenth for building and one-fifth for vehicles. Net investment in the absence of lags in the adjustment process of actual capital stock to desired capital stock, would be

--------------------------------------------------------- (2.9)

Thus we can see that net investment depends on changes in equilibrium level of capital stock, whereas replacement investment depends on the level of capital stock.

Looking at net investment first using the Cobb-Douglas function gives

-------------------------------------------- (2.10a)

If we assume that the ratio of user cost of capital to the price level, ceteris paribus, remains fairly constant overtime, we can rewrite equation (2.10a) as

32

---------------------------------------------------- (2.10b)

This makes it clear that over the long run, with no trend in , it is the growth of output or demand that gives us the level of net investment. The relationship between the change in output and the level of investment is the flexible accelerator model that introduced a basic dynamic relationship into the model of the economy. Thus, if net investment is related to by equation (2.10b) and net investment is also some fraction-the net saving ratio -of ; that is

Then we have the basic growth relationship

----------------------------------------------------- (2.11)

Dividing both sides of equation (2.11) by and solving for the growth rate of ,

, dividing both sides by , we have

Growth rate of ----------------------------------- (2.12)

Since investment increases the supply of output by increasing the capital stock, but it is also associated with the level of demand through the multiplier, equation (2.12) gives the rate of growth of output that would maintain supply equal to demand.

Second let’s look at total investment using the concept of net and replacement investment we have developed. Ignoring for a moment the lagged adjustment of actual to desired, we have from equation (2.7), (2.8), and (2.9) that

----------------------------------------- (2.13)

In the general case, we can write the investment equation (using equation 2.6)----------------------------------------- (2.14)

In the Cobb-Douglas example, is given by

----------------------------------------------- (2.15)

And in the special case where the real user cost of capital, is fairly constant we have

--------------------------------------------------- (2.16)

as the accelerator relationship.

33

The accelerator and stabilization policy: The accelerator relationship in the gross investment function, equation (2.14) poses an interesting difficulty in the short-run stabilization policy. This is shown in figure 1.10. The Figure shows what happens to investment as output rises from one stable level in two time period, 0 to and on and a transition period of unspecified length between the two.

Real

0

Figure 1.10: The “accelerator principle” on investment

In the first period there is a given level of output, which implies a given equilibrium capital stock .At time , the government increases government purchases to stimulate demand and output and equilibrium capital stock move to new higher levels in the second period, from on. Since the capital stock is constant both before and after , the level of investment is zero in each period and the level of is positive in each.

In order for the capital stock to increase to its new higher level in the second period, there must be a positive level of net investment in the transition period. This is indicated by the bulge in between and . Since is the sum of and , this means that during the transition period gross investment has also this bulge as shown by the dashed line in figure 1.10. Thus, total or gross investment in each period is summarized as follows

From 0 to :From to :From on:

1.2.3 The neoclassical model of investmentThis investment theory assumes:

34

1. A firm is a forward looking; that is it cares about the future stream of income not only the present

2. The firm operates under perfect competitive; that is it is a price taker3. There is no uncertainty about profit; there is no difference between expected

and actual profit. With these assumptions

-------------------------------------- (3.1)

The above profit maximization is subject to two constraints: technological constraints and capital stock. Assuming CRS, we write the first constraint as

------------------------------------------------------------------- (3.2)

Where, is workers hour of input and capital stock - plants and equipments. Besides, and

The second constraint, which is capital stock, is written as------------------------------------------------------- (3.3)

Where, is capital stock in the next period. Whereas and refer to capital stock available and additional investment in period .On the other hand, is the depreciation or obsolete of capital stock in the production process. Constraint (3.2) implies investment is a flow and capital is a stock. Thus, is determined by the difference between.

The profit maximization equation is thus

------------ (3.4)

However, based on the first constraint we know that can be expressed as . Thus, equation (3.4) can be written as

------- (3.5)

The question we want to address is that what will the optimum amount of labour to hired ( ); capital stock/goods to employ ( ); and additional investment ( ) to make in order to maximize profit or equation (3.5). These can be achieved by the first order derivative of equation (5) with respect to our variable of interest. That is

---------------------------------------------- (3.6a)

35

This refers to the demand for labour. Rearranging (3.6a) gives us MPL is equal to real

wage. That is

-------------------------------- (3.6b)

Where, refers that whatever capital stock that will be available next period is dependent on what some one has this year. This comes because is the end of period capital stock for .

--------------------------------------------------------- (3.6c)

----------------------------------------------------- (3.6d)

What is the profit maximizing capital stock? Rearranging (3.6c) gives us:

. This implies that

Substituting these two into (3.6b) for and we will obtain the users cost of capital.

--------------- (3.6c1)

Recall that, by the rule of exponent or . When

we substitute this in equation (6c1) gives you

------------------------------------------- (3.7)

Equation (3.7) says that the value of marginal productivity of capital or is equal to the users cost of capital.

Finally, dividing both sides of equation (3.7) by we have the expression like equation (3.8), which shows the users cost of capital relative to the price of the product or the marginal cost of capital is equal to the real cost of capital.

---------------------------------- (3.8)

Where, the rate at which the investment good/capital stock depreciates at time

36

The interest charge for investment or holding capital valued at the beginning of period

The gain or loss (overvaluation or undervaluation) in the price of investment good in period

1.2.4 Tobin’s Q theory of investmentTobin (1969) devised a way of relating investment demand to financial variables which is more amenable to empirical treatment than other investment models, while still having a firm theoretical basis. In fact the crucial variable, Tobin marginal Q has already been defined under the neoclassical model above in equation (3.7), which states is equal to the users cost of capital. That is

----------------------------------------- (4.1)

Rearranging this equation gives ------------------------------------------- (4.2)

Dividing both sides of equation (4.2) by , it becomes

----------------------------------------- (4.3a)

Expression (4.3a) is last year supply price of capital goods. In current time this dynamic equation becomes

------------------------------------- (4.3b)

This relationship says that the supply price of capital goods, , is the discounted future revenue stream plus the part of capital still in use. This is therefore identical to the concept discussed earlier.

Dividing the above expression first by , the price of new capital goods, gives the expression for Tobin’s marginal Q as

-------------------------------- (4.4)

Note that the numerator has three components: the term in the first bracket is the discount rate; inside the second bracket the first term is the additional revenue from the sale of output and the second term is simply the increase in the value of the firm’s capital in period that is the value of capital in next period less any depreciation. Therefore, the numerator is the increment to the value of the firm from the purchase of one more machine, discounted back to the current period. So Tobin’s marginal Q is the rate of change in the value of the firm to the added cost of acquiring new capital. If the firm is in equilibrium, then as in (expression 4.4)

37

Under the constant return to scale , from elementary theory of the firm, the marginal cost is proportional to average cost and thus under the CRS marginal Q is proportional to average Q. That is, marginal Q can be expressed as the ratio of the firm’s total valuation, , to total cost of its capital, , which is known as average Q.

----------------------------------------------------------------------- (4.5)

1.2.5 Determinants of investment in the case of Developing CountriesApplicability: Tobin’s suggestion is easy to measure from the stock market, but this is not applicable

in LDC’s for the financial sector is not well developed in many developing countries The assumption of perfect competition is not valid because markets in LDCs are more

of imperfect than perfect Exchange rate is more of rationed than auctioned in LDCs Political instability which is more common in LDCs implies uncertainty that affects

investment adversely is not mentioned The existence of huge public sector investment has also an impact on private

investment; depending the type of investment. It might be complementary (such as investment on infrastructure, transportation, electricity etc) that crowed in (encourage) private investment or supplementary that crowed out (affect adversely) to private investment

Transaction cost, the cost of doing business such as bureaucracy, corruption, bribe etc are very high in Africa.

1.3 THE SUPPLY OF AND DEMAND FOR MONEY1.3.1 Money Supply and monetary expansion

A. MONEY STOCK (SUPPLY)Introduction: There are three measures of money stock- M1, M2, and M3. M1 is the narrowest of the fed’s money supply definition. It includes currency held by non-bank private sector (or held outside bank for circulation including travelers checks (TC)) and checkable or demand deposits held by non-bank private (firms and households) sector (

). M1 is the potential base for deposit expansion and money supply creation.

M2 is the broadest measure of money supply than M1. It includes M1, other quasi money or deposit (D2) such as time deposits (TD), saving deposits (SD), and money market mutual funds (MMMFs) of individuals and firms (for example, dollar denominated deposits in foreign banks and agreements in which a corporation purchases T-bills from a bank and the bank agrees to buy them back the next day at a slightly higher price) on which limited checks can be written. Funds in quasi deposit and MMMFs are typically regarded as investment in short-term bonds. M2 is the most widely accepted measure of money supply.

38

Finally, M3 includes M2 and other assets less liquid than M2 such as money market mutual funds held by institutions (MMMIs)-such as provident funds, pension contributions, and saving and credit associations fund- and other assets (for example, gold deposits of individuals) (OAs). Funds, which are not counted as part of M2, are typically invested in long-term securities. M3 is used less frequently as a measure of money supply than M1 and M2. In short,M1 = C+D1 ---------------------------------------------------------------------------------------- (1)M2 = M1+ D2 (TD+SD +MMMFs) ------------------------------------------------------------ (2)M3 = M2+MMMIs + OAs------------------------------------------------------------------------ (3)

B. Monetary expansion mechanismAs we have defined it, money supply consists of currency and demand deposits which are supplied by the commercial banks. These banks have balance sheet made up of liabilities including demand deposits and assets reserve and loans. The Federal Reserve System requires that commercial banks retain a certain percent of their liabilities as reserve, mainly as deposits in the Federal Reserve Banks, in our case in the NBE. This reserve is called the reserve requirement.

Suppose the Fed decides to expand money supply. The managers of the Fed’s open market account buys in the bond market a certain amount of treasury bonds; say worth of Birr 100 thousand and issues a check, drawn by the Fed for Birr 100 thousand to the seller. The seller then deposits the check in his/her checking account in Bank A, creating a Birr 100 thousand liability for the bank, the claim o the bank by the depositor and also a Birr 100 thousand in asset for the bank , the claim on the Fed. If there is a 20% reserve requirement, bank A can loan Birr 80 thousand of its increase in assets and must retain Birr 20 thousand as a reserve as shown in table below.

Bank A Bank B Assets Liabilities Assets Liabilities

Br 100 Deposits 100 Br 80 Deposits 80 Reserve 20 Reserve 16 Loan 80 Loan 64

Bank C

Assets Liabilities Br 64 Deposits 84 Reserves=12.8 Loan 51.2

39

From the balance sheet of the three banks we understand that, the increase in money supply from the Birr 100 thousand reserve increases is given by

Thus, in this simple example assuming1. The banks are fully loaned up or there is no

excess reserve and2. There is no linkage into increased public

holding of currency, the change in money supply is given by

-------------------------------------------------------- (1.3.1)

Where, is the initial reserve increase due to OMO and is the reserve requirement ratio. With the above two assumptions and reserve ratio is 20%, the initial reserve increase will increase money supply by Birr 5 thousand

Consolidated money stockGiven information regarding the reserve requirement ratio as well as assets and liabilities of both the commercial and central/national banks the consolidated money stock/supply in an economy can be computed and posted in the balance sheet shown in table 1.1.

Table 1.1: The Banking System Consolidated Balance sheetNational Bank

Assets Symbol Liabilities Symbol

Gold & foreign exchange reserves High powered money Lending to the government

Commercial BanksAssets Liabilities Symbol

Currency and deposits with the national bank Deposits from the public Lending to the personal and corporate sector

Consolidated Banking sectorAssets Symbol Liabilities Symbol

Gold & foreign exchange reserves Currency in circulation: Domestic credit: Deposits from the public Money supply: Money supply:

3.2. Money Demand: The Transaction and Portfolio theories of money demand 1) The transaction demand for money: Baumol and Tobin noted that money is held to smooth out the difference between frequent income receipts and continual expenditure payments. This view of transaction demand for money assumes that individuals hold all the proportion of their income that they intend to spend in any on period in cash. Cash balances are, however, typically non-interest bearing and so is costly to hold large amount of cash. Individuals therefore

40

generally choose to hold only the cash they need for current transactions while leaving the rest in a bank deposit where it earns interest. This implies that, individuals and business firms maintain certain average level of cash and deposits because they need to make day-to-day transactions. If receipts of income and expenditure were always synchronized perfectly with respect to time, there would be no need for such idle cash balances. Because people are paid once a month or once a week and because they do not make all their disbursements as exactly the time they receive their income, they must maintain (hold) some amount of cash for the purpose of meeting their transaction needs.

In developing their model, Baumol and Tobin considered a hypothetical individual who receives monthly nominal income (say Birr 2,400) at the beginning of the month and spends it on transaction during the month (this period) at a uniform rate. If the individual keeps certain proportion of money his/her income in cash to carryout transactions, then his/her money balance follows the Saw-tooth pattern displayed in Figure 1.11. Time is measured horizontally and the amount of money balance held at hand and balance in bank account (bond holding) at the beginning of the time period is measured in the vertical axis.

In panel (a) we assume that the person received Y Birr of income (say Birr 2,400) at the beginning of the month (time zero) and spends the entire amount on transaction that occur at a uniform or constant rate during the course of the month. At the beginning of the month he has Birr 2,400, and by the end of the month he/she has zero balance because he/she has spent all. In other words, at the beginning of the month the person holds Y Birr and at the end, no money (cash) left. Since money is spent at a uniform rate (constant rate or stable intervals) throughout the month, his/her average holding of cash balance over the course of the month is simply Birr (or Birr 1,200)-holding at the beginning of the month, Birr 2,400 plus holding at the end of the month, Birr 0, divided by 2. It is this average idle balance that we call the transaction demand for money. Household average cash balance for number of withdrawals over any period can be written as:

--------------------------------------------------------------- (1)

Beginning bond balance is thus------------------------------------------------------------ (2)

Where, and denote beginning bond and beginning cash balance respectively.

Part of money balance ( ) that yields return to the bond holder is called average bond balance, which is half of beginning bond balance. It is expressed as

------------------------------------------------------------- (3)

Assuming for a moment there is no transaction cost (this assumption will be relaxed shortly), net interest total revenue (TR) earned by the individual or is given by

------------------------------------------------------ (4a)

41

Equation (1.4a) says that net interest earned by the individual or total revenue is the rate of interest multiplied by the unspent income in bank deposit or bond balance less the amount withdrawn in cash in the half way point. The expression in the bracket is equal to average bond holding. Hence, total revenue can also be written as

---------------------------------------------------------- (4b)

Suppose now the household withdraws half of the money from the bank at the start of the period and withdraws the other half at the start of the third week. When , panel (b) of Figure 1.11 shows that average cash balance is . Alternatively, panel (b) can be interpreted as the case in which the individual decides to make one bond-cash transaction by holding half of his/her Birr 2,400 in cash and put the remaining half into income earning bonds. In other word he/she holds Birr 1,200 in cash and uses the other Birr 1,200 to buy a Treasury bond at the beginning of the month.

Since bonds cannot be used directly to carryout transactions, he/she must sell the bonds and turn them into cash so that he/she can carryout his/her half month transactions. Thus, the individual’s bond holdings drop to zero at the middle of the month, and his/her cash balance rise up to Birr 1,200. By the end of the month all the cash is gone. When he again receives his/her next Birr 2,400 monthly payments, he/she again divides it into Birr 1,200 cash and Birr 1,200 of bonds, and the process continues. Using equation (3), the net result of this process is that the bond balance that yields return to the individual is

. It is clear that using equation (4a) or (4b) net interest or total revenue (TR) obtained from this process is 24. The value of marginal revenue ( ) is also 24.

Panel (c) shows when the household makes three times (per ten days) withdrawal or two bond-to-cash transactions. In this case, two third of the income (or Birr 1,600) will be put into bonds initially. Ten days into the month, half of the bonds [ ] or third of ; that is Birr 800 can be cashed. Each bond will then yield [ . Ten days latter the other half can be cashed having earned revenue for this third of . Total revenue in the three withdrawals or two bond-to-cash transactions cases will then be

. You can verify this also using equation (1.3.4a) or (1.3.4b). Marginal revenue is simply 32 less 24 or

This analysis entails that for withdrawals greater than one ( total revenue (TR) can also be obtained by analyzing the revenue is obtained each time when withdrawals are made9 or bonds are cashed using the expression below.

9 Where, multiplied by , and indicate amount of money that yield interest during the second , third,…, and last withdrawals. For instance, if is the amount of money withdrawn for the 5th time

42

---------------------------------- (5a)

(a) Plan/strategy/ 1: or no bonds-to-cash transaction

Y

Av. Mb =Birr 1,200

1 2 3 4 Weeks

(b) Plan/strategy/ 1: or one transaction

Y

Bond

Y/2=1200 Mb=Cash Av. Mb=Y/4=Birr 600

1 2 3 4 Weeks

(c) Plan 3: or 2 transactions Y

Bond

Y/3=800 Mb=Cash Av. Mb=Y/6=400

1 2 3 4 Weeks

43

(d) Plan 4: or 3 transactions Y

Bond

Av. Mb=Y/8=400 Mb=Cash

1 2 3 4 Weeks Fig 1.11: Individual’s transaction demand for money

For instance, for ,

This revenue is the sum of which give net earning equal to 10.67 and 21.33 in the second and third withdrawal or first and second bond-to-cash transaction.

Finally, panel (d) depicts that if the household makes four times (weekly) cash withdrawal or three times bond-to-cash transactions. In this case the average cash balance held is only Birr 300 or , which is .These example shows that the average cash balance held by the individual household falls as the number of cash withdrawals increase.

Examples above prompt the question as to what determines the number of withdrawals or transactions ( ) demand for money at any given period. There are two main factors. First, since a bank deposit account offers interest on funds remaining in the account, as interest rate rise households will economies/decrease their holding of idle/average cash balance for transaction purpose, thereby increasing . In figure 1.12 below, other things being equal, the number of withdrawals that maximize the TR of the individual increases from

to when the market interest rate increases from to Therefore, the transaction demand for money is sensitive and inversely related to the level of interest rate.

44

Assuming the interest rate is 4% per month and no transaction cost, the expression for the net interest or total revenue earned when the individual makes two to five times withdrawal or one to four bonds-to-cash transactions at a constant interval using equation (1.5) will be:

For

For

For

For

Results discussed so far regarding the revenue side of transaction demand for money are is illustrated in table 1.2 below given and no transaction cost.

Table 1.2: Marginal revenue from increasing transactions from bonds to cash

No of withdrawal (& duration

Initial (Beginning) Average (mid point)Cash

balanceBond

Balance( )Cash balance Bond

balanceTotal

RevenueMarginal Revenue

Amount withdrawn

1(beginning of the month)

Y=2,400 - 1,200 - - -

2 (Per 15 days) Y/2=1,200 Y/2 =1,200 ¼(Y)=600 ¼(Y)=600 24 r(Y/4)=243 (Per 10 days) Y/3= 800 2/3(Y) =1,600 1/6(Y)=400 1/3(Y)=800 32 r(Y/12)=84 (Per 7 days) Y/4= 600 ¾(Y) =1,800 1/8(Y)=300 3/8(Y)=900 36 r(Y/24)=45 (Per 5days) Y/5= 480 4/5(Y) =1,920 1/10(Y)=240 2/5(Y)=960 38.4 r(Y/40)=2.4

Note: TR in this table is computed on the assumption that transaction cost is zero. In this case TR and net interest earned are equal. However, TR will be greater than net interest earned when transaction cost is involved in making transaction.

From these strategies, it is clear that:1) The lower the average holdings of cash balance and

the higher the bond holding the more interest the individual will earn. But increases at a decreasing rate

2) The marginal revenue from increasing the number of transactions is positive and decreasing as the number of transactions increases.

3) Looking at the differences in MR column in table 1.2, we can see that as increases the drop in MR decreases. This gives us

45

curve in figure 1.12, which shows MR is a function of the number of transactionsfor given interest rate

The second factor that determines the size of is the transaction cost in terms say . On the cost side, we assume that each transaction has a give cost, , perhaps a brokerage fee for the buying and selling of bonds, the implicit cost of time spent transacting business, transportation cost, or trouble of making frequent visits to the bank in order to affect cash withdrawals, for making more trips. Then we can add a MC schedule to the figure 1.12. Combining with the initial curve gives the profit maximizing number of transaction , where similarly, the number of withdrawals will be when

interest rate increases from to

Figure 1.12: Determination of the number of transactions

The above figure also indicates that as transaction cost per withdrawal or MC increases from to other things being equal, the number of withdrawals made by the individual decreases from to .This also mean that average cash holding will increase and that of bond balance or deposits will likely be decline.

When making withdrawal or converting bond-to-cash involves transaction cost the TR is not also net interest earned on average bond holding, which is shown in column 6 of table 1.2 for the net declines by the amount of transaction cost multiplied by the number of withdrawal. Instead, TR is considered as gross interest earning. The expression net interest ( ) when transaction cost is involved thus

------------------------------------------------------ (5b)

For example assume that transaction cost per withdrawal is Birr 2. In this case, when an individual makes 2 withdrawals transaction cost will be . Thus, net interest will be 24 minus 4, which is equal to Birr 20. Similarly, net interest ( ) declined by Birr 6, 8, and 10 when 3,4, and 5 withdrawals were made.

Aggregate money demandTo move to the aggregate money demand for each representative consumer whose money transaction balance is given by equation (1), there is assumed to be someone on the other

46

side of the market. Suppose, for example that the consumer buys goods from a representative firm and that firm periodically converts its money holding into bonds. The firm’s pattern of bond and money would follow the same saw-tooth pattern exactly complementary to the consumers’ pattern in Figure 1.11. The aggregate money DD in the transaction s model is therefore, the sum of the households’ demands and that of the firms on the other side of the market. This means that we must double, in equation (1) to get

the aggregate demand for real money balance . Aggregate money transaction balance or simply cash balance in nominal and real term are given by

----------------------------------------------------------- (6a)

----------------------------------------------------------- (6b)

Where, the subscript indicates aggregate or total.

Exercise 1.4:1) If interest rates on bonds go to zero, what does the Baumol-Tobin analysis suggest the

individual’s average holding of money balances should be? Explain2) If brokerage fees or time and transportation cost go to zero, what does the Baumol-

Tobin analysis suggest regarding total revenue and net interest earning on holding of money balances should be? Explain

3)Consider an individual who earns Birr 3600 per month, who can earn 5% interests per month on saving deposits, faces Birr 2 transactions cost per withdrawal, and has an initial withdrawal plan of 4. Moreover, assume that the individual’s elasticity of withdrawal with respect to change in interest rate and transaction cost are ½ and 2 respectively. Given the above information: (A) Compute the individual’s average monthly cash and bond

balances for the information given above and illustrate the values using the saw-tooth pattern graph.

(B) Other things remain constant, by how much will the individual’s number of withdrawals and hence average monthly cash and bond balances change if the rate of interest falls to 3%?.

(C) While interest rate remains constant, what will happen to the number of withdrawals and hence individual’s average monthly cash and bond balances change if transaction cost declines to Birr 1? Calculate the values and show graphically

(D) Compute the net interest earned from money kept in the bank or holding of short term bonds in the case of (a) to (c) by rounding the values to nearest whole number.

1.3.2. The Portfolio Approach (Reading assignment)Introduction: According to Keynes, the demand for real money balance function, divided into speculative component, inversely related to interest rate, and transaction component, positively related to income and inversely related to interest rate, is given by

47

------------------------------------ (1)

Where, is negative and is positive

The portfolio approach is attributed to Keynes speculative (regressive) expectations model and described by Tobin in his article on liquidity preference. The portfolio approach says that people hold money when they expect bond prices to fall, that is, interest rates to rise, and thus expect that they would take a loss if they were to hold bonds. Since people’s estimates of whether the interest rate is likely to rise or fall, and by how much, vary fairly widely, at any given interest rate there will be someone expecting it to rise, and thus someone holding money.

The obvious problem with the liquidity preference theory of Keynes is that it suggests individuals should, at any given time, hold all their liquid assets either in money or in bonds, but not some of each. This is obviously not true in reality. Tobin’s model of liquidity preference deals with this problem by showing that since the return on bonds is uncertain, that is, bonds are risky, then the investor worrying about both risk and return is likely to do best by holding both bond and money-diversification of portfolio.

Tobin assumes that a bond holder has an expected return on bond from two sources, the bond’s yield – the interest payment an individual receives – and a potential capital gain – an increase in the price of the bond from the time he/she buys it to the time he/she sells it. The bond’s yield is usually stated as a percentage of the face value of the bond. The market rate of return on the bond is the ratio of the yield to the price of the bond .

For example, if a hundred-dollar bond has a yield of $5, the percentage yield is 5 percent. If the price of the price of the bond rises to $125, the $5 yield corresponds to a market rate

of 4 percent - $5/$125. Thus, the market rate is given

--------------------------------------------------------------- (2)

And, since the yield is a fixed amount stated as a percentage of the bond’s face value, the market price of a bond is given by

-------------------------------------------------------------- (3)

The expected percentage capital gain is the percentage increase in price from the purchase price to the expected sale price . This gives us an expression for the

percentage capital gain; From equation (2) and (3), with a fixed on the

bond, an expected price corresponds to an expected interest rate . Thus, in terms of expected and current interest rates, the capital gain can be written as

48

Canceling, the terms and multiplying the numerator and denominator by gives us

---------------------------------------------------------- (4)

As the expectation for the expected capital gain in terms of current and expected interest rates. For example, if the present market interest rate is 5 percent and the purchaser of the bond expects the rate to drop to 4 percent, his expected capital gain would be

or 25%

The total rate of return on a bond - for earnings – will be the sum of the market rate of interest at the time of purchase and the capital gains term. Thus,

--------------------------------------------------------- (5)

And substituting for from equation (5), we have an expression for the total rate (percentage) of return

----------------------------------------------------- (6)

James Tobin in his famous article “Liquidity Preference as Behavior towards Risk” formulated the risk aversion theory of liquidity preference based on portfolio selection. This theory removes the following two major defects of the Keynesian liquidity preference theory.

1) Keynes’s liquidity preference function depends on the inelasticity of expectations of future interest rate, and

2) Individuals hold either money or bond.

Tobin starts his portfolio selection model of liquidity preference with this presumption that an individual asset holder has a portfolio of money and bonds, even if the return from bonds is higher that the return from money. Money neither brings any return nor imposes any risk on holders. But bonds yields interest and also bring income. However, income from bonds is uncertain because it involves a risk in capital gains and losses. The greater the investment in bonds the greater is the risk of capital loss from the bonds. An investor can bear this risk if he/she is compensated by an adequate return from bonds.

As a result, the portfolio balance approach begins with the same expression to the total percentage return- - that we have developed in equation (5) earlier.

We have also assumed earlier (under 4) that the percentage rate of expected capital gain given by

is determined with certainty by the individual: he chooses as a function of and no consideration of uncertainty or risk enters the problem. The basic contribution of the

49

portfolio balance approach is to enter risk contributions explicitly into the determination of the demand for money.If is the expected capital gain or loss, it is assumed that the investor bases his/her actions on his /her estimate of its probability distribution. It is further assumed that this probability distribution has an expected value of zero and is independent of the level of the current rate of interest, , on bonds. Now in place of a return expected with certainty,

, we can have an expected return, , where

-------------------------------------------------- (7)

And is the mean expected capital gain from the probability distribution.

The Individual portfolio DecisionIndividual portfolio consists of a proportion of money and of bonds where both and add up to one. They do not have any negative values. If asset holder is puttingdollars of his/her liquid assets into bonds, his/her expected total return on a portfolio

is then

, where ----------------- (8)

Similarly, if the standard deviation of the probability distribution of return/capital gains on a bond is , which is a natural measure of uncertainty or riskiness of bonds, a number like 2 percent, and all bonds are alike, then the total standard deviation of bond holding is given by

-------------------------------------------------- (9)

Equation (11) and (12) give us the technical situation facing the asset holder – the budget

constraint along which he/she can trade increased risk for increased expected return .

They also give the investor a formula for deciding how much funds to put into bonds to achieve a given risk-return mix along the budget line. From (9) we have

------------------------------------------ (10)

With fixed by the asset holder’s probability distribution (10) gives the total bond holdings needed to attain any given level of risk . Using this expression to replace in (8) gives us the budget constraint,

-------------------------- (11)

Here is a known current vale, fixed, at least to the individual, by the bond market. The

investor knows and , at least implicitly, from the probability distribution in Figure

50

1.13. Thus, the expression in parenthesis (13) is a given, determined number which gives

the constant rate of trade-off between return and risk . Differentiating (11) we have

------------------------------------------ (12)

If is 5%; is 15% and is 5%, then is 3%. In this case, an increase of one

percentage point in the standard deviation in the total portfolio will buy a 3% increase

in the expected total return .

Tobin describes three types of investors. The first category is of risk lovers who enjoy putting all their wealth into bonds to maximize risk. They accept risk of loss in exchange for the income they expect from bonds. They are like gamblers. The second category is of plungers. They will either put all their wealth into bonds or will keep it in cash. Thus, plungers either go all the way or not at all.

But the majority of investors belong to the third category. They are risk averse or diversifiers. Risk averters prefer to avoid the risk of loss which is associated with holding bonds rather than money. They are prepared to bear some additional risk only if they expect to receive with it greater increases in returns. They will, therefore, diversify their portfolios, and hold both bonds and money. Although, money neither brings any return nor any risk, yet it is the most liquid form of assets which can be used for buying bond any time.

In order to find the risk averter’s preference between risk and expected return, Tobin uses indifference curves having positive slopes indicating that the risk averter demands more expected return in order to take more risk.

Risk ( )

Fig 1.13: The “diversifier’s” portfolio selection between risk and return

51

In Figure 1.13, the horizontal axis measures risk ( ) and the vertical axis the expected return ( ). The line is the budget line of the risk averter. It shows both the risk and return on the basis of which he/she arranges his/her portfolio of wealth consisting of money and bonds. and are indifference curves. An indifference curve shows that he/she is indifferent between the pairs of expected return and risk that lie on curve. Points on curve are preferred to those on curve. But the risk averter will achieve an equilibrium position between expected return and risk where his/her budget line is tangent to the indifference curve ( ), at point .

In the lower portion of the figure the length of the vertical axis shows wealth held by the risk averter in his/her in his portfolio consisting of money ( ) and bonds ( ). The line shows risk as a proportional to the share of the total portfolio held in bonds. Thus, point on this line drawn as a perpendicular from the point determines the portfolio mix of money and bonds. It is of bonds and of money. Thus, the risk averter diversifies his/her total wealth by putting partly in bonds ( ) and partly keeping in cash ( ). That is why he/she is called a diversifier. He/she is not prepared to accept more risk unless he/she can also expect greater expected return. However, the risk averter possesses an intrinsic preference for liquidity which can be only offset by higher interest rates.

The aggregate demand for money in the portfolio balance modelThe higher the interest rates, the lower the demand for money and the higher the incentive to hold more bonds. On the contrary, the lower the interest rates, the higher the demand for money and the lower the willingness to hold more bonds. This is illustrated in Figure 1.14 below.

Expected Return 2I

Risk Wealth

Fig 1.14: Aggregate Portfolio selection with rising interest rates

52

In Figure 1.14 the slope of the budget line increases with the increase in the interest rate. This is shown by the budget line rotating upward to and . Consequently, returns increase in relation to risk with increase in interest rate and the budget line touches higher indifference curves. In Figure 1.18, budget lines , ,and are tangent to , 2I ,and at

and respectively. These points trace out the optimum portfolio curve, in the figure, which shows that as the tangency points move upward from left to right, both the expected return and risk increase.

These tangency points also determine the portfolio selection of risk averters as shown in the lower portion of Figure 1.15. When rate of interest is , people hold amount of bond and money. As the rate of interest increases from to and , risk averters hold successively more bonds and but reduce money to and in their portfolios.

The figure also shows that as the rate of interest increases by equal amount from to and to, risk averters hold bonds by decreasing increment . This also means that

the demand for money falls by smaller amounts, as the rate of interest increases. This is because the total wealth in the portfolio consists of bonds plus money. The demand for money can be drawn on the basis of Figure 1.14 and derived in Figure 1.15 below. The curve shows that when the rate of interest falls from a higher level, there is a smaller increase in the demand for money.

Interest Rate

Speculative DD for money

Fig 1.15: The demand for money

For instance, when the rate of interest falls from to the demand for money increases by amount, which is smaller than . This is because the risk averters prefer to hold more bonds than money. But when the rate of interest falls at a lower level from to the increase in the demand for money is much larger; in figure 1.15. This demand for money relates to the speculative demand for money not to the aggregate demand for money.

1.4 Labour market1.4.1 Labour demand

53

(A) Individual firm labour demandIntroduction: The demand for labour is a derived DD. That is to say firms do not demand labour for its own sake but for what it is able to produce for sale in conjunction with other factors of production, such as capita. It follows, therefore, that firms will only demand labour if it is profitable to do so. It will be profitable to employ more labour in the marginal revenue earned from the sale of extra output exceeds the marginal cost of producing that output. Hence, the demand for labour by an individual firm operating in competitive markets is based on the notion of profit maximization. Profit maximization implies that additional labour will be demanded until the marginal cost of labour (real wage) just equals the marginal revenue of labour obtained from the sale of extra output produced by the marginal worker. The marginal revenue and marginal cost of a firm is determined by the state of technology and the nature of production function. Figure 1.16 shows the production function, which describes real output ( ) is a function of labour input and the capital stock.

The capital stock is fixed at , which implies that this model of labour market is strictly a

model of the short run.

Fig 1.16: The production function

The shape of the production function, , shows increases with labour input, so

that . Initially output increases at an increasing rate with the first additions of labour to the capital stock, shown over the range in Figure 1.16. Beyond the level of employment given by , however, begins to increase at a decreasing rate, exhibiting diminishing marginal returns as the fixed capital stock is shared among more and more workers.

54

In the lower panel of Figure 1.16, the relationship between the production, average and marginal product of labour. It can be seen that as employment increases the first increases up to and then decreases beyond .The , which represents the additional output produced by the last worker employed and is derived from the slope of the production function. The slope is initially rising, peaking at , the point of inflection point where the production function changes from convex to concave, and then falling beyond ; intersects the at its maximum, and reaches zero at , where the production function becomes flat. Beyond the therefore, falls with N, that is

, and the exhibits a diminishing marginal product of labour.

With this information the firm’s labour demand decision can be examined. First, the employment of one more worker will lead output to rise by the . If the addition to total output is sold in a competitive market, such that the price it sells for is the same as that for all previous units, then marginal revenue received by the firm is the price of

output multiplied by the ; . This is called the marginal revenue product of

labour ( ). Thus the profit maximization condition where by the marginal cost of extra worker is the money wage, W, equals marginal revenue product of labour is given as

------------------------------------------- (1)

------------------------------------------------------ (2)

--------------------------------------- (3)

This indicates that at equilibrium is equal to nominal wage. Alternatively, labour demand is also written in real term as

------------------------------------------------ (4)

The above expression entails that firms determine how much labour to hire by equating. The marginal cost of the firm is real wage. In Figure 1.16, the falls

as N increases, beyond , the demand for labour is inversely related to real wage rate. Since the price deflator used in the calculation of real wage rate is the price of the firm’s output, this measure of real wage is referred as the real product wage.

(B) Aggregate labour demandIn the aggregate it is assumed that the demand for labour is the horizontal summation of individual firm’s demand for labour, which gives the downward slopping curve as depicted in Figure 1.17 below. The aggregate demand for labour function is therefore denoted as

55

Or ----------------------------- (5)

Where denotes the economy wide schedule. Since the marginal product of labour schedule falls as increases and the real product wage is inversely related to the aggregate demand for labour.

Fig 1.17: The aggregate Demand for labour 1.4.2 LABOUR SUPPLYIntroduction: The individual supplier of labour is assumed to supply labour in direct relation to the real (consumption) wage. In developing the aggregate demand for labour, we do not make any explicit assumption about price or wage expectation of employers on the demand side of the labour market. This is because we assume that an employer has good information on or perhaps control of the particular prices changed and the wage rate paid. The employer is thus in a position to know the real wage at each point in rime. For the employer, this real wage ( ) is the money wage deflated by the particular employer’s product price ( ).

However, a worker’s information concerning price level (and subsequently about his/her real wage) is not adequate as that of the employer. This is because workers may not know in advance exactly what products will they need to purchase with their money (nominal) wages and second, even if they did, they do not know the exact prices (consumers price index) of the goods in advance. Thus, a worker must deflate his/her nominal/known wage income (W) by a an estimated consumers price index (CPI) or that covers a wide range of products in order to arrive at an estimated or expected real wage, . Therefore, an explicit assumption linking workers estimation

56

or expectations on price level ( ) and the actual price level ( ) is important. Hence, it is important to note that the price deflator used by the worker when deciding the amount of labour to supply is different from the price level used by the producer in determining how much labour to employ. These two real wage rates are referred to as the expected wage- (or ) and the real producer wage- (or ) respectively.

THE AGGREGATE LABOUR SUPPLY CURVEThis is obtained by summing all individual labour supply curves for a given expected wage rate ( ) to get the aggregate labour supply curve for the entire economy; that is

. Therefore, the aggregate supply curve of labour in expected price can be represented mathematically as:

In real value: ----------------------------- (6a) or

In nominal value: ----------------------------------- (6b)

In equation (6a), can be written in the current actual real wage ( ) and the level of employment, , relationship by converting the expected real wage ( ) in to the actual real wage ( ). By definition:

, by substituting by from equation (6a)

----------------------------------------------- (7a)

This is another version of equation (6a). However, the labour supply function in nominal wage derived from equation (7) is similar to that of (6b). That is

---------------------------------------------- (7b)

Aggregate labour supply ( ) derived in current actual real and nominal wage rather than expected real wage (equation 7) are depicted graphically as follows,

57

Fig 1.18: Aggregate labour supply Curve

1.4.3. Frictionless Labour Market Equilibrium and the Aggregate Supply Curve (A) Frictionless Labour Market Equilibrium (Classical equilibrium)We have already derived that the aggregate demand and supply of labour equations in the labour market, both as a function of real and nominal wage in equation (5) and (7) respectively, as

Or ; equation (5)

Or ; equation (7)

The labour market equilibrium is obtained by equating labour DD ( ) to labour SS ().That is,

In real wage: ---------------------------------------- (8)

In nominal wage: ---------------------------------- (9)

The graphic representation of labour market equilibrium is represented by the intersection of the two curves indicated in equation (8) and (9) above. For a given value of actual price level, and the expected price level equilibrium real and nominal wage are 0w and ,

respectively while equilibrium employment is , and real income, . At point the labour market clears. But this does not imply that there is zero unemployment. Note that if all the workers are in employment the labour supply curve would become vertical since no matter how high real wages were pushed up, there could be no increase in employment because all workers are employed. In Figure 1.19 the level of full employment is given at . The distance between therefore denotes the level of voluntary unemployment. The level of voluntary unemployment expressed as a percentage of total labour force in an economy is usually referred to as the natural rate of unemployment. The voluntary unemployment due to the labour market frictions is frequently believed to consist of two specific kinds of unemployment, namely frictional unemployment and structural employment.

58

Frictional unemployment is explained by the special characteristics that it takes time to match workers to jobs. In reality however, workers have different preference and abilities and jobs have different characteristics and the geographical mobility of workers is often low. Hence, searching job takes time and effort and because different jobs require different skills and pay different wage rates, unemployed workers may not accept the first job offer they receive. The unemployment caused by the time it takes workers to search for a job is called frictional unemployment.

Fig 1.19: Equilibrium in the labour market

As structural change occur in the economy, some industries of the country may decline and some labour skill categories become redundant as others expand. This can lead to structural unemployment.

Thus, the natural rate of unemployment or the level of employment consistent with the labour market clearing is voluntary in the sense that the number of job vacancies is equal to the number of workers seeking job. In other words, the natural rate of unemployment means frictionless labour market equilibrium. It corresponds to the classical labour market equilibrium. Because the classical assume that workers have perfect foresight of the current and expected price levels and hence price and wage rates are flexibility conclude that the labour market always clears both in the short and long run along the aggregate supply (AS) curve. Thus any changes in unemployment are entirely voluntary.

(B) The Aggregate Supply (AS) Curve

59

Aggregate supply curve is derived from the aggregate labour market and production function to give a direct relationship between output and price level for a given state of technology and the work-leisure preference of workers.

The derivation of the curve is based on the labour market equilibrium expressed in real and nominal wages as . That is

(1)

Real product wage or = Real consumption (money) wage(2)

Actual money wage = Expected nominal wage

The degree to which the expectation of workers about adjust to the movement of is given by

------------------------------------------- (10)Where, is the slope of the price function (or ) and its value lies between 0 and 1

Now let us see first what will happen to labour market equilibrium level of employment, income, and wage (real and nominal) rates of the classical and extreme Keynesians as the price level changes and then derive their aggregate supply (AS) curves. To do so, we assume for simplicity the following two assumptions: 1) Initially both actual and expected prices are equal or and

2) The price level rises from to .

With these assumptions we can then derive the classical curve of the frictionless (classical) and extreme Keynesians school of thoughts by examining what happens to the equilibrium level of employment, income and wage rates for a closed economy (an economy without international trade)as price level increases exogenously?

a) The extreme Classical case:The basic assumption of the classical regarding the labour market is that there is complete and correct adjustment or perfect foresight of to .That is and hence in equation (10) above. This assumption stems from its two core assumptions about the aggregate economy: price and wage flexibility and economic agents are rational.

When moves by the same proportion as rises from to or , the ratio ofremains unchanged. This is evident from Figure 1.20(a) below that when the expected price fully adjusts to the change in the actual price the labour market equilibrium remains at point A leaving the initial labour market equilibrium value, and space undisturbed. This is known as the classical result, in which movements of the price level do not affect equilibrium level of employment and real wage.

60

In the second figure, however, an equal (proportional) increase of and shifts the labour demand and supply curves up by the same amount (magnitude), again leavingundisturbed. In Figure 1.20(b), the exogenous increase in actual price from to shifts the labour demand up (or to the right) from the initial to . This is because, the increase in price level reduces real wage and hence encourages employers to demand more labour and increase production. The rise in the price level can be shown by the vertical distance , because the price level is combined multiplicatively with the marginal product of labour increase.

On the supply side of labour market, the higher price level translates into a higher consumer price index (CPI), so workers will perceive a fall in their real wages, and so contract/reduce their labour supply to the labour market. As a result, the labour supply curve shifts up (to the left) proportionally as far as the demand curve from to

. This proportional shifts the labour demand and supply curves in turn hold

equilibrium employment at .The implication of proportional shift of labour supply to that of labour demand is that MC has increased by the same proportion to that of MR. With employment fixed at output ( ) also becomes fixed at in figure 19c. Therefore, we can conclude that with or perfect foresight of to only the nominal wage rate ( ) rises by the same proportion to the increase in price level, holding equilibrium real wage, employment, and income constant at , ,and respectively.

The insensitivity of equilibrium level of employment ( ) and output/income ( ) when the price level rises from to due to perfect foresight ( )of workers about the change in price in a closed economy give us a VERTICAL AGGREGATE SUPPLY CURVE of the classical as shown in Figure 1.20(d).

A (a)

B (b)

61

A

(c)

P

(d)

Fig 1.20: The Classical Labour market equilibrium and Aggregate supply (AS) curve

b) The extreme Keynesians Case:

This is the opposite of the extreme classical case. That is, the extreme Keynesians assume zero (no) adjustment of the expected price level ( ) as the actual price level changes from to . Hence, when or , implying imperfect foresight (myopia or shortsightedness) or complete money illusion. This is because of the assumption of price and wage rigidity and static expectation of economic agents about price level.

With constant as the price level changes labour supply depends only the money (nominal) wage rate- . When there is no adjustment of to , only the demand for labour curve shifts to the right along the unchanged labour supply curve from to the higher in figure 1.21b due to the decline in real wage. Since the increase in the price level has shifted only the labour demand curve, but not the labour supply curve, employment raises from to and the nominal wage from to . Hence, unlike the classical case where the nominal wage raises proportional to the change in the price level nominal wage in the extreme Keynesian case rises by less than the rise in the price level for expected price ( ) is fixed due to myopia.

62

The less than increase in nominal wage than the price level is then followed by a decrease in real wage (see panel Figure 1.21a). In Figure 1.21a, the rise in with unchangedreduced the ratio of from to and hence shift the labour supply curve in

the space to the right. Thus, the rigidity of price expectations at on the supply side of the labour market permits a reduction of the real wage rate as the price level increases, inducing an increase in equilibrium employment from to (see panel a and b) and hence output/income from to (see panel c).

With given and not responsive to changes in actual ( ), the above equilibrium condition in the labour market not only gives the equilibrium employment N depending on the price level but also the aggregate SS curve with a positive slope. This is because as price increases, shifting the labour DD up, the labour market equilibrium moves up along the given labour supply curve in the space. Therefore, if the money illusion assumption or holds the labour SS curve is constant, generating an increase in employment and output and upward sloping AS curve.

The extreme Keynesians are criticized on the ground that the assumption of is appropriate to examine the impact of the movements of price level on equilibrium level of employment and output during the market period (i.e., very short period of time where supply cannot respond to demand) when the labour force has not had time to absorb new price information on price level and adjust to . This criticism gave rise to the new (general) Keynesian theory of labour market, which postulate though the degree of adjustment of workers expected price to actual price improves with the availability of information in the long run, the shape of the aggregate supply curve is always upward sloping and the equilibrium level of employment and output higher than the classical but lower than the extreme Keynesians.

A (a) B

N

B (b)

63

A B A

(c)

P (d)

Fig 1.21: Labour market Equilibrium and AS curve for extreme Keynesian 1.4.4. The New Keynesian view of the labour market This model is some how in between the two extreme (polar) assumptions-the extreme classical and the extreme Keynesian. The aggregate supply curve of in the general Keynesian model, at least in the short run, in which . That is, the model in which expectations adjust to changes in the actual price level, but not fully. It could be labeled as imperfect foresight model.

In Figure 1.22 below, adjustment of the labour market equilibrium to an exogenous increase in the price level from to by less than the exogenous increase in . Figure 1.22(a) shows that the increase in reduces the ratio of the expected to actual price level from to since adjustment expectation is less than perfect or . This shifts the labour supply curve down in the space reducing real wage and increasing employment from to . The same movement is also shown in the space of Figure 1.22( )where we see the increase in shifts the demand curve up from to

while the rise in shifts the labour supply curve up, but only by less than the

movement in the demand curve, from to and cutting the demand curve at point C in stead of at point , since .

64

Furthermore, the excess demand for labour at pulls up the nominal wage to , an increase less than proportionate to the price level, since . Thus, employment rises to . The movement in employment is translated to the change in output in Figure 1.22(c), using the production function. Finally, an upward sloping aggregate supply curve passing through ( ) and ( ) pairs is obtained in panel . This implies that the less than perfect foresight assumption eliminates the verticality and flatness of aggregate supply curve of the classical and extreme Keynesian, respectively.

B

D C

65

Fig 1.22: Labour market Equilibrium and AS, the New (general) Keynesian case

EXCERSISE 1.5: (1) Suppose the production function and

labour supply are given ; and , respectively. Further, assume that the price levels in period zero; and it has doubled in period 1; that is . Given this information,

A) Calculate the equilibrium employment ( ), output ( ), money (nominal) wage and real wage for the extreme Classical, extreme Keynesian, and New Keynesian case in real and nominal term.

B) Discuss the reasons why the results you have obtained in question 1A above happened to be and show the results graphically.

C) Derive the AS curve for the three cases and show the results in 1A graphically.

(2) Using the labour market equilibrium, equation (9) and equation (10) and assuming expectations are perfect initially and set the price index

A) Derive the slope of Aggregate Supply curve algebraicallyB) Evaluate whether the slope of the Aggregate Supply (AS) curve of extreme

Classical, extreme Keynesian, and new Keynesian are positive, negative or zero

C) Show also the values of for the three cases is similar to that of

66

CHAPTER 2: MACROECONOMICS DYNAMICS

2.1 Economic growth and technical growth2.1.1 Economic growth:Economic growth is an expansion of an economy’s productive potentials over a long period of time. It is concerned with the long term sustainable trend rise in output than short term fluctuation. In other words, the dynamic behavior of macroeconomics is concerned with the rate of change of key economic variables overtime.

Thus, economic growth is thus expressed as the change in income or output ( ) level overtime as follows:

Economic growth ------------------------------------------- (2.1)

Where, read as hat is the time deviation or change in the level of output or GDP and is

time. That is, or simply . To express growth rate in percentage we should multiply it by 100.

For instance, according to MoFED (2006) macro data real GDP in Ethiopia in 2003 and 2004 fiscal year were Birr 16,941.5 and 18,900.9 million respectively. Thus, economic growth in 2004 was:

From the above example, the value of equation (2.1) is 0.115657. But when multiplied by 100 and rounded to one decimal digit it becomes 11.6%.

The above simple analysis raises the question what are the potential sources of economic growth? The neo-classical growth model, developed by Solow in 1956, postulates that growth rate is derived by the rate of growth of the labour force and technical growth. However, the endogenous growth model, which is alternative classification of technical progress and considers the principles of to the neo-classical growth model, suggests that savings/investment are an important factor in determining the level of economic growth.

2.1.2 Technical progress (Total factor productivity)

67

The study of the potential sources of economic growth stems from the aggregate production function which links factor inputs to output for a given level of technology. That is

----------------------------------------------------------- (2.2a)

To keep the analysis simple consider a Cobb-Douglas constant return-to-scale (CRS) production function

----------------------------------------------------------- (2.2b)

Where, Y is the level of output; represents the state of technology; and and are capital and labour inputs. In equation (2.2b), is the share of capital in output and the share of labour input in output.

Differentiation of (2.2b) with respect time gives the rate of change of output overtime, which can be written as

------------------------------------ (2.3a)

Or using the hat notation as

----------------------------------------------------- (2.3b)

Thus, the rate of growth of out put or simply economic growth is identically equal to the rate of change of technology (technical progress ), called total factor productivity (TFP) plus the rate of growth of each factor inputs multiplied by their respective shares in total output (that is, for capital and for labour). Equation (2.3b) is called the growth accounting.

Technical progress or total factor productivity is the amount by which output would increase as a result of improvement in methods of production with all factor inputs unchanged and is distinct from labour productivity10.

The problem with equation (2.3b) is that the growth of total factor productivity (TFP) cannot be measured directly. Solow (1957) derived an estimate of TFP by inverting equation (2.3b) and driving TFP as a residual as shown in equation (2.4) below. This measure of TFP is therefore sometimes referred to as the Solow residual. Due to his inability to describe why this TFP occurred and its growth process Solow called it simply ‘Manna from heaven’.

---------------------------------------- (2.4)

10 Labour productivity is the ratio of output to labour input . Labour productivity may grow because of the improvement in capital inputs per worker,

68

To understand the applicability of equation (2.4) let us use a simple example. Suppose capitals share of income ( ) is 0.3 and that of labour ( ) 0.7. Then if the labour force grows (or ) by 1 percent, the capital stock grows (or ) at 3 percent with the total factor productivity of 1 percent, then the growth rate of output must be, by accounting identity of equation (2.3) be 2.6 percent. More examples are shown in table 2.1 below.

Table 2.1: Growth accounting for selected countriesCountries Growth rate

of GDP ()

Growth rate contribution of Growth rate ofCapital Labour TFP

( )Capital

( )Labour

( )GDP per

worker( )

USA 3.1 0.9 1.2 1.1 2.7 1.8 2.2Japan 3.73 2.28 0.67 0.78 6.84 1.005 2.725Germany 1.8 1.28 -0.49 1.01 3.84 -0.735 2.535Source: Summer and Heston (1991) for USA and Maddison (1991) for others, and own calculations for the last three columnsNote: The figures in the table are for the period 1960-1990 for the USA and 1973-1987 for other countries. : The value of is used in the calculation

Given the value of , how the growth rates of capital and labour and GDP per worker, shown in the last three columns, are calculated is illustrated as follows. Example, for USA the growth rate of: (3) The growth rate of capital is

calculated from the growth contribution of capital = 0.9. That is

(4) The growth rate of labour:

(5) The growth rate of GDP is simply the growth rate of GDP less the growth contribution of labour. That is,

2.2 Stylized facts1. There are significant variations in the per capita income across countries. For example,

Jones (2000, page 56) documented that a typical person in the United State earns the annual income of a typical person in Ethiopia in less than ten days.

2. The rate of economic growth varies across countries. Between 1960-1990 average growth of the USA and Tiger countries was 1.4% and 5%, respectively while some African countries had negative economic growth.

69

3. Growth rate of many countries is not constant or sustainable but it fluctuates.4. A country’s position in the world is not fixed. That is countries which were poor in the

past are now growing fast and catching rich countries. China which grows by double digits over the past 20 years is the best example in this regards. Some contraries whose economic growth and per capita income were relatively better than others in the 1970’s are now growing slower and lagging behind their counter parts. For example, Ethiopia’s economic growth and per capita income which were better than that of South Korea in 1975 are now not only incomparable to the economic growth and per capita income of South Korea but also is one of the least in the glob11.

5. Economic growth and investment in human capital or education are highly correlated due to the later contribution in ensuring social equity and improving labour productivity.

6. Both skilled and unskilled workers are migrating from poor countries to rich countries, which is contradictory to what economic theory postulated regarding the flow of resources. Economic theory postulate resources should flow from where they are abundant to where they are scarce. Thus, though the migration of unskilled labour from developing countries to developed countries is consistent with what economic theory postulate the migration of skill skilled workers or brain drain of developing countries against economic theory.

2.3 Growth modelsTheories of economic growth are concerned with the rate of long run equilibrium growth that is with the rate of growth of output that yields full employment of labour and capital. Rising unemployment of labour would, by definition, violate the full employment assumption, and it would probably would be accompanied by the deficient demand and falling prices. On the other hand, under utilization of capital stock would drive profit and investment incentives down, reducing investment and the demand for output.

2.3.1 The Solow ModelThe neo-classical Solow growth model is based on the following six assumptions.

1) Because the economy is assumed to be closed and there is no public sector, in equilibrium investment will be equal to savings. That is,

------------------------------------------------------------------------- (1)2) Savings are assumed to be proportional to income. That is,

----------------------------------------------------------------------- (2)Where the MPS and assumed to be 3) It is assumed that no technological progress, such that in equation (2.4)

4) The change in capital stock overtime is and is equal to gross investment, less

depreciation ( ) times capital stock ( ). That is, ------------------------------------------------------------------ (3)

5) The labour force, is assumed to grow at a constant (equal to population growth), exogenous rate of . That is, the rate of growth of labour force is

11 Jones (2000), “Introduction to Economic Growth” explains this fact adequately

70

------------------------------------------------------------ (4)12

6) The neo-classical assume a constant rate to scale (CRS) production function such that .CRS means that multiplying all factor inputs by, will give an increase in

output by . Formally,

----------------------------------------------------------- (5)

In other word, if we double labour and capital inputs are doubled, then output will also double. With these assumptions, the production function can be written in per capita income form. To do this let , then the production function becomes

------------------------------------------------------------------ (6)

In equation (6) lower-case letters denote variables measured relative to population. Hence, is output per head/worker, , and capital per head/worker is . Hence, the equation is per head production function, in general form, which depends only on capital per head/worker- . As a result increasing both and by the same proportion will not change . Thus, there is no gain in output per head from increasing both labour and capital as long as ratio, is the same because of the assumption that the production function exhibits CRS. The per capita production function is illustrated in Figure 2.1.

Fig 2.1: The per capita production function

The marginal productivity of increasing the capital-labour ratio is positive but diminishing. That is, the first order derivative is positive or and the second order derivative is negative or . If the production function is assumed to take the Cobb-Douglas form as in equation (1), then there are CRS since the factor shares sum to unity. In per capita term the Cobb-Douglas form is written as

---------------------------------------------- (7)

12 If , then the labour force and population are growing at one percent per year.

71

This production equation is sometimes called the AK model. The marginal productivity of is given as

And the second order derivative;

Which is negative because 0 and hence . This shows that the is decreasing with additions to ; that is the production function is concave downward as shown in figure 2.2.

From the per capita production function, equation (6), it should be apparent that the growth rate of GDP per capita is going to be determined by the growth rate of capital per head-, which is written as (using assumption 5)

--------------------------------------------------------------- (8a)

Recall also

--------------------------------------------------------- (8b)

Using the assumption that growth over time of capital stock is equal to investment less depreciation, equation (3); that savings equal to investment, equation (1), and that savings are directly related to income from equation (2), and substituting into equation (8a)

, equation (3) and (4) substituted into equation (8a)

, equation (1) then equation (2) substituted. Multiplying both sides by gives

, we know . Substituting this in the first tern for we get

, this can be rearranged as

, we know that cancels out and finally substituting ,

-------------------------------------------------------- (9)

72

Equation (9) is the fundamental dynamic equation for the neo-classical SOLOW GROWTH MODEL and known as the capital accumulation equation in per worker terms. The equation says that the change in capital per worker each period is determined by three terms: investment per worker, increases ; depreciation per worker reduces , and

change in labour force, which reduces capital per worker .

In the steady state or equilibrium, when , equation (9) will be

-------------------------------------------------- (10a)Equation (10a) says that the proportion of income per head/worker that is saved must be equal to the rate of growth of capital per head. In other words, to maintain continuous full employment, savings per head must be sufficient to replace the worn-out machines and to purchase new machinery in sufficient quantity to keep the growing of population employed .

Dividing both sides of equation (10) by we get;

----------------------------------------------------- (10b)

The two rays from the origin are and . The first and second rays are shown in the last term of equation (10a) and (10b) respectively. The Solow model is illustrated graphically as follows.

The flatter ray represents the saving/investment requirement of the model or the amount of new investment per person required to keep the amount of capital per worker

constant-both depreciation and the growing of workforce tend to reduce the amount of capital per person in the economy. By coincidence the difference between the two curves is

the change in the amount of capital per person .In the lower panel of the figure the

dynamics of adjustment are shown such that at any level of , other than , the model

automatically converges back to .

73

Consumption

Fig 2.2: Solow growth model equilibrium

To consider a specific example, suppose an economy has an initial capital-labour ratio oftoday as shown in Figure 2.2 above. What happens overtime? At the amount of savings/investment per worker or per head of the population, exceeds the amount of savings/investment required to keep capital per worker constant; that is to replace the worn-out machines and fully employ the workforce. Thus, capital deepening occurs or capital-labour ratio will increase over time. Indeed, this capital deepening will continue

until reaches , at which , so that . At this point the amount of capital per

worker remains constant, and we call such a point a steady state. Similarly when the economy starts at an initial capital-labour ratio of the amount of new investment coming from saving is insufficient to keep the growing labour force fully employed. In other words, the amount of investment per worker provided by the economy is less than the amount needed to keep capital per worker constant; the term is negative, capital widening is occurring. Therefore, since population growth is at a rate of , the capital stock must increase be growing at the rate of and hence the economy as a whole is growing at rate .

The model can now be used to understand determinants of economic growth. In this section we will examine what happens to the per capita income in an economy that begins in steady state but then experiences a “shock”. The two shocks we will consider are the increase in saving rate and the increase in the rate of population growth.

Comparative statistics 1) The increase in saving rate

74

Consider the economy has arrived at its steady state value of output per worker. Now suppose that consumers in an economy decide to increase the saving/investment rate permanently from to . An increasing in saving rate can come from a cut in the implicit tax rate (inflation) on saving through a change in the tests of individuals between consumption and saving. What happen to and ?

The increase in saving rate shifts the saving line upward from to in figure 2.3. At the current value of capital stock , saving per worker now exceeds the amount of investment required to keep the capital per worker constant, and therefore the economy begins capital deepening again. This capital deepening continues until and the capital stock per worker reaches a higher value indicated by . From the production function, we know that this higher level of capital per worker will be associated with higher per capita income. That is, the level of income per head rises from to . The economy is now richer than it was before.

B E

Fig 2.3: An increase in investment rate

2. The increase in population growthConsider an alternative exercise. Suppose the economy has reached and its steady state, but then due to immigration, for example, the population growth rate of the economy rises from to . Due to population growth, the curve rotates up to the left to a new

. At the current value of capital stock , saving per worker is now no longer high enough to keep the capital per worker constant in the face of rising population. Therefore, the capital per worker began to fall until the point at which indicated by . The economy has less capital per worker than it begins, and is therefore poorer. The per capita income is ultimately lower after the increase in population growth in this example.

75

E B

Fig 2.4: An increase in the population growth rate

2.3.3. Endogenous Growth ModelsThe alternative model of growth process seeks to explain why the rich gets richer, that is why the supply of capital does not flow from the rich countries to the poorer countries where the marginal productivity of capital is higher. The reason must be that the marginal productivity of capital does not in the rich countries despite the rising capital-labour ratio. The new growth theory, therefore, is ultimately concerned with moving the assumption of diminishing returns to reproducible factors of production, such as capital. This is achieved by the endogenous technical progress. In the neo-classical model technical progress drives economic growth, although it does not offer any explanation for technical progress. In other words, , the labour-augmenting technical progress is exogenous: in a common phrase, technology is like “manna from heaven”.

The endogenous growth theories, on the other hand, postulate that the extent of labour-augmenting technical progress is endogenous in the model, depending on the capital-labour ratio to generate sustained growth in per capita income. This is to say better technology is produced as a by product of capital investment.

To be specific, we must follow Solow and introduce technological progress, which is labour-augmenting or “Harrod - neutral”. As was in the case with Solow model, there are two main elements in the Romer (1990) model of endogenous technological change: an equation describing the production function and a set of equation describing how the inputs for production evolve over time. The main equation is similar to the equations for Solow, with one important difference. The aggregate production function in the Romer model describes how the capital stock, , and labour, , combine to produce output, using the stock of idea or human capital, .

----------------------------------------------------------- (1)

For a given level of technology, , the production function in equation (1) exhibits a constant return to scale in capital, , and labour, . However, when we recognize that ideas are also input into production, then there are increasing returns.

The accumulation equations for capital and labour are identical to those in Solow model. Capital accumulates as people in the economy forgo consumption in some given rate and depreciates at the exogenous rate .

76

Labour grows exponentially at some constant and exogenous rate, which is equivalent to population growth. Using the notation, , for labour than what we have used earlier

In the Romer model, growth in is endogenized. According to him, is the stock of knowledge or number of ideas that have been invented over the course of history until time . Then, is the number of new ideas produced at any given period of time. In short, is equal

to the number of people attempting to discover new ideas, multiplied by the rate at which they

discover new ideas . That is, the production function for new ideas can be written as

------------------------------------------------------------------ (2)

Labour is used either to produce new idea or produce output, so the economy faces the following resource constraint:

To proceed with the endogenous growth model, emphasizing on the economics of idea or human capital we must make the following assumptions.

(1) The rate at which researchers discover new ideas ( ) may depend on the stock of ideas that have already been invented.

For example, perhaps the invention of ideas in the past (that is ) raises the productivity of human capital or researchers in the present. In this case, would be an increasing function of . The discovery of calculus, the invention of computer and laser, and the development of integrated circuits are examples of idea that have enhanced the productivity of the later researchers. On the other hand, the most obvious ideas discovered first and subsequent ideas become increasingly difficult to discover. In this case, would be a decreasing function of . This reasoning suggest

modeling, the rate at which new ideas are produced ( ) as

---------------------------------------------------------------- (3)

Where, and are constant. In equation (3), if it indicates that the productivity of research increases with the stock of ideas that have already been discovered or simply a positive knowledge spillover. This also most popularly known as the “standing on shoulders” effect13;

corresponds to the difficulty of discovering subsequent ideas. Finally, indicates that

13 In this regards, Isaac Newton who has benefited from the knowledge created by previous scientists such as Kepler, in developing his theory of gravitational force has recognized in his famous statement, “If I look farther than others, it is because I was standing on the shoulders of the giants”.

77

the tendency for the most obvious ideas to be discovered first exactly offsets the fact that the old ideas facilitate the discovery of new ideas- i.e., the productivity of research is independent of the stock of ideas.

(2) On the other hand, the average productivity of researchers depends on the number of people searching for new ideas at ant point in time.

For example, perhaps duplication of efforts is more likely when there are more persons engaged

in research. One way of modeling this possibility is to suppose that it is really , where is

some parameter between 0 and 1, rather than that enters in the production function for new ideas. Thus, focusing on equation (2) and (3) suggests focusing on the following GENERAL PRODUCTION FUNCTION FOR IDEA.

----------------------------------------------------------------- (4)

In equation (4), for example, if it reflects an externality associated with duplication; some of the ideas created by an individual researcher may not be new to the economy as a whole of “stepping the toes” effect.

Growth in the Romer modelWhat is thus the growth rate in the endogenous model along the balanced growth path? Provided that a constant proportion of the population is employed producing ideas, the model follows the neo-classical model predicting that all per capita growth is due to technological progress. Letting lower-case letters denote per capita variables, it is easy to show that

That is, per capita output, the capital-labour ratio, and the stock of ideas must all grow at the same rate along the balanced growth path. It implies that, if there is no technological progress, there is no growth. Therefore, the important question is, “What is the rate of technological progress along the balanced growth pats?” The answer to this equation is found by rewriting equation the production (4). Dividing both sides of equation (4) by yields

or

or

--------------------------------------------------------------- (5)

Along a balanced growth path, is constant. But this growth rate will be constant if and only

if the numerator and the denominator of the right hand side of equation (5) grow at the same rate. Taking logs and derivatives of both sides of this equation

78

-------------------------------------------- (6)

Along a balanced growth path, the growth rate of the number of researchers must be equal to the growth rate of the population – if it were higher, the number of researchers would eventually

exceed the population, which is impossible. That is, . Substituting this into equation

(6) yields

-------------------------------------------- (7)

Thus the long run growth rate of this economy is determined by the parameters of the production function for ideas and the rate of growth of researchers, which is ultimately given by the population growth rate.

Comparative static: A permanent increase in the R&D shareWhat happens to the advanced economies of the world if the share of the population searching for new ideas increases permanently? For example, suppose there is a government subsidy for R&D that increases the fraction of labour force doing research.

Notice that technological progress in the model can be analyzed by itself – it does not depend on capital or output, but only on the labour force and share of the population devoted to research. Now consider what happens if the share of the population engaged in research increases permanently. To simplify things slightly, let’s assume that and again; none of the results are qualitatively affected by this assumption. It is helpful to write equation (5) as

--------------------------------------------------------- (8)

Where, is defined as the share of the population engaged in R&D – i.e., . Figure 2.5

shows that what happens to technological progress when increases permanently to , assuming the economy begins in steady state. In steady state, the economy grows along a balanced growth path at the rate of technological progress, , which happens to equal the rate of population growth under our simplifying assumptions. The ratio is therefore equal to . Suppose the increase in occurs at time with a population of , the number of researchers increases as increases so that the ratio of jumps to a higher level. The additional researchers produce an increased number of new ideas so the growth rate of technology is also higher at this point. This situation corresponds to the point labeled “ ” in the figure.

79

/Ag

Fig 2.5: Technological progress: An increase in the R&D share

At , technological progress exceeds population growth so that declines overtime, as indicated by the arrows. As this ratio declines, the rate of technological change gradually falls also, until the economy returns to the balanced growth path where . Therefore, a permanent increase in the share of the population devoted to research raises the rate of technological progress temporarily, but not in the long run.

CHAPTER 3: RECENT DEVELOPMENTS IN MACROECONOMICS

3.1 Rational Expectation (Ratex hypothesis)Before discussing the rational expectations (Ratex hypothesis), it is essential to understand the meaning of static and adaptive expectations used in macroeconomics and how these expectations were formed before the Ratex hypothesis was developed.

Definition: Expectations are forecasts or predications by economic agents regarding the uncertain economic variables which are relevant to their decisions. They are based on past trends as well as current information and experience.

People make expectations about economic variables; say price level in three ways.

a) STATIC (NAÏVE) EXPECTATIONS: What happened in the past or yesterday will happen today and in future. Therefore, since inflation tomorrow will be the same as today and yesterday (that is, price level in period Pt + 2 = Pt +1 = Pt –1 or Pt0) there will be no change in equilibrium real wageworkers receive (w0), level of employment (N0), and income (y0).

b) ADAPTIVE EXPECTATIONS HYPOTHESIS:

80

The pioneering work was done by Cagan14 in 1956 and Nerlove15 in 1957. According to adaptive expectations hypothesis, economic agents expect the future to be essentially a continuation of the past. They expect the future values of economic variables like prices, incomes, wage rates, etc. to be an average of past values and to change very slowly. The economic agents make the expected values of these variables equal to weighted average of their present and past values. They revise their expectations in accordance with the last forecasting error. Errors resulting from past behavior represent an important source of information in forming future expectations. But such expectations are based on the assumption that the economic agents expect them to change very little.

In short, adaptive expectations say what will happen tomorrow (say to price) is a function of what has happened yesterday or in the past and some adjustments made today from the errors of last period. For instance, peoples’ expectation made last year about this year price level is given as,

------------------------------- (3.1)

Equation (3.1) says that the expected price level ( ) in year ; that is current period/this

year- but expectations are made in the previous (last) year ( ) is equal to inflation or price level in last year ( ) plus adjustments made ( ) about the previous year’s mistake in forecasting the previous year or a year before( ) and to price in that year ( ). Then, expectations made two years before about last year expected price level is

-------------------------------- (3.2)

Substituting equation (3.2) into (3.1) for gives, rearranging this we have

----------------------- (3.3)

Equation (3.3) simply says that the expected price level depends on the past trend of price or is the weighted average of past price levels, but the weights are ordered in such a way that more recent prices have larger effect than more distant ones. As a result, adaptive expectation is also sometimes called the Partial Adjustment Principle.

c) RATIONAL EXPECTATIONS HYPOTHESIS: The idea of rational expectations was first put forth by John Muth16 in 1961 who borrowed the concept from engineering literature. His model dealt mainly with modeling price movements in markets. By assuming economic agents optimize and use all information available efficiently when forming expectations about the future, he was able to construct a theory of expectations in which consumers’ and producers’ responses to expected price changes depending on their responses to actual price changes. Muth pointed out that

14 Cagan, P. (1956), “The Monetary Dynamics of Hyperinflation”, in M. Friedman (ed), studies in the Quantity theory of Money.

15 Nerlove, M. (1957), “Adaptive Expectations and Cobweb Phenomenon”, Quarterly Journal of Economics, May16 John F. Muth (1961), “Rational Expectations and the Theory of Price Movements”, Econometrica, July

81

certain expectations are rational in the sense that expectations and events differ only by a random forecast error.

Muth’s notion of rational expectations related to micro-economics. The hypothesis did not convince many economists and lay dormant for ten years. It was in the early 1970’s that Robert Lucas, Thomas Sargent, and Neil Wallace applied to problems in macro-economics.

Basis properties of the rational expectations hypothesisThe Ratex hypothesis holds that economic agents form expectations of the future value of economic variables like prices, incomes, wages, etc., by using all available and relevant17

economic information to them in an intelligent fashion. This information includes the relationship governing economic variables, particularly monetary and fiscal policies of the government. That is, economic agents will incorporate all “news” as it comes in. News would come from personal experience in buying and selling, from private contact or from newspapers and from one’s own past prediction of errors. The last resource is especially important for it brings the difference between the rational and adaptive expectations. Thus, the rational expectations assume that economic agents have full and accurate information about the future economic events.

Thus, with rational expectation the expected error is zero and the errors are not linked in any way by a spiral correlation. This is an implication for the unbiased ness of rational expectations. That is, t – 1. The implication is that the expectation made in period , of the prediction that will be made at time about is equal to the actual prediction at t -1 of Pt + 1. In short, the expected forecast equals current forecast. This is known as the law of ITERATED EXPECTATION. Rational expectation is also called Model Consistence because it is as if everyone knows the model and uses this knowledge fully.

The conclusion based on equation (3.3) is that, if , then which implies static (naive) expectation; if , then , which implies adjustment are perfect or rational.

17 It is important to recognize that this does not imply that consumers or firms have “perfect foresight” or that their expectations are always correct.

82

CHAPTER 4: MACROECONOMICS THEORIES AND AFRICAN ECONOMIES4.1 Introduction: The Classical and Structuralist School

Two schools of thoughts emerged to explain the applicability of the conventional macroeconomic models in LDCs in general and in Africa in particular. These are the orthodox approach and the structuralist view

4.1.1 The Orthodox approach (Classical and monetarists)These schools of thoughts examine the short and long term behavior of the economy in Africa. They argued that the problem in developing countries is caused by misallocation of resources. This is mainly due to the huge hand of the government in the economy.

The solution to long run growth problems is getting the price right or enhancing market mechanisms to address misallocation of resources. That is, pursuing non interventionist domestic policies or reducing government intervention and the huge hand of the state in the market so as to avoid market distortions and leaving the market to equilibrate demand and supply. In other hand, following sound market economy and adhering strictly to the market economy principles are vital for sustainable long run growth. In the short run however, solving problems of inflation and balance of payment imbalances through tight monetary and fiscal policies, devaluation of domestic currency to become competitive in international trade and increase revenue export and reduce BP problem, and rise interest rate to increase savings are the optimal solutions.

4.1.2 The structuralist view: As the name implies structural rigidities within the domestic economy are the main factors for low aggregate demand in LDCs. This school of thought is divided into the early and recent.

83

(A) The early structuralist view: This school of thought was dominant in 1960’s and 1970’5. Exports of developing countries consist more of primary products. As a result the products have low income and price elasticity of demand compared to that of manufacturing outputs of developed countries. This in turn leads to continuous deterioration of terms of trade (TOT). That is when they produce more, the price of their exports declined significantly.

The solution proposed by the early structuralist is moving to the production of industrial goods under the protection of infant domestic industries to replace imported goods from abroad in the long run. This argument is simply referred as the import substitution argument. According to the early structural school thinkers this can be facilitated among others through high tariff barriers on imported goods, providing subsidies of various forms, and improving access to credit and foreign exchange.

(B) The recent structuralist view:Taylor was the most notable and influential leader recent structuralist. The recent structuralist focuses mainly on the short run stabilization or adjustment policies. They questioned the validity of the orthodox policy prescriptions of tight monetary and fiscal policies and devaluation to LDC economies and argued that monetary policy or increase in money supply is only accommodative and not the cause of high inflation. According to them, prices and wages are not flexible and the source of inflation in LDCs is slow productivity growth in agricultural, the backbone of the majority of African countries, not money supply.

Furthermore, they argued that the main causes of slow agricultural productivity and also that influence monetary policy in LDCs are poor land tenure system, administrative prices, and wage indexation. Consequently, given that working capital and imported inputs play a significant role in terms of addressing structural rigidities and limited substitution possibilities in production a policy package combined devaluation with tight monetary and fiscal policies will lead to stagflation. To the recent structuralists, if prices and wages are rigid monetary or fiscal policy becomes effective in the short-run. Hence, the solutions are some degree of government intervention in the market is necessary to eliminate structural problems/rigidities in production before applying the standard orthodox prescriptions. This includes undertaking interventions related to export promotion and export diversification; such as the provision of subsidy, tax-holiday, information, etc., to exporters

4.2 Basic Features of African EconomiesThe distinguishing macroeconomic features of African economy include more openness to trade in both commercial and assets; the nature of the financial markets, different attributes of both short and long run fluctuations; the nature of fiscal deficits; determinants of the private sector credit behavioral function (biasness or preferential treatments of public sector enterprises for credit); and the stabilization policy regimes.

1) Openness to trade

84

Relative to developed countries, African economy tend to be more open and to have little control over the price of products they exports and import. The standard measures of degree of openness are looking into the ratio of exports plus import to GDP and the tariff structure. The implication of these characteristics is that:(a) The standard open macro economy policies may not hold at all or are irrelevant (b) Given their share in the world trade and composition of their exports they do not have

control over the prices of their exports and imports have huge policy implication. That is, first they export primary products, which are not demand determined but supply determined. Second, they are small relative to MDC and DC. Therefore, the standard open economy model, which assumes endogenous TOT, has little use in explaining their macroeconomic behavior.

2) The exchange rate regimeIn contrast to MDC the vast majority of African economies have exchange rates either fixed or pegged to a foreign country, which leads in most cases to exchange rate retention or control. In many cases the actual exchange rate deviates from the equilibrium exchange rate. Recently many African countries have adopted flexible exchange rate but not market determined. That is they are administered rather than auctioned or demand and supply determined. The Ethiopian exchange rate regime is called managed floating, which is between the two extremes - fixed and flexible exchange rates;. Since it is only the financial institutions who buy the foreign currency through the bi-weekly inter-banks auction market, this indicates some degree of government influences over the exchange rate.

3) Capital inputsAlmost all African economies are net importers of capital (both physical and financial capital). Therefore, dependence on foreign market is an important issue.

4) The role of the stateThe state plays an important role in the production and distribution of goods and services in LDCs. In MDCs, however, the private sector has the larger share in the economy as compare to the public sector. The policy implications are:

(A) Imported intermediate goods play important role in the aggregate production function.(B) An increase in cost of intermediate goods affect the exchange rate and the exchange

rate affects AS because we may import more or less unlike the MDCs where the exchange rate does not enter into AS because their exchange rate is floating/flexible/ and do not import much intermediate goods.

5) The financial sectorThe financial sector in LDCs is weak and inefficient. It is characterized by the prevalence of rudimentary/underdeveloped financial market and financial repression. That is, the financial sector is dominated by commercial banks with little or no secondary stock and security markets, which implies allocation inefficiencies. The two most important implication of underdeveloped financial sector in LDCs are financial dualism and financial repression:

85

(A) Financial dualism: It is the coexistence of organized and unorganized/traditional money markets in LDCs.

The organized money market consists of commercial banks and other financial intermediaries, which lend short-term credit at low interest rates to the modern business sectors consisting of big companies, large scale manufacturing enterprises, and the government. On the other hand, the unorganized money market consisting of non-institutional money lenders, such as village money lenders, traders, shopkeepers, or the combination of some of them, which charge higher interest rates on loans. The main reason is that there is real shortage of savings in the traditional sector as substantial amount of savings is horded in gold and jewelry. As a result,

not only a significant part of financial transaction takes place control and direct policy reach of the central banks but also there is interest rate differential

whatever monetary policy is to be practiced must be affected by other than open market operation. Since the government debt with its artificially low interest rate is not sold and bought in free market the monetary authorities/central bank cannot affect the monetary base ( ). It is rather determined by the past and current government deficits and trade balances.

(B) Financial repression/ compartmentalization: It is a policy of the state in terms of financial sector where nominal interest rate ( ) that the commercial banks pay on their deposits and charge for their loan are kept low/hold down without taking into account the demand and supply.

Credits are given to public enterprises on preference basis than on demand basis; implying the private sector does not have adequate access to credit as the public enterprises. The implication of financial repression is that the transmission mechanism and effectiveness of monetary policy- that is as money supply increases interest rate declines, investment increases, and hence output grows does no work in LDCs for interest rate is fixed.

6) Government budgetMost countries have huge budget deficits and hence the policy implication of budget deficits has become an important issue.

7) Objectives of macroeconomic policies in LDCsThe main macroeconomics objectives of the MDC are full employment, increase output and price and exchange rate stability. Apart from these LDCs have other issues to address and objectives to achieve. These include among others:(A) Exchange rate management: This is because there is an overvalued exchange rate in

most African countries(B) Stabilization of high inflation: Achieving a targeted low level of inflation per annum

is the main objective of LDCs. Nevertheless, inflation in many African countries is higher (for example in Zimbabwe it has now become around 2000%) than targeted due to failure of stabilization policies to yield the desired target. Low level of investment, slow output growth, high public expenditure and use appropriate budget deficits financing mechanisms and in ability of managing imported inflation triggered such as

86

by the rise in oil prices, which rises mainly transportation cost are the main reasons for high inflation in Africa.

(C) Debt management: Both the stock (what a country borrow) and flow (unsettled & what are to be paid) of debt to GDP are very high in Africa. Full stock is defined if the debt flow is greater that revenue generated from foreign trade. If they are equal it is defined as constant stock. Even if debt is also very high in MDCs they can pay without affecting the economy. Failure to achieve sustainable economic growth and mitigate vulnerability to adverse natural calamities such as drought are among the major reasons

(D) Reducing capital flight: Both the profits and assets of citizens usually transferred abroad for security and/or other purposes

8) The characteristics of AD and AS curves in LDCs

AGGREGATE DEMAND: Before arriving at the AD curve in LDC, we should examine the four components; aggregate real consumption ( ), real disposable household income ( ), real private investment , and net export ( ) of total DD for domestic output.

To examine the nature of AD in LDC we assume hereafter that world price is fixed and the effect of a change in on the IS curve is zero in the standard LDC model. The curve is downward sloped in ( ) space like the standard MDC AD curve. However, it is much steeper than MDC AD due to the following two reasons.

1) The IS curve, which shifts to the left in the standard MDC model when domestic level rises because of its effect on net exports, doesn’t shift in the standard LDC model because exchange rate is fixed in LDC. In fact, the effect on shifts IS to the left in MDC.

Recall that the export function is and . From the export function . Because the increase in domestic price level (inflation) will reduce

implying the exchange rate has appreciated. This will in turn reduce the of a country where the price level has increased, reduce or and thus shifts IS and AD to the left.

2) However, the IS curve is steeper in LDC due to a high marginal propensity to import () and a low interest elasticity of investment DD.

AD for Developed countries AD for LDCs

87

AGGREGATE SUPPLY IN LDCs: The equation is given by

Where, Price and interest rate are endogenous while exchange rate and nominal wage are exogenous variables. Moreover, , and

. The main difference between the standard LDC AS curve and that usually pictured for an MDC are the following.

1 The AS curve of LDC is flatter than MDC. The reason for this is that the MDC is normally close to full employment with less nominal wage rigidity. In LDC however, it is more frequently found not only unemployed labour but also an underutilized capital stock. Thus, due to rigidity of nominal wages and excess ideal (unutilized) resources, output can be increased without increasing employment (the supply of labour and employment in an economy), which implies DMPL.

2 The second characteristic is that the increase in affects AS of LDC through its effect on the cost of working capital, which is scarce due to low saving in LDCs.

3 Changes in the exchange rate ( ) shifts the AS curve in LDCs for the domestic price of imported intermediate inputs and raw materials will be affected.

P AS P AS

AS for MDCs AS for LDCs

4.3 The Applicability of Conventional Theories to African EconomiesUnder this section the impact of restrictive fiscal policy and monetary policies on AD and AS curves as well as the net effect will be covered.

4.3.1) Restrictive fiscal policy ( ): While restrictive monetary policy is likely to increase both unemployment and inflation in LDCs in the short run, restrictive fiscal policy is likely to become more effective (successful) in reducing the price level without the costs of a major recession. A decrease in will shift the IS curve to the left from to . This results not only in a small leftward shift of the AD

curve from to but also a larger shift in AS to the right because interest rate has fallen

from to . Finally, the net effect (result) is a decline in the price level from to and possibly even an increase in output from to . In fact, in the standard MDC model restrictive fiscal policy reduces both price and output. The increase in output in the case of LDCs is that because the decline in domestic price level will reduce the cost of intermediate

88

inputs and raw materials (due to appreciation of domestic currency for real exchange rate or has decreased). Graphically,

Fig 4.1: The impact of concretionary Fiscal Policy in LDC

If the increase in output is small for the LDC, then import demand is affected very little. This is because the reduction in G, which increases the government surplus will leave the balance of trade surplus (or deficit) essentially unchanged. The cumulative effect is thus a reduction in the monetary base (reserves) and as a result of which economic recession appears (or will worsen) overtime

4.3.2) RESTRICTIVE (CONTRACTIONARY) MONETARY POLICY (↓Ms):

89

The standard result following of a decrease in is to increase interest rate , which then reduces investment, output and P.

However, in LDCs reducing the money supply has a larger impact on LM curve (for a given P level) because of the low interest elasticity of DD. The availability of low interest rate on loans from commercial bank also reduces retained earnings, shifting the IS curve down. The reason why the interest rate enters into the AS function in LDCs is that:

A) The interest rate in the formal market when auctioned is not high as in the informal market

B) Cost of borrowing is very high for cost of collateral is very high

The impact of concretionary monetary policy is thus a relatively small horizontal shift in the AD curve. And due to the flatness of the AS curve, any shift that does occur is relatively ineffective in reducing the price level. In LDC, this restrictive monetary policy also rises the AS curve to the left through the increase in the interest cost on variable inputs.

The net impact for the MDC is that the price level falls and output declines moderately; for LDC, output also falls, but the price level may increase. Therefore, in the short run restrictive monetary policy has few appealing implications for the policy maker.

90

Fig 4.2: The impact of restrictive monetary policy in LDCs

REFERENCE BOOKS 1) Branson, William H. (1998), “Macroeconomics: Theory and Policy”, 2nd Ed.,

Universal Book Stall, 5 Ansari Road, New-Delhi-110 002 (India).2) Dornbusch, R and Fischer, S. (1994), “Macroeconomics”, 2nd Ed.3) Jones, C. (2000), “Introduction to Economic growth”, 2nd Ed.4) Mankiw, G. (200), “Macroeconomics”, 3rd Ed.5) Pentecost, Eric, (2000), “Macroeconomics: An open Economy Approach”, 2nd Ed.,

Macmillan Press LTD, London6) Pilbeam, K. (1998), “International Finance”, 2nd Ed.

91

Quiz number 1:1) Using the Cobb-Douglas production function ,

A) drive and show that the equilibrium capital stock rises with an increase in and falls with an increase in real user cost of capital in the flexible accelerator investment model

B) Drive also the gross investment assuming that the real user cost of capital remains fairly constant overtime, ceteris paribus.

2) Assume that the valves of and in an economy are 10, 4, and 1respectivelly. Further, assume that is 80% and net saving ratiois 40% in 2009. Further assume that the real user cost of capital remains fairly constant overtime, ceteris paribus. Given these information, calculate the value of

A) real user cost of capital B) net investment (the change in

equilibrium capital stock) if output ( ) increases to 12 in 2010C) growth rate of output in the

economy in 2010 that would maintain supply equal to demandD) output changeE) gross investment, if the

depreciation rate of capital stock in the economy ( ) is 10% in 2010

92

93