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2NQ. 1. Derive the conditions for steady state in the Solow model. What are its implications? In what respects is

the golden rule different from the steady state?Ans. According to Solow model, an economy is in equilibrium when investment per unit of effective labour s equal

to savings per unit of effective labour.I = sY

Where I is investment, s is MPS and Y is income.Since Y is a function of capital, we can say that

I = sf(k)Where, k is existing capital stock of an economy.It implies that

k = sf(k)Where k is change in K i.e. existing capital stock of the economy.This equilibrium condition is true for an economy where,(a) Depreciation is zero;(b) Population is constant;(c) Technology is given and constant.Now let us see what happens when we relax these unrealistic assumptions.The Growth of Capital and Steady State: In Solow model, it is assumed that capital depreciates at a fixed rate. Let

us denote it by . Therefore, every year k amount of capital is depreciated.Investment and depreciation act in opposite directions and the growth in capital stock is net of the two quantities.

k (t) = i (t) k (t))

Since i = sf (k (t))(t) = sf (k (t)) k (t)) ...(xi)

From eqn. (xi), we can conclude that(a) Capital stock increases when f (k (t)) > k (t)(b) Captial stock falls when f (k (t)) < k (t)(c) And capital stock remains constant when

k (k (t)) = k (t)We can show it with the help of following diagrams.

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Y

XO

Rate

of

de

prec

iatio

n

Capital per unit of effective labour

KDepreciation rate

Steady State of an Economy

K

X F(k)

K1 K2KO

Y

X

K2

i = K2i1

K2

Population Growth and Steady State: In this section we shall elaborate on the changes in population and labourforce at a constant rate n. When there is a growth of labour force, we need to increase capital; to maintain same level of k.It is essential that the economy has adequate investment to take care of depreciation ( k) and population growth (nk). Ifwe introduce n in the equation (xi) above, it will be equal to:

k (t) = sf (k(t) (n + ) k (t) ...(xii)If we want to maintain steady growth rate we need to cover depreciation which is equal to (k) and to provide new

workers with capital equal to (nk). In this case, break-even investment will become equal to ( + n) k. The economy willattain steady growth rate at a point where investment curve intersects ( + n) k curve. It is shown with the help offollowing diagram:

Steady State in two countries

Steady state capital declines( + )Kh2

Ou

tpu

t per

u

nit o

f ef

fect

ive

labo

ur

K1K2O

Y

X

( + )Kh1 (K)f

K1L = K

If k1 < k*, this means investment is greater than break-even investment and it will cause capital and output to rise.If k2 > k*, then k will decline until it becomes equal to k*.Population growth gives us an explanation for steady economic growth rate. It is however, assumed that output per

effective labour remains constant. It is also seen that at steady growth rate k and y remain constant. But capital stock (K)and output (Y) keep increasing at the rate of n so as to keep k and y constant. This feature explains the cross-countrydisparities in income. If country one is experiencing population growth @ n1 and country two is experiencing populationgrowth at n2 such that n1 > n2 and if the saving rates are same in both the countries then ( + n2) k with a slope greater than( + n1) k has been drawn.

A country with higher rate of population growth rate n2 has lower k* (the steady level of capital) and hence lower y i.e.output per effective labour. And the country with lower rate of population n1 has a higher k* (the steady level of capital)and hence higher y i.e. output per effective labour.

Technological Progress and Steady State: By introducing technological progress, we can explain growth n outputper effective labour in Solow model. It is assumed that technological growth is labour augmenting i.e. it increasesproductivity per efficiency of labour. Therefore, with the technological progress, there will be an increase in the quantityof effective labour (AL). If we assume that the rate of technological improvement is g then the change in k over time canbe written as:

k (t) = sf (k(t) (n + g + ) k (t) ...(xiii)

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Capital per unit of effective labourO

Y

X

Steady state

Ou

tput

pe

r u

nit

of

effe

ctive

la

bou

r ( + + )Kn g

Break-eveninvestment

K

F(k)

Actually equation. (xiii) is the key equation of the Solow model. We have explained this equation with the help of adiagram. It is clear from the equation (xiii) that the analysis of steady state remains unaffected with the inclusion oftechnological progress but the new break-even investment becomes equal to (n + g + ) k (t). Out of total investment, kwill be used for recovery of depreciation, and nk amount of capital will be required to maintain capital per effective labourat a constant rate. But with the result of technological improvement y increases at the rate of g. Individually, n, and gmay be positive or negative but their sum total is assume to be positive in the model. Total output will grow at the rate of(n + g). Therefore, we can conclude that introduction of technological progress leads to an increase in output per worker.

Solow model claims that persistent rise in standard of living always owe to technological progress.The golden rule

In this section, we shall consider the effect of change in saving rate on steady state. Let us assume that saving rateincreases while the n, g and remain to be same. As we know that i = sf(k), there will be higher investment which will leadto capital accumulation and output growth and the economy will finally reach to a new steady state with higher capital andoutput. When rate of savings increase from s1 to s2 then the investment curve also increases from s1 f(k) to s2f(k). Therefore,the economy reaches at new steady state k*2 through the process of capital accumulation and output growth.

From the above explanation, one may jump to a hurried conclusion that a higher saving is always desirable as highersavings will lead to higher capital accumulation and thereby increased output in the economy. You may also misinterpretthat the 100% saving rate will lead to highest possible capital accumulation and output in the economy, but it is not true.At different levels of s, there are different levels of capital accumulation but there is one optimum level of capitalaccumulation which is called golden rule level of capital.

O

Y

X

Impact of saving rate

K2

( + )kh+g 2F( )k

1F( )k

K1

Y= YAL

K/AL

At the golden rule level of capital the level of saving is such that consumption per effective labour is maximum at thesteady state. The reason is that individuals are concerned with the amount of output they consume. T = for them capitalstock or total output of the economy is not of much significance. Therefore, that level of saving rate which maximizes theconsumption per effective labour is the most desirable and the optimum. It is known as Golden rule level of saving rate.We can say that in a two sector economy national income is the sum total of consumption and investment assuming thatsaving and investment are equal to each other. Therefore, steady state consumption can be found by deducting investmentfrom income.

c* = y* i*and we know y is a function of capital and i is a function of n, g and , therefore we can rewrite above equation as:

c* = f (k*) (n + g + ) k* ...(xiv)

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It is interesting to see that this increase in steady state capital has a contrasting effect on steady state consumption.Increase in steady state capital leads to more output which means increase in consumption and also a higher break-eveninvestment equal to (n + g + ) k*.

It is shown with the help of following diagram. In the diagram steady state consumption is the difference between thesteady state output and steady state break-even investment. It is maximum at k*gold level of capital per effective labour.It has been explained in the beginning of this chapter that the slope of the production function is the marginal product ofcapital i.e. MPK. It is also clear from the diagram that c*gold level of consumption is the golden rule level of consumptionand at this level of consumption the slope of production function equals the slope of break-even investment, i.e.

Marginal productivity of capital, MPK = ((n + g + )MPK = (n + g) ...(xv)

O

Y

X

Golden rule of steady state

Steady Gold State

(h+g+ )k

F(k)GoldY= YAL

This golden rule level of steady state is not achieved automatically. It requires a particular rate of saving subscript asshown in the diagram given below.

In order to attain golden rule steady state of capital k*subscript, a saving rate of subscript is required in such a waythat maximizes c*subscript. If s > subscript then there is dynamic inefficiency in the economy. If we decrease s tosubscript it will lead to increase in consumption. If s < sgold then a rise n saving will decrease consumption in the short runbut lead to a higher consumption in the long-run in the economy.

O

Y

XSteady State K

kp Gold

( + + )n g k

Y= YAL

Gold

Gold

C

i

P( )k

Gold( )k

Transition of the golden rule steady stateIn this section, we shall discuss the effect of change in saving rate on golden rule level of consumption, investment

and capital. There can be two situations: one in which s > sgold i.e. steady state capital per effective labour is greater thanthe required level for golden rule and second in which s sgold: In this case we need to decrease the saving rate to sgold to achieve the golden rule level ofsaving rate. When there is a fall in saving rate, there will be a rise in consumption per effective labour immediately andinvestment declines. The economy does not remain in a steady state any more because investment is less than break-eveninvestment of (n + g + ) k*. It causes capital stock per effective labour to fall. Output per effective labour is a function ofk therefore, k also falls.

Since c = y I; consumption per effective labour also falls. The c, y, and i keep on falling until the economy attains anew steady state which is golden rule steady state.

At this level consumption is higher than the previous steady state. but the levels of output and investment are lower.Case-II: When s < sgold: When at a steady state s < sgold, it means we have k* < k*gold. In such a situation we need to

increase s to attain golden rule steady state. When there is increase in s, there is an increase in investment which is more

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than break-even investment (n + g + ) and there is a state of transition in the economy. There will be accumulation ofcapital leading to rise in output per effective labour declines. Therefore, when saving is increased, consumption pereffective labour declines immediately but with an increase in output per effective labour which increases to a level that ishigher than the initial level. There is dilemma whether we should try to reach golden rule of steady state as it is a choicebetween current and future consumers. There exists a trade- off between present and future levels of consumption.

Q. 2. Explain how IS and LM curves are derived. What are the implications of IS and LM curves? What arethe factors on which the shape of the IS and LM curves depend?

Ans. It is shown in the previous chapter that an economy is in equilibriumwhen aggregate demand is just equal to aggregate supply. In a two sectoreconomy, AD comprises of consumption and investment. While aggregatesupply comprises of consumption and savings. Therefore, at equilibrium levelof output, savings is equal investment. If for simplicity sake, we take investmentas autonomous and therefore, a horizontal line parallel to income axis, theneconomy is in equilibrium at point E as shown in the diagram. On the rightside of point E, unplanned investment will be positive and on the left handside, unplanned investment is negative.

Investment is an inverse function of rate of interest and saving is a positivefunction of income. Both savings and investment can be integrated to getequilibrium level of income and interest rate. The IS curve shows theequilibrium in the real sector of the economy. Let us see how IS curve is derived.

In order to understand how IS curve is derived, let us first understand what are we taking on y-axis and x-axis. In firstquadrant, we have taken rate of interest on y-axis and income on x-axis. In second quadrant, we have taken rate of intereston y-axis and investment on x-axis. In third quadrant, we have taken saving on y-axis and investment on x-axis. In fourthquadrant, we have taken savings on y-axis and income on x-axis.

Second quadrant is showing that there is an inverse relationship between investment and rate of interest. More is therate of interest; less is the level of investment and vice-versa, other things being constant. In the third quadrant, we haveshown a 45 line to exhibit that on this line at all levels saving is equal to investment. In the fourth quadrant positiverelation between savings and investment has been shown. It is showing the different levels of savings at different levels ofincome. Hence, by implication that saving is directly related to income and investment is inversely related to rate ofinterest and saving is equal to investment at equilibrium level, it is clear that there is an inverse relation between rate ofinterest and income. It is shown by IS curve in I quadrant which is the locus of equilibrium levels of income. In otherwords, every point on IS curve represents equilibrium level of income and interest rates.

When there is change in the level of investment, there will be a chain of reactions.Change in investment required level of savings will change Equilibrium level of income will changeIt is implied in IS curve that real sector can be in equilibrium in any combination of lower rate of interest and higher

income or higher rate of interest and lower income.

ISISr

I + GI

I

S = Is S

Y

IS Curve

LM curve is based on the concept of transaction demand for money and speculative demand for money. According toKeynes, transaction demand for money is a positive function of income i.e. at higher level of income the transactiondemand for money is more and vice-versa. Speculative demand for money is an inverse function of rate of interest. At

Output

Savi

ngs

&

Inve

stm

en

t

S = a + (1b)y

XO

Y

Y1

EI

-Y

} a

IO

8N

Government makes use of two policy instruments to intervene in the market: fiscal policy and monetary policy. Fiscalpolicy is the policy of the government related to tax and expenditure. Monetary policy is the policy of the governmentrelated to money and credit supply. Fiscal policy of the government affects IS curve while changes in monetary policyaffects LM curve.

Fiscal policy and IS curve: An increase in government expenditure leads to an increase in investment and therebyan outward shift in IS curve. Another tool of fiscal policy is tax. When government reduces taxes, it will increase theconsumption level and thereby lead to upward shift in IS curve. Shift in IS curve leads to establishment of equilibriumlevel of income and rate of interest at a higher level. Opposite will happen when government expenditure is reduced ortaxes are increased.

Monetary policy and LM curve: When there is an increase in money supply, an increase in real balances takes placewhich leads to decrease in rate of interest. When rate of interest decreases, for each level of income, there will be adownward shift in LM curve and accordingly there will be change in new equilibrium level of Y and R opposite willhappen when a decrease in real balances take place.

It is shown with the help of following diagram:

r LM

YMAD

MTD

M = + MAD MTD

LM Curve

Q. 3. What does the Phillips curve signify? How do you reconcile the difference in the shape of the curve in theshort run and the long run?

Ans. A.W. Philips gave this concept which is known as Phillips curve after his name which describes the relationshipbetween the rate of unemployment and the rate of inflation. He tried to establish a relationship between the level ofunemployment and changes in wage rates. His empirical work proved that the lower is the initial rate of unemployment;the greater would be the rise in the money wage rate corresponding to a given rise in the rate of unemployment. Hecollected data for a period of around 100 years (1861-1957). This data got fitted into a hyperbola. This data providedproof to his hypothesis. He made an assumption that the ratio between prices and nominal wage rates is constant in theshort run. On this assumption the Phillips curve showed the inverse relation between the rate of unemployment and therate of inflation i.e. the existence of trade off between unemployment and inflation.

He took a simple linear equation of the following form: c = abuWhere is the rate of wage increase, a and b are constant and u is the rate of unemployment. He found that there

exists an inverse relationship between and u i.e. wage rate and rate of unemployment.Later, data was collected for many other countries and the relationship held true for almost all countries. Therefore,

it represented a stable relation between inflation and unemployment over time, which suggested to economists that theywill have to bear one problem in the economy to get rid of other and it is up to them which combination of these problemsthey would like to choose. If we choose low rate of inflation, unemployment rate would be high and vice-versa.

In the late 1960s, USA experienced unemployment rates that were much higher than what was expected as perPhillips curve from the past. On the one hand, there was economic stagnation depicted by a low rate of increase in GDPand on the other hand, there was high rate of inflation. In economics such a situation was given a term Stagflation. Alimitation of the Phillips curve is that the decision by the workers and firms is taken on the basis of real wage and notnominal wage. When we enter in to a contract for future period, we adjust the wages for inflation. But in case the rate of

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inflation is more than inflationary expectations, the Phillips curve will not work Milton Friedman in 1968, gave anexplanation as to why the Philips curve might not represent a stable exploitable trade off between unemployment andinflation rate. His arguments gained a lot of popularity in later years.

He gave an explanation that workers are not interested in an increase in their money wage rates but in an increase inthe real wage rate. He also gave a concept of NAIRU (Natural Rate of Unemployment). He claimed that at natural rate ofunemployment, firms as well as workers will be satisfied with the existing real wage rate and equilibrium will get establishedat a lower real wage rate.

There may be following reasons for it:(a) Jobs are of heterogeneous nature and firms and workers need appropriate time to search for right jobs and

workers.(b) Unemployed workers may not be able to seek employment by lowering wages due to costs of mobility or labour

market imperfections.In the short-run, Philips curve is stable but in the long-run, Phillips curve keeps shifting from one level to another. It

makes the Phillips curve a straight vertical line. Let us explain long-run Philips curve through an example taken bySamuelson.

Let us assume that an economy is operating at natural rate of unemployment u*. Suppose economy is operating atpoint A with low inflation rate I1. People expect inflation rate to remain same in next period also. Now suppose in the nextperiod, government follows expansionary policy so as to reduce the rate of unemployment. It will lead to increase incompetition amongst firms to hire workers. Output can not be expanded further therefore, this policy change will lead toincrease in wage rate and prices and the economy will now operate on point B on SRPC1. But their expectations aboutfuture inflation rate are still same and hence, they are operating on same SRPC1. Now if in next period, they expectincrease in inflation rate, SRPC1 will shift to SRPC2. If we suppose they expect inflation rate to be I2or I3 which is equalto I2 then there is decline in demand for labour, the unemployment rate starts increasing and the economy moves to pointC as shown in figure given below:

O

Y

XUnemployment

Rate

o

f Inf

latio

n

LRPC

AB

C

SRPC2I1

I2,3

SRPC1

The result of the above process is that the economy experiences an increase in inflation rate without any decrease inunemployment. Real GDP of the economy does not change only nominal GDP changes.

This natural rate of unemployment is called Non-Accelerating Inflation Rate of Unemployment (NAIRU).Whenunemployment rate is less than natural rate of unemployment, the firms which are employing more labour would bewilling to pay a real wage rate lower than what they pay at a higher natural rate of unemployment. If there is trade unionor otherwise a contractual real wage rate then actual rate of unemployment will never be less than natural rate ofunemployment. But in reality, firms and workers enter into stipulated agreements on money wage rates and not real wagerates. Now it would depend on the expectations of the workers and the firms regarding future prices whether real wagerate would be lower or higher. If at the time of accepting a job offer, a worker expects a lower future price level than firms,then rate of unemployment will be lower than natural rate of unemployment. It is so because the expected real wage ratefor workers would be greater for workers than for firms. On the other hand, if at the time of accepting a job offer, a workerexpects a higher future price level than firms, and then rate of unemployment will be more than natural rate of unemployment.It is so because the expected real wage rate for workers would be lower for workers than for firms.

Q. 4. Lucas point of view, what are the limitations of the Keynesian model? What improvements does hesuggest?

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Ans. Keynes General Theory gave birth to a new branch of economics and therefore, Keynes is also known as fatherof macro-economics. But the teaching of macroeconomics as a discipline was based on many mathematical formalizationswhich were perceived to be containing the essence of Keynes economic doctrine. IS-LM model, AS-AD model which arethe base of macro-economic theories and models and which were used in many countries to predict the effect of alternativepolicies on macro-economic variables. Keynes never recommended using these models for policy formulation but stillthey were used in varying degrees in most developed countries.

Before we proceed further, it is better to understand some basic terms:(a) Structure of the Model: The whole complex of features which are assumed to remain constant, are called

economic structure or structure of the model.(b) Structural Parameters: There are some numerical constants that characterize the structure of the model, they are

known as structural parameters.(c) Endogenous Variable: Those variables that are determined within the model are known as endogenous variable.

In other words, the value of these variables is determined within the system of equations given by the model.(d) Exogenous Variable: Those variables whose values are assumed to be known and given and the value of these

variables are not determined by the system of equations given by the model are called exogenous variables.A simple model of income determination is given below:C + I = YC = a + b(1 t) Y ...(1)Where,C = Aggregate consumption expenditurea = Autonomous consumptionb = MPC i.e. Marginal propensity of consumptionI = Aggregate investment expenditureY = Real National Incomet = Revenue from direct taxesIn this equation a and b are structural parameters; C and Y are endogenous variables and I and t are exogenous

variables. (1 t) Y is personal disposable income. It is an example of deterministic model in which the endogenousvariables c and y are entirely determined given the values of exogenous variables I and t. From eqn. (1), we get

Y = (I + b) / [1 a (1 t)]C = {a (1 t) I + b]/ [1 a (1 t)]There are some limitations of deterministic models.(a) The most important one is that a deterministic model is generally used to isolate the most important determining

factors for the variables of interest, like y in the above example.(b) Second, these models are used to represent the relationships between the variable in the model in a simple and

clear manner. These models are over simplified versions of reality and do ignore many factors that can affect thevariables of interest.

Hence, we cannot expect that these models will exactly describe the relationship between the endogenous variablesand exogenous variables as the former are being determined in a simplified version that is too away from the reality whilethe latter is being determined by the actual data.

Now the question arises that how to solve this problem? How to relate deterministic economic models to actual data?The usual strategy is to introduce new variables in different deterministic equations of the model. The new variable (s)corresponding to each equation is expected to compensate for the effects of all other factors that can affect the relationshipbetween exogenous and endogenous variables in the model. These newly introduced variables are random in nature andrepresent random disturbances to the deterministic relationships between exogenous and endogenous variables in themodel. So, in order to introduce random variable we can modify the eqn. (1) as follows:

C = a + b (1t) Y+ u ...(2)Where, u is representing an additive disturbance term which will help to judge the exact relationship between exogenous

and endogenous variables in the model. When we introduce additive disturbance term in a deterministic equation, it iscalled stochastic equation as stochastic term u is introduced here.

The above equations are an example of a simple macro-economic model. But the real life economic models which areused for policy formulation, are certainly, much larger and complicated as these models include many more variables and

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equations. For example, a classic macro-economic model was developed by L.R. Klien and A.S. Goldberger in 1955which contained twenty stochastic equations, twenty endogenous variables and eighteen exogenous variables.

For example, in eqn. (2) above, t is a policy variable. If we assume that the stochastic variable u is distributed withexpected value 0, then from eqn. (1) and eqn. (2) we can say that the expected value of y, given the value of i and t, willbe given by:

E(Y) = (I + Ib) / [1 a (1 t)]Now, suppose the government wants to know the effect of alternative choices of t on the expected value of national

income y in the economy, then we must obtain the estimates of the structural parameters a and b for the economy by usingthe past data on the variables in the economy.

The estimates of b give us an estimate of average change in aggregate consumption expenditure due to change indisposable income in the economy. It is also clear that the aggregate consumption expenditure in an economy depends notonly on current disposable income but also on expected levels of disposable income in the future as explained by life-cycle theory of consumption or Permanent-income hypothesis. Then, the future expected level of disposable income alsodepend on the expectations about the value of t. It implies that the change in consumption expenditure as a result ofchange in current tax rates and disposable income will depend on, to a great extent, how expected values of tax rates anddisposable income change in response to change in current values.

Therefore, when we estimate the value of b statistically from the data of a given period of time, it would tell us howconsumption expenditure is expected to change in tax rates and disposable income but only when current changes in taxrates would have a similar effect on future expectations of tax rates as in the period from which the data is taken.

Let us explain two cases:(a) When most tax rate changes have been temporary in nature: In such a policy environment, households will change

their expectations according to the nature of policy changes. In these circumstances, households would have interpretedthat changes in current tax rates will bring about little change in expected future tax rates and future disposable incomes.Hence, in such a policy environment, there will be a weak relationship between permanent incomes of households,consumption expenditure of the economy and changes in tax rates and disposable income. The estimated value of b willbe relatively small.

(b) When most tax rate changes have been permanent in nature: In such a policy environment, households willinterpret any changes in current tax rates will bring about significant change in expected values of future tax rates andfuture disposable incomes. Hence, in such a policy environment, there will be a strong impact on permanent income ofthe households and the level of consumption expenditure in the economy. Thus, there will be strong relationship betweenpermanent incomes of households, consumption expenditure of the economy and changes in tax rates and disposableincome. Therefore, using statistical estimate of b which is derived from past data will underestimate the impact of taxpolicy changes on consumption expenditure and income in the economy.

Problems with the use of econometric policy evaluation:(a) Macro-economic models which are used to evaluate policy includes equations which are related to aggregate

variables. Since aggregates are summation of individual behaviour, these aggregate variables are the resultant ofthe multitude of decisions taken by different economic agents.

(b) Decisions taken by individual economic agents is of intemporal nature. For example, a household considers thetrade-off between the current and future utility derived from consumption and considers both current and futuredisposable income in evaluating total consumption possibilities.

Therefore, the relationship between different aggregate variables will depend on: (a) how expected future values ofthese variables changes with the current values; (b) how expectations about future values of policy variables are affectedby changes in current values of policy variables. Keeping these facts in mind, Lucas critique is that the parameters ofbehavioural equations which are assumed to be unchanging over time in a macro-economic model, forming a part of thestructure of the model, cannot be considered to be so because the same changes in the current value of a policy variablemay induce different effects on the expectations of individual economic agents at different points of time.

In nutshell, this is Lucas critique of the use of macro-econometric models in formulation of policies.To exemplify, let us consider inflation unemploy-ment trade-off that we studies in the previous chapter. As long as,

the government is not making any effort to manage the level of nominal demand in the economy, workers expect the sameaverage growth rate of nominal expenditures as in the past because they accept that fluctuations in the growth rates ofnominal expenditure in the economy due to government policy are random in nature.

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But if workers feel that government is systematically using this trade-off by targeting a level of unemployment lowerthan NAIRU, workers will be expecting a higher rate of growth in nominal aggregate expenditure and therefore, a higherrate of inflation in the economy. As a result, the government would expect the policy to be effective but due to changes inworkers expectations, the policy will not be as effective as expected by the government. It proves that macro-econometricmodels cannot be used for policy evaluation as they are getting affected by multiple factors, many of which are non-quantifiable.

Q. 5. What is meant by endogenous growth? Explain the main features of endogenous growth models.Ans. Endogenous growth theory began with the efforts of Paul Romer in 186 and Robert Lucas in 1988. Endogenous

growth models originated in two sources: one, to give a coherent explanation of convergence controversy, and the other,to go beyond an unrealistic simple world of perfect competition and constant returns to scale in growth models. Theirwork differs from Neo-Classical economists who took economic growth is caused by factors that are exogenous. Theendogenous growth theory is an extension of Solow Model in the sense that the latter introduced increasing and diminishingreturns to the theories of economic growth but the latter also included technical change as an endogenous variable i.e. avariable which is being measured internally, in growth models.

The Endogenous Growth Theory gives a great emphasis on accumulation of human capital even more than physicalcapital. They laid a great stress on knowledge capital. Secondly, since knowledge capital can be acquired by transfer oftechnology, developing nations would do well if they open up their economies for developed economies. It would increasethe sharing of technology. Thirdly, the theory also recognizes the role of policies and government in promoting the rateof knowledge capital and thereby human capital formation. Government need to formulate favourable policies to promotethe rate of human capital formation. And most importantly, the Theory also suggests that automatic convergence in thegrowth rate does not occur and therefore, a planned effort is required. Rather it explained logically that in spite of samesaving rate, population we can see different countries growing at different rates due to difference in their level of humancapital. And hence, government needs to formulate favourable policies to promote the rate of human capital formation. Itis a way to break vicious circle of poverty.

Endogenous theory is called new growth theory because it came into picture later than exogenous growth theory.Endogenous theory is modern as it explains technology as an endogenous variable. Exogenous theory was outdated withthe introduction of endogenous growth models. The idea of the fact that technology is and must be incorporated as anendogenous variable in growth models was also recognized by the economists like Marx and Schumpeter.

Exogenous theories claimed that economies converge towards equal growth rates but endogenous theory expandedthe notion of capital to include human capital ad claimed that different countries diverge from each other depending uponthe level of human capital formation.

Q. 6. An economy with fixed exchange rate cannot maintain an independent monetary policy. Do you agreewith the above statement? Substantiate your answer with appropriate diagrams.

Ans. The major difference between domestic trade and international trade is that the former is undertaken within thegeographical boundaries of a country and therefore, only one currency is involved. But trade between countries typicallyinvolves exchange of one countrys currency for that of another. For example, if country A, say USA wishes to importsomething from country B, say India, payments are to be made in Indian rupee. For this, USA must earn Indian rupee orbuy the same from foreign exchange market. How many dollars are to be paid to purchase Indian rupee would depend onthe exchange rate of the two currencies? It has been explained in the previous chapter that a rise in the external value ofrupee is called appreciation while the fall in the external value of currency is called depreciation. Suppose, the exchangerate of Rupee-US dollar is Rs. 40/$, if it becomes Rs. 42/$, the value of rupee has depreciated while the value of dollar hasappreciated. On the other hand, if it becomes Rs. 38/$, the value of rupee has appreciated while the value of dollar hasdepreciated.

In a simple economy, the exchange rate is determined by the intersection of the demand for and supply of onecurrency for the other. As exchange rate is the value of one currency in terms of other currency, it is certain that when onecurrency appreciates, other depreciates. But when a country is trading with many other countries, which is more realistic,exchange rate between two currencies will also be affected by the changes in the value of other currencies. For example,if the exchange rate between US $ and Euro changes and India is trading with US as well as EU, then the exchange ratebetween Rupee and US $ will also be affected. NEER (Nominal Effective Exchange Rate) and REER (Real EffectiveExchange Rate) are two statistical indices which are used to analyze these changes.

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Exchange rate of a country is also influenced by the exchange rate policy regime of the government. Between flexibleand fixed exchange rate regime, there are midway paths also.

(a) Adjustable Peg System: It is an exchange rate system in which government maintains the par values for theexchange rates but explicitly mentions the circumstances when the par value of exchange rate can be changed.

(b) Managed Floating: It is an exchange rate system in which government does not fix exchange rate at a pre-determined par value but it seek to have a stabilizing influence on it.

The biggest limitation of flexible exchange rate regime is that in the flexible exchange rate regime, exchange ratesare highly volatile which increases uncertainties in international transactions. These uncertainties hinder the developmentagenda of a nation. Therefore, government makes an effort to bring about stability in exchange rate.

When a country follows fixed exchange rate regime, the government intervenes to ensure that exchange rate ismaintained at a fixed rate say Rs. 40/$. Suppose that the S is the supply curve and D1 and D2 are the demand curves fordollar. The exchange rate when supply is S and demand is D1 is Rs. 40/$. If demand for dollar increases and demand curveshifts to the right, new exchange rate will be determined at Rs. 45/$. In order to ensure that the exchange rate does not riseto Rs. 45/$, it must sell Q1Q2 dollars. And if demand for dollar decreases and demand curve shifts to the left, newexchange rate will be determined at Rs. 35/$. In order to ensure that the exchange rate does not fall to Rs. 35/$, it must buyQ1Q3 dollars.

Y

XO

Rs/

$

S

S

E2

D1

D1E0

E

Q Q1Qty of $ ('000)

Determination of Fixed Exchange Rate

r1

ro

D2

D2

Q2

It makes clear that if government wishes to maintain exchange rate at a fixed level, it must maintain fixed exchangereserves fro which it can buy or sell foreign exchange to maintain stability in exchange rates. To exemplify, if BOP is indeficit, it means demand for foreign currency > supply of foreign currency. It implies reserves will have to be sold tomaintain stability of exchange rate and therefore, the monetary authoritys foreign exchange reserves will reduce. On theother hand, if BOP is in surplus, it means demand for foreign currency < supply of foreign currency. It implies reserveswill have to be bought to maintain stability of exchange rate and therefore, the monetary authoritys foreign exchangereserves will increase.

Point to be remembered is that in flexible exchange rate regime, BOP surplus/deficit led to appreciation or depreciationof currency but in fixed exchange rate regime it leads to rise or fall in monetary authoritys foreign exchange reserves. Butany country has a limited amount of foreign exchange reserves. If the disequilibrium in deficit continues for a long time,monetary authority will not be able to maintain stability in exchange rate. In that case government will have to devaluatethe currency.

Q. 7. Write short notes on the following:(a) Rational ExpectationsAns. If we make following assumptions:(a) Primary role of economic theory is prediction of future values of variables of interest.(b) It is possible to choose amongst alternate theoretical models under any particular set of circumstances.These assumptions imply that an economic model must be capable of providing predictions in the form of quantitative

relationships between objectively measurable variables and these predictions could also be checked by using past data.It also implies that either the same relation between the variables has prevailed over two time periods or the difference

in time and space can be accounted for in quantitative terms within the model.

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It means that once a model is selected, it must provide objective quantitative predictions along with historical data onthe variables in the model. Econometric methods are used to derive this objective conditional probability distribution.

The Hypothesis of Rational Expectations: Keynes assumed expectations to be given and explicitly recognized thatany changes in policy variables or other independent variables will bring about changes in expectations. But the degreeand nature of change in expectations will depend on prevailing psychology of the economic agents which in turn isdependent on several socio-economic-political factors.

If we wish to use a model to get a probability distribution for dependent variables on objectively quantifiable variables,then it is incorrect to assume that expectations are an exogenous variable. It must be explained endogenously in themodel. If we assume economic agents to be rational, then they would try to maximize their utility functions subject toconstraints to their choices. So, they will make decisions on the basis of objective conditional probability distribution. Itis called hypothesis of rational expectations. It implies that subjective probability distribution that individual economicagents use will be consistent with the objective conditional probability distribution that will be given by the model.

In most economic models, it is assumed that the decisions of economic agents are dependent only on one or twoparameters of the subjective probability distribution and it is assumed that it is not dependent on entire distribution. Insuch a case, instead of assuming that the subjective probability distributions that economic agents have coincide with theobjective probability distribution implied by the model, it is sufficient to assume that the expectations of these distributionsare equal. The second one is known as weak version of the rational expectations hypothesis and the first is known asstrong version of rational expectations which assumes that the entire objective probability distribution is known. If weassume a world where there is no uncertainty and deterministic predictions are available then the rational expectationshypothesis implies that the expectations held by the economic agents in the model must coincide with the predictions ofthe model. it would imply perfect foresight for the economic agents.

(b) Search and Matching ModelAns. In this section, we shall elaborate on Howitt model of search and matching theory. Peter Howitt originally

developed the model as Business cycles with Costly Search and recruiting in the Quarterly Journal of Econometrics in1988. Our exposition is based on Blanchard and Fischer model given in 2000.Model Specifications

1. There are fixed number of competitive firms (say H) and homogenous workers say W). In each discrete time perioda fraction S, which has been called rate of separation of the employed is laid off and joins the unemployed pool. Firmswill hire new workers from this unemployed pool and not directly from other firms.

2. The marginal cost of hiring of each function keeps on increasing as it hires more workers and it implies that withincreased rate of hiring, firms might have to increase their intensity of search, accept a mismatch between workers andjobs etc. On the other hand, the marginal cost of hiring is a decreasing function of aggregate unemployment i.e. withhigher rate of aggregate unemployment marginal cost of hiring a worker is low and vice-versa.

3. A firm attains its equilibrium when marginal cost of hiring a worker is just equal to the marginal benefit of hiringa worker. Therefore, it is important to know the marginal benefit of hiring a labour. If we assume firm to be risk neutral,the marginal benefit to the firm from the worker can be determined by discounting the value of its marginal product. Twodiscounting factors are time and the probability that worker may leave the job after some interval.

4. Net marginal benefit is the difference between marginal cost of hiring a worker and the marginal benefit fromhiring the worker. Search and matching models assume that wages are not predetermined in labour market but are determinedby a continuous process of bargaining. If we assume that workers get no profits from unemployment nor they get anylosses from it, then marginal benefit will be equal to marginal value determined above. If we assume that the worker gets share of this surplus, rest will go the producer. Hence, the marginal benefit of hiring a worker to the firm will be:

xt

= (1 ). qt

5. Each firm chooses the rate of hiring ht by equating the marginal benefit of hiring a worker obtained in point 3 aboveand marginal cost of hiring a worker obtained in point 2 above.

Model Solution and the Equilibrium Rate of Unemployment: Given the above specifications, we can get marginalbenefit t and hiring rate ht as follows:

Let the employment in the firm is denoted by nt, then n

t = (1 ). n

t1 + ht. it is so because employment in period t isadjusted for the rate of separation and the rate of hiring. Let us assume that there are F identical firms in the economy thenunemployment rate will be given by:

ut

= 1 (F. nt)/N

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where N is referring t total number of workers in the economy. These four equations of r t, h

t, n

t and ut can be solved to

the equation characterizing the dynamics of the equilibrium unemployment rate.u

t = + {1 (F/G)

t }. U

t 1G is a parameter for the cost of hiring function which denotes that larger is the value of G, higher is the level of

difficulty in locating workers. Unemployment also depend on its own lagged value shown by . It also depends on thestate of technology because it affects marginal benefit from the worker t.

If we assume that marginal productivity of labour has a zero variance, then:u* = /{ +F/G.k}.

It clarifies that the larger is the separation rate , , and larger is the value of parameter G, the higher is the rate ofunemployment.

Optimality of the Equilibrium Unemploy-ment Rate: The equilibrium rate of unemployment obtained in aboveequation is not expected to be socially optimally. It can be explained by two reasons.

(a) Hiring decision of one firm affects the search cost and cost of hiring of other firms. In other words, hiring by onefirm imposes a cost on other firms. It is an externality that has not been taken into consideration. When a firmhires more workers, t increases the cost of hiring for other firms because marginal cost of hiring a worker is adecreasing function of aggregate unemployment. This effect leads to too much hiring compared to the socialoptimum.

(b) There is also divergent between the social and the private benefit of hiring. Social benefit of hiring a worker isgiven by q

t, but the private benefit to the hiring firm is given by (1 ) of q

t which depends on the bargaining

power of worker and firms.The above two effects are working in opposite direction and the former is tending to keep it above socially optimum

and the latter is trying to keep it below socially optimum. Therefore, there is ambiguity in the model whether equilibriumrate of unemployment will lie above or below or exactly at socially optimum level of unemployment.

Dynamics of Unemployment and Real Wages through Productivity Shocks: It is a real business cycle kind ofmodel which reacts to shocks to productivity. This model has following implications to employment and wages:

(a) A temporary negative shock to productivity decreases marginal productivity of labour and hence the marginalbenefit of hiring him and hence decreases hiring and increases unemployment. Since the shock is temporary, theunemployment rate returns to normal through increased hiring. Moreover, since it is cheaper for firms to hirewhen there are more unemployed, a productivity shock has higher effect when unemployment rate is high thanthe situation when it is low.

(b) The model explains why fluctuations in employment may be related to minor fluctuations in real wage rate. Realwage are varying in the model with productivity and higher rates of hiring. Therefore, the model explains theobserved empirical fact of a pro-cyclical increase in real wages, but to a smaller extent than the increase inemployment, if the share received by the workers is small in relation to that obtained by the hiring firms.

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