A COURSE IN MACROECONOMICS: Joakim Persson, fall 2010.Topics: 1. INTRODUCTION. Plots over Swedish Macro series.2. NATIONAL INCOME ACCOUNTING IMain lesson: The production of a country is roughly the income of its citizensFLEXIBLE PRICE MACROECONOMICS:3. THE PRODUCTION FUNCTION AND FACTOR MARKETSMain lesson: A higher capital-to-labor ratio (K/L) increases the real wage and decreases the return on capital4. THE LABOR MARKET5. NATIONAL INCOME ACCOUNTING II: National Saving, Domestic Investment, Trade Balance and the Current Account6. ANALYSIS OF THE ECONOMY IN THE LONG RUN:The capital stock (K) is flexible: Flexible Prices leads to full employment of physical capital (K) and labor (L).

A. Growth accountingB. The Solow growth model

Output is determined by the amount of inputs.Main lessons: Increased saving increases the capital-to-labor ratio (K/L) and thereby production per capita. Decreased population growth increases the capital-to-labor ratio (K/L) and thereby production per capita. Better technology increases production per capita.7. MONEY AND INFLATION IN THE LONG RUN.Main lesson: A high money growth leads to a high inflation rate, to a high nominal interest rate, and to a depreciating currency.8. THE CLASSICAL MODEL = The Keynesian model in the long run. Assumption: The levels of capital (K) and labor (L) are fixed. Prices are flexible which leads to full employment of K and labor input (L): Actual output = potential output.A. The closed economy: The interest rate is flexible. Main lesson: Increased government spending or lower net taxes (which implies a higher government budget deficit) increases the real interest rate and thereby lowers private investment to the same extent so that aggregate demand and output are unchanged.B. The small open economy with its own currency: The real interest rate is fixed. Main lesson: Increased government spending or lower net taxes increases the real exchange rate and thereby lowers net exports to the same extent so that aggregate demand and output are unchanged.9. Introduction to the Keynesian model in the short and the long run. Assumption: Capital is fixed (more or less): The amount of physical capital is assumed to be fixed but in a recession some of it may not be used. Lessons: 1. A higher aggregate demand (AD) stimulates output in the short run but not in the long run. 2. Higher nominal wages or temporary higher oil prices increases the price level and decreases output in the short run but have no effect in the long run.9.1. Keynesian model in the short run= Prices are fixed. The SRAS-curve is horizontal. Aggregate demand determines production.9.1.1. The simple Keynesian model for the closed economy without its own currency: The interest rate is fixed. The multiplier effect: Increased government spending by 1 dollar Increases output by more than a dollar. 9.1.2A. The closed economy with its own currency: The interest rate is flexible. Main lesson: Fiscal policy: Increased government spending or lower net taxes increases aggregate demand and output but increases the real interest rate and thereby lowers private

investment. Monetary policy: A higher money supply decreases the interest rate and thereby private investment, aggregate demand and output.9.1.2B. The small open economy with its own currency. The interest rate is fixed but the exchange rate is flexible. Main lesson: Fiscal policy is less effective in a small open economy. Increased government spending or lower net taxes increases momentarily aggregate demand and output, which momentarily increases the interest rate which leads to an appreciation of the real exchange rate and to lower net exports. There is no net effect on output. A higher money supply decreases momentarily the interest rate which decreases the demand for the currency which lowers the real exchange rate and thereby increases net exports, aggregate demand and output.9.2.Keynesian model in the short and long run when the SRAS-curve has a positive slope. Aggregate demand and supply jointly determines output in the short run. The AD-curve is consistent with equilibria in the goods and money market.Main lesson: Fiscal and monetary policy increases aggregate demand, which leads to a higher price level and to a higher level of production in the short run because A higher price level decreases the real wage which leads To increased employment. In the long run the real wage is restored so that the employment level reverts to the full employment level.9.3. The Phillips-curve is the SRAS-curve in percentage terms. Main lesson: A given level of expected inflation, fiscal and monetary policy may lower unemployment in the short run at the expense of a higher rate of inflation. Higher rate of inflation decreases real wages and thereby Increases employment and production.10. Stabilization policies. Main lesson: It is difficult for the government to pursue stabilization policies in order to dampen business cycle fluctuations. Exercise: Debate of pros and cons of active stab policiesFLEXIBLE PRICE MACROECONOMICS:11. CONSUMPTION.Main lesson: Expected future income may impact current Consumption.12. GOVERNMENT DEBTMain lesson: A budget deficit may imply higher taxes in thefuture which may lower private consumption today.13 The life-cycle model: A mathematical example.

MACROECONOMICS: STUDIES THE ECONOMY AS A WHOLE Questions studied:Why are some countries growing faster than others?Why is there unemployment? Why inflation? Why is the interest rate high?Why are there recessions and booms?Recessions are periods in which aggregate production falls mildly-- and depressions are periods when aggregate production falls more severely. Booms are periods when aggregate production increases rapidly.

INTRODUCTION: EXOGENOUS AND ENDOGENOUS VARIABLES

The basic demand and supply diagram for pizza.Demand: Supply:

Which variables are exogenous variables and which variables are endogenous variables. Endogenous variables are the variables whose values are determined within the model.

Holding constant the exogenous variables, what will the price of a pizza be in equilibrium? Assume: Income=2, and wage=1.5.

What happens when income increases to 4?Show in diagram, and calculate the new equilibrium price and quantity.

Can the actual price be above or below the equilibrium price? Are prices sticky? In other words, does price adjustment take some time?

Economists use models to understand what goes on in the economy.Here are two important points about models: endogenous variables and exogenous variables. Endogenous variables are those which the model tries to explain. Exogenous variables are those variables that a model takes as given. In short, endogenous are variables within a model, and exogenous are the variables outside the model.

PricePrice

DemandDemand

QQ*

PP

SupplySupply

QuantityQuantity

*This is the most famous

economic model. It describes the ubiquitous relationship

between buyers and sellers in the market. The point of intersection is called an

equilibrium.

NATIONAL INCOME ACCOUNTING I (NATIONALRÄKENSKAPER)MEASURING PRODUCTION AND INCOME Gross domestic product (GDP) is the market value of all final goods and services produced within an economy during a year.In Swedish: Bruttonationalprodukt (BNP) till marknadspris

GDP can be measured in 3 ways:Method 1. through expenditures on final goods and services.Method 2. through income (wages and capital income).Method 3. through production. GDP is calculated by adding up value added in all sectors of production. Value added = total revenue – expenditures on inputs other than capital and labor. These inputs are intermediate goods (insatsvaror). Value added = förädlingsvärde

In an economy without a government sector and without international trade (Exports=imports=0).

HOUSEHOLDS supply the factors of production (capital and labor) to FIRMS which use these factors of production to produce final goods and services that are sold to the HOUSEHOLDS.

Method 1 is to measure GDP from expenditures on goods, method 2 is to measure GDP from income.Households supply the factors of production (capital and labor) to the firms. In other words, the households own the firms. Firms use factors of production to produce final goods and services that are sold to the households.The households’ expenditures on final goods and services equals factor incomes (wages, interest, profit) from the firms in this economy.Example of method 3; that is, measuring GDP by adding up value added in the different sectors of production. Assume one final good in the economy, bread:

There are 2 ways of viewing GDP

Total income of everyone in the economy

Total expenditure on the economy’s output of goods and services

There are 2 ways of viewing GDP

Total income of everyone in the economy

Total expenditure on the economy’s output of goods and services

Households Firms

Income $

Labor

Goods

Expenditure $

Households Firms

Income $Income $

LaborLabor

GoodsGoods

Expenditure $Expenditure $

For the economy as a whole, income must equal expenditure. GDP measures the flow of dollars in this economy.

Income, Expenditure And the Circular FlowIncome, Expenditure And the Circular Flow

Sector: Total revenue=P*Y

Försäljningsvärde

Cost of inputsOther than KAnd LKostnad för insatsvaror

Value Added.Förädlings-värde

Capital andLabor income

Peasant: Wheat 100 0 100 100Miller: flour 150 100 50 50Baker: bread 200 150 50 50Sum: 200 200Method: 1 3 2

Comparing GDP over timeNominal and real GDP: GDP in current and constant pricesIn Swedish: BNP till marknadspris i löpande och fasta priser.

The value of final goods and services measured at current prices is called nominal GDP. It can change over time either because more goods and services are produced or because there is a change in the prices of these goods and services. We calculate real GDP to see whether the country is producing more or less goods and services over time.

Compute GDP in current prices (BNP till marknadspris i löpande priser) according to method 1. Assume two goods in the economy:

Nominal GDP in 2000:

Real GDP 2000 (in 2000 year prices) = nominal GDP 2000.Real GDP 2001 (in 2000 year prices) =

If real GDP 2001 > real GDP 2000, then the economy produced more goods and services in 2001.

Often in news papers and statistical reports you get data on GDP in current prices and data on a price index. How do we calculate GDP in constant prices?Real GDP in 2005 (in 2000 year prices) = nominal GDP in 2005/ price index in 2005Year Nominal GDP=

GDP in currentPrices: P*Y

Price index =GDP-deflator: P

Real GDPin 2000 year prices: (P*Y)/P=Y

2000 2500 billion kr 1.00 25002001 2600 billion kr 1.02 2600/1.02=25492002 2700 billion kr 1.04 2700/1.04=25962003 2800 1.07 2800/1.07=26162004 2900 1.10 2900/1.10=26362005 3000 1.12 3000/1.12=26782006 3100 1.14 3100/1.14=2719Note that Q can not be observed as there are many goods in the economy.Nominal GDP increases by (3100-2500)/2500=0.24; that is by 24 percent

The price level increases by (1.14-1)/1=0.14; that is by 14 percent between 2000 and 2006.

The real GDP increases by (2719-2500)/2500=0.088; that is, by 8.8 percent.

Real GDP (Y) = Nominal GDP (P*Y)/Price level (P)

Calculating the growth rate of real GDP using an approximate formula:

1.2 percent difference between the exact and the approximate formula.

Real wage = nominal wage / price levelIf the nominal wage in percentage terms increases more than the price level increases, then the real wage increases, which means that you can buy moregoods and services: your purchasing power increases.

More rules for computing GDP:2) used goods are not includes in the calculation of GDP.3) If newly produced final goods is stored, it is inventory investment which is part of private investment. When the goods are finally sold, they are considered used goods.4) Some goods are not sold in the market place and do therefore not have market prices. We must use their imputed value as an estimate of their value.For example, home ownership and government services.

Price indexes provide an overall measure of the price level in the economy. We have to choose a base year. CPI = Consumer price index.In Swedish: KPI = konsumentprisindex

Assume CPI (2000) = 100. Assume 2 goods in the economy:

When we use the original basket of consumption to calculate the price index, it is a Laspereys index. If CPI (2001) > CPI (2000) then the overall price level has increased.

Alternatively:

When we use the current basket of consumption to calculate the price index, it is a Paasche index.

CPI versus the GDP deflator (BNP deflatorn)The GDP deflator measures the development of the prices of all goods and services produced. The CPI measures the development of prices only of the goods and services bought by consumers, including imported goods.

GDP-deflator (2001) = Nom. GPD in 2001/real GDP in 2001 in 2000 year prices

The GDP-deflator is a Paasche index.In macroeconomic models real GDP is denoted by Y (instead by Q that is used for quantity in microeconomics) and the price level is denoted by P.

Measuring GDP through expenditures on final goods and services (method 1) in the real world: that is, with a public sector and internatinal trade.

Availability of newly produced goodsAnd services

Use of newly produced goods and services

GDP = 3000 billions kronor Private consumption = 1500Imports = 1500 billions kronor Private investment = 400

Public consumption = 700Public investment =300Exports = 1600

Sum: 4500 billions kronor Sum: 4500

In Swedish: FÖRSÖRJNINGSBALANSTillgång på nyproducerade varor ochtjänsterr

Användning

BNP = 3000 miljarder kronor Privat konsumtion = 1500Import = 1500 miljarder kronor Privata investeringar = 400

Offentlig konsumtion = 700Offentliga investeringar =300Export = 1600

Summa: 4500 billions kronor Summa: 4500

In other words, GDP+imports = private consumption+private investment +Public consumption and public investment + exports

Rearranging:

GDP = private consumption+private investment +Public consumption and public investment + exports - imports

Expressing this NATIONAL INCOME IDENTITY in real terms (in constant prices):

Real GDP (Y) = real private consumption (C)+real private investment (I) +Real Public consumption (GC) and public investment (GI) + exports – imports (NX)

Thus, Real GDP (Y) = C+ I+ G+NXWhere G = GC+ GI. Note that P*Y= GDP in current prices.C = real expenditures of households on final goods and services. Goods are sometimes categorized into nondurable and durable goods.I = real expenditures on new machines, new buildings, and inventory build-up by firms. I is gross private investment.

G: real government spending on (/purchases of) final goods and services. Often (but not in the Mankiw textbook) G is split up into government consumption (GC) and government investment (GI).Examples of GC are expenditures on teachers’ and doctors’ salaries.Examples of GI is expenditures on new roads and government buildings.

Note: Government transfers to households such as unemployment benefits etc. are not included in G: Total government expenditures = G + government transfers to households (unemployments benefits, transfers to poor, to kids, to retired people) and to firms.

NX = real net exports = trade balance = value of exports of final goods and services – value of imports of final goods and services. Thus, NX is net expenditure from abroad on our goods and services.

Note: Capital stock this year = capital stock last year + I – depreciation (= reduction of the value of the capital stock). Net investment = I – depreciation.

One way to think about real variables. Assume that only one good is produced in the economy; e.g. corn. Then production, Y, is measured in tonnes of corn. Some of this corn is used for private consumption (C), some for private investment (it is planted in the ground to yield production next year) (I), some for government consumption and investment (G), and some of the production is shipped abroad (Export) and some corn is imported (Imports).(NX=exports-imports).Ex.: Y=C+I+G+NX: 100 = 50 + 20 + 20 + 10

One aim of this section is to show that GDP is roughly the income a country’s citizens.

Other measures of income:Gross national product (GNP) = GDP – (wages and capital income of Swedish workers and firms operating abroad – wages and capital income of foreign workers and firms operating in Sweden).By Swedish worker I mean a Swedish resident.

Gross National Product (GNP) = GDP + net factor income from abroad (NFI)In Swedish: Bruttonationalinkomsten till marknadspris (BNI) = Bruttonationalprodukten till marknadspris (BNP) + faktorinkomster från utlandet, netto (NFI).

GNP counts all final output produced by domestically owned inputs (workers and capital), no matter where those inputs are situated in the world.GDP counts all final output produced within the country regardless of who owns the inputs (foreign or domestic citizens) involved.

GNP is a income measure whereas GDP is a production measure.In a closed economy: GNP = GDPIn Stockholm: GDP > GNP as many workers compute to Stockholm but live in other regions e.g. Uppsala. That is, they contribute to GDP in Stockholm but their incomes are not part of the Stockholm GNP. GNP (Stockholm) = GDP (Stockholm) – wages of workers that live in other regions than Stockholm.

Another concept is disposable GNP (DGNP) DGNP = GNP + (transfers from foreign countries – transfers to foreign countries) = GNP + net transfers from abroad (NFTr).For Sweden: DGNP < GNP as net transfers from abroad are negative. From now on we assume that net transfers from abroad = 0.In Swedish: Disponibel bruttonationalinkomst (DBNI) = bruttonationalprodukt till marknadspris (BNP) + faktorinkomster från utlandet, netto (NFI) + transfereringar från utlandet, netto (NFTr).

Other income measures continued:Net national product (NNP) = GNP – value of depreciation of capitalIn Swedish: Nettonationalinkomst till marknadspris (NNI) = Bruttonationalinkomst till marknadspris (BNI) – kapitalförslitningNet national product (NNP) = indirect taxes (e.g., value added tax) + compensation to employees (70 %) + capital income before tax (30%).Note: compensation to employees (workers) is total labor cost = income before tax of employees + social insurance contributions. Disposable Personal Income = NNP – taxes (indirect and direct) - social security contributions) + government transfers to individualsIn Swedish: Hushållens disponibla inkomst

Summary: Gross National Product (GNP) = Gross Domestic Product (GDP) + net factor income from abroad (NFI)Net National Product (NNP) = GNP – depreciation of physical capital. NNP = taxes (indirect + direct + social security contributions) + labor- and capital income net of tax. Dispsable Personal Income = NNP – taxes (including social security contributions) + transfers to households = Labor- and capital income net of tax + transfers to households.

In Swedish:Bruttonationalinkomst till marknadspris (BNI) = Bruttonationalprodukt (BNP) + faktorinkomster från utlandet, netto.Nettonationalinkomst till marknadspris (NNP) = BNI – kapitalförslitning =indirekta skatter (t ex moms) + arbetsinkomster inklusive direkta skatter på arbete och arbetsgivaravgifter + kapitalinkomster före skatt.Hushållens disponibla inkomst = nettonationalinkomst till marknadspris – indirekta skatter -direkta skatter på arbete och kapital – arbetsgivaravgifter + transfereringar till hushållen (barnbidrag, studiebidrag, A-kassa) = arbets- och kapitalinkomster efter skatt + transfereringar.

Simplifying assumptions in Classical and Keynesian models:The basic identity in national income accounting: Y = C+I+G+NXAssume that Net Foreign Income (NFI) =net transfers from abroad (NFTr)=0Then Y=GDP=GNP. GNP is the income used by government (T) and households, Y-T, which is household disposable income. (Households earn both labor and capital income.)Thus, T + (Y-T) = Y = C+I+G+NX.T = net taxes = tax payments (indirect and direct taxes plus social security contributions) – transfers to households and firms.

Households use their real income, Y-T, to real private consumption (C) and to real saving, Y-T-C:(T+C+Sp=T+C+(Y-T-C)=Y=C+I+G+NX. Note: Sp=private real saving=Y-T-C. Subract by T+C:Sp = Y-T-C=I+(G-T)+NX. Sp+(T-G)=I+NX. Note: T-G is government financial saving. Or:Sp+(T-GC)=(I+GI)+NXThus, private real saving + gov real saving = domestic inv. + trade balance

Comparing standard of living across countries/regionsWho has a higher material standard; that is, is richer in terms of goods and services they can consume?

2 methods to compare GDP across countries: 1. The Exchange Rate Method uses the current exchange rate to convert GDP in domestic currency to GDP expressed in dollars:Formula for calculating GDP from spending when assuming 2 goods in the economy: GDP (kr) = Pnt(kr)*Qnt + Pt(kr)*Qt Pnt = price of the non-tradable good, e.g. hair-cuts, housing services, etc Qnt = quantity of the non-tradable good, Pt= price tradable good, Qt=quantity of the tradable goodGDP in dollars:GDP ($) = e ($/kronor)*GDP(kr) = e ($/kronor)*Pnt(kr)*Qnt + e ($/kronor)*Pt(kr)*Qt

e ($/kronor) is the nominal exchange rate: In 2007: e ($/kronor) =1/6.

1. Purchasing Power Parity Method controls for the fact that prices differ across countries. The method replaces domestic prices with average prices across countries (in $).

GDP in dollars according to the PPP-method:GDP ($) = e ($/kronor)*GDP(kr) = Average Pnt ($)*Qnt + Average Pt ($)*Qt

We want to use the same prices because we want our measure of income to reflect the quantity of goods that are available in one country during a year. Using different prices for different countries distorts the picture.

If the law of one price holds for tradable goods, thenaverage Pt ($) = e ($/kronor)*Pt(kr)

That is, the law of one price says that the price of a tradable good expressed in the same currency should be the same in all countries. We expect to hold if transportation costs and differences in VAT are zero across countries. Assuming zero transportation costs and no country-differences in VAT, arbitrage tends to equalize prices across countries: It is profitable to buy the good where the price is low, and ship it to the country where the price is high. Higher demand in the country in which the price was initially low tends to put an upward pressure on the price in this country, and a higher supply in the country where the price was initially high tends to put a downward pressure on the price in this country. Thus, the market mechanism tends to equalize prices across countries for tradable goods.The law of one price does not hold for non-tradable goods and services:In a poor country, the price of a non-tradable good tends to be lower because of lower labor costs than in a richer country.Ex: e($/Etiopian currency)* Pnt(Etiopia) < Average Pnt($) PPP-adjusted GDP ($) for Etiopia > Not PPP-adjusted GDP ($) for Etiopia= GDP ($) according to the exchange rate method.Thus, the exchange rate method understates GDP ($) in poor countries.Because domestic prices (in $) are lower in poor countries. In news reports you hear that in this country they earn 400 per capita and year. I have often thought: How can they survive? The explanation is that this income figure is not PPP-adjusted.

Purchasing Power Parity means that prices expressed in the same currency are the same across countries and regions. PPP does empirically not hold as prices on non-tradable goods tend to be lower in poor countries.

Application on Regions within a country: If nominal income per capita in the Stockholm region is twice as high as the nominal income per capita in the Karlstad region, the purchasing power of income per capita in the Stockholm region might be less than twice as high due to a higher price level; e.g. on non-tradable goods and services such as housing.

The BIG MAC INDEX:The law of one price implies: e($/kronor) P(kronor) = P*(dollars)

If e($/kronor) P(kronor) > P*(dollars)

Then the Swedish currency is too strong; “ overvalued” according to the journal Economist.Critique: The law of one price should not hold for Big Mac as it is not a tradable good.

AGGREGATE SUPPLY: FACTOR MARKETS: CAPITAL AND LABOR MARKETSAssume an aggregate production of Cobb-Douglas type:

, where 0 < < 1. Ex.: , easy to calculate with…

If there is one good in the economy, then Y is the quantity of this good.In kilograms, or liters depending on what the good is.

K = aggregate physical capital (machines and buildings)Should be measured by machine-hours and by hours buildings are used per year. But in reality K is measured by the real dollar value of the aggregate physical capital. It is then implicitly assumed that the real dollar value of K is proportional to the number of machine hours and hours buildings are used.L = aggregate labor input is measured by total hours worked (or by number of workers if every worker works the same number of hours). A = totalfactorproductivity, captures the effect on Y of all factors apart from K and L that impacts Y. For example, technological progress (innovations) or increased education of workers increases Y at given levels of K and L. Higher energy prices should decrease the use of energy and thereby also A and Y at given levels of K and L. Empirically is estimated to be around 1/3, which is the typical value of the share of capital income of national income.

The aggregate production function:Assume that K and A are constant: A=1, K=9, and =0.5. L Y/L

0 0 01 3 3 32 4.2 4.2-3=1.2 4.2/2=2.13 5.2 1 5.2/3=1.75 6.7 (6.7-5.2)/2=0.75 6.7/5=1.348 8.5 (8.5-6.7)/3=0.6 8.5/8=1.1From the table we see that:When L increases, Y increases but at a diminishing rate; because the capital-labor ratio decreases when L increases. Each worker gets less capital to work with.*MPL and APL(=Y/L) falls when L increases and K and A are constant.MPL is below APL (=labor productivity).

Plotting the production function for A=1, K=9 and alpha = 0.5:

MPL is the slope of the production function.

If the stock of physical capital is higher: Parameters: A=1, K=16,

=0.5.A=1, K=16,

=0.5.A=1, K=16,

=0.5.L Y/L

0 01 4 4 42 5.6 1.6 5.6/2=2.83 6.9 1.3 6.9/3=2.35 8.9 1 8.9/5=1.88 11.3 0.8 11.3/8=1.4* MPL and APL increases when K (or A) increases and L is constant.This is shown by comparing the 2 tables above.

If A Y and MPL and APL at a given L (and K):Assume that A=1 and A=2 , K=9, and =0.5.

Summary:

MPL (= ) and Y/L decrease when L increases and K and A are constant.

MPL and Y/L increase when K (or A) increases and L is constant. By symmetry, the same holds for MPK and K: that is,

MPK (= ) and Y/K decrease when K increases and L and A are constant.

MPK and APK(=Y/K) increase when L (or A) increases and K is constant.

Review of exponents

Definition: . E.g. and

Rule 1: Ex.:

Rule 2: Ex.:

Rule 3: Ex.:

Rule 4: Ex.:

Or more generally,

Production per worker, Y/L, increases if technology improves (A) or if every worker gets more capital (K/L)

Deriving the mathematical expression for MPL:

Review of the derivative: (1) If then

(2) If where b is a constant then

(3) More generally, then

Thus, MPL = (1-alpha)*(Y/L). That is, MPL is always lower than Y/L

2. exhibits constant returns to scale.If you e.g. increase each factor of production by 10 percent, then production also increases by 10 percent.If production increases by more, increasing returns to scale (IRS), and if production increases by less, decreasing returns to scale (DRS). CRS imply constant long-run average costs, IRS imply decreasing long-run average costs and DRS imply increasing long-run average costs when production increases.

THE DEMAND OF K AND L IN THE LONG RUN BY FIRMSIn macro models households/individuals supply L and K (through saving as saving equals investment in a closed economy). Firms demand L and K.

Assumptions: There exist many identical firms that produce an identical good. Perfect competition is assumed The firms maximize profits.

The problem of the representative firm is to choose K and L and thereby output (Y) so that profits are maximized. Assuming two factors of production (K, L):

Profits ($) = Total revenue ($) – capital cost ($) – labor costs ($) Profits ($) = – –

where , P=price of the good, Y = quantity of the good, R= rental price of one unit of capital per period of time, W= nominal wage per worker per period of time.

Problem of the firm: Choose K and L (and thereby output) to maximize profits: Profits ($) = – –

Assuming perfect competition implies that the individual firm cannot influence prices: P, R and W are exogenous from the point of view of the firm. We also assume that A and are exogenous from the point of view of the firm as they are assumed to be given by the technology. To maximize profits, the firm should choose K and L so that:

and

or and

and

These 2 conditions should hold simultaneously:If we combine them we find the profit-maximizing firm’s capital-labor ratio, K/L, which is independent of the level of production. In other words, when assuming a Cobb-Douglas production function the optimal (=cost-minimizing) capital-labor ratio is identical for a low level and for a high level of Y.

Divide by W/P on both sides of the first condition:

Thus, a higher Wage relative to the Rental price of capital makes it optimal to use more capital relative to labor at a given level of production.

Determining Equilibrium Factor Prices: They are found where Supply = DemandAssume that the supply of K and L is fixed: ,

Thus, a higher capital labor ratio increases the equilbrium real wage relative to the equilibrium real rental rate. Example: Assume: , and A=1, = 0.5 , =9, =9:

Assume now that =16 due to labor immigration

Thus, If (due to labor immigration) and constant and W/P=MPL .

Domestic workers loose in terms of W/P from labor immigration, whereas domestic capital owners gain as .

2 other examples:(2) If (due to black death) and constant , W/P=MPL Workers gain and capital owners loose income.(3) If and constant and W/P Workers gain and capital owners loose.

Conclusion: w/p and if

The distribution of income (Y) between workers and capital-owners.Assume no government sector.

Assuming perfect competition in the rental market for capital: , where r=real return to capitalNote that: if : PY=GDP=GNP=NNP (net of taxes; that is, taxes are ignored.)If , PY=GDP=GNP= NNP + (depreciation)where = nominal capital income

Real Profits =

where = real capital income, W/P= real wageAssuming perfect competition in the goods market means that the profits are zero and that firms maximizes profits by choosing K and L so that W/P=MPL and

.

Thus, the share of GDP (net of taxes) that goes to capital owners is . The share of GDP (net of taxes) that goes to workers is 1- .We have data on labor and capital income. Thereby, we get an estimate of , which is around 1/3 for both developing and developed countries. Why?In poor (rich) countries: K is low (high), r is high (low), L is high (low) and W/P is low (high)

Real wage and labor productivity:

When perfect competition:

If the share of income (Y) that goes to workers: (1-alpha) is constant,

Then the real wage grows at the same rate that labor productivity, Y/L, grows.

Elaborating on the production functionA in the production function depends on business climate, tax levels, knowledge of workers, energy used, etc. If we particularly want to focus on energy used we might want to include this variable specifically in the production function:

, where 0 < , < 1 0<1- - <1.

Knowledge of the work force measured by educational levelIn the basic formulation of the pf: , where 0 < < 1, an increase of the knowledge of the workforce e.g. measured by the educational level increases A. In an alternative formulation:

, where 0 < , < 1 0<1- - <1.Where H = number of workers with higher education, L = number of workers with low education. With this formulation of the production function, A does not capture the knowledge or the educational level of the work force.

THE LABOR MARKET FROM A MACRO PERSPECTIVEIn macro models households/individuals supply L and K (through saving as saving equals investment in a closed economy). Firms demand L and K.

Assumptions: There exist many identical firms that produce an identical good. Perfect competition is assumed The firms maximize profits.

The problem of the representative firm is to choose K and L and thereby output (Y) so that profits are maximized. Assuming two factors of production (K, L):

Labor Demand in the short run (=when the capital stock, K, is fixed)The firms are assumed to be price-takers in output and input markets; that is, P (=product price), W (nominal wage per period of time), and R (rental price per unit of capital per period of time) are exogenous from the individual firms’ point of view; that is, an individual cannot impact P, W, and R. Assume also that the capital stock (K) is fixed; in other words, assume short-run analysis. The firm has to pay for a fixed factor of production regardless of its chosen level of production.

If the representative firm maximizes profits it should choose L (and thereby the level of production, Y) so that: P*MPL = W W/P = MPL

In the graphs above we assumed:, and if A=1, , and

The profit-maximizing level of employment, , is given by:

Solving for as a function of the exogenous variables:

If e.g. W/P=0.75, then =4.

In top figure above: where is Y/L-curve? The producer surplus in real terms (= real profits + real fixed costs = real profits + ) is the area between the MPL-curve and the real wage, W/P=0.75.

More generally:The problem of the representative firm is to choose L (and thereby Y) in order to maximize Profits ($) =

Where P = Product price, W = nominal wage, R= nominal rental price of capital, and

The profit-maximizing level of employment, , is given by:

This is the inverse demand curve for L.

Solving for : that is, deriving the demand curve for L:

If W/P ; If

Equilibrium in the labor market and taxes

If there is perfect competition, the equilibrium real wage is where labor demand = labor supply. See graph below.

Labor Supply: 3 possibilities:(1) Labor supply is unrelated to the real wage; vertical labor supply-curve. (2) Labor supply increases when the real wage increases; a positively sloped labor

supply-curve. (3) Labor supply decreases when the real wage increases: when the real wage increases

the individual can afford to take more leisure, which she likes. Factors that increase aggregate labor supply at a given real wage:1. Labor immigration. 2. Lower unemployment benefits should increase the labor supply of the domestic population at a given real wage.

Introducing labor taxes that creates a difference between the labor costs of the firms and what the worker receives:

Introducing a tax creates a wedge between what the firm pays (producer real wage) and what the worker receives (consumer real wage). A tax decreases employment. L decreases in figure from 5 to about 3.5. The producer real wage increases to 0.8 (from 0.7 when tax is zero) and the consumer real wage drops to below 0.4. Taxes on labor include social insurance- and income taxes.

The consumer real wage drops more than the producer real wage increases as the labor supply is more inelastic than labor demand in the figure above. The inelastic side of the market bears the most of the tax burden.

Flows on the labor marketThe average rate of unemployment around which the economy fluctuates is called the natural rate of unemployment.THE POPULATION Between 19-64 years are either employed (work or study) or unemployed or outside the labor force. The labor force is employed + unemployed. Also people below 19 or above 64 may work, but we ignore this.NOTE: This model is a simplification: some that get jobs or become unemployed are initially outside the labor force; they are students that finish school, or house-wife or husbands that return to the labor market after having raised kids.

(1) Labor force (L)=Employment (E)+number of unemployed (U)(2) Number of people finding jobs per period of time (f*U) = Number of people loosing jobs per period of time (s*E)

f = the job finding rate (e.g. 0.1), which tells us what proportion of the unemployed that finds jobs per period of time (e.g. 10 percent).s = the job separation rate (e.g. 0.05 = 5 percent) tells of what proportion of the employed that looses their jobs per period of time.

Solving for the natural rate of unemployment (U/L) as a function of the exogenous parameters(s,f): Insert equation (1) into (2): f*U=s*(L-U)Divide by 1/L: f*U/L=s*(L-U)/L f*U/L=s-s*U/L (f+s)*U/L=s U/L=s/(s+f)If f U/L; If s U/L . Plug in numbers see that this is true.But s and f tend to be positively correlated.Relative to old EU-countries, the US have a higher f and a higher s. A high f and a high s can theoretically yield the same natural unemployment rate as a low f and a low s. However, the natural unemployment rate is higher in the old EU-countries than in the USA. This model relates the long-run unemployment rate to job finding and to job separation rate. It does not explain why there is unemployment.

The reasons of unemployment are often divided into job search and too high real wages which lead to too few jobs.

The natural rate of unemployment = frictional and structural unemployment.The unemployment rate = the natural rate + cyclical unemployment.

Cyclical unemployment > 0 or < 0 or = 0.In a recessions cyclical unemployment is above 0. Also machines and factories are unemployed during a recession, which means that K used in production is less that the K that is available in the economy.The unemployment caused by the time it takes workers to search for a job is called frictional unemployment. Because changes in the composition of demand among industries or regions are always occurring, and because it takes time for workers to change sectors, there is always frictional unemployment. The fact that the European unemployment rate is higher than the unemployment rate in the USA is often explained by a more generous unemployment insurance: The replacement rate = Unemployment benefits/previous labor earnings.

3 reasons for structural unemployment:

1. Minimum wages.

2. Trade unions Unions and collective bargaining between unions and employer organizations may lead the actual real wage to be higher than the equilibrium real wage. Unions cares about the average union member who has a job.

3. Efficiency wages. Efficiency wage theories imply that firms voluntarily (that is, even in the case when unions do not exist) pay a higher real wage than they have to pay to attract workers (=equilibrium real wage). Why?Higher real wages than the equilibrium real wage may induce higher labor productivity (as workers value their job and do not want to loose it) and is therefore consistent with profit-maximization and perfect competition. Moreover, paying higher real wages than they have to attract workers is a way to lower labor turnover and a way to attract high quality workers. Labor turnover might be costly for the firms as it may be costly to recruit labor.

One main lesson: A higher real wage decreases labor demand;A larger stock of physical capital increases labor demand;decreased unemployment benefits increases labor supply at a given real wage.

Wage rigidity is the failure of wages to adjust until labor supply equals labor demand.

The unemployment resulting from wage rigidity and job rationing is called structural unemployment. Workers are unemployed not because they can’t find a job that best suits their skills, but rather, at the going wage, the supply of labor exceeds the demand. These workers are simply waiting for jobs to become available.

S

D

Labor

Real wage

UU

Rigidrealwage

If the real wage is stuck above theequilibrium level, then the supplyof labor exceeds the demand. Result: unemployment U.

Labor supply and unions in depthThe model assumes that the union organizes all workers, and it is also assumed that the union acts as a monopoly. The good it sells is labor. We also assume (to start with) that the union faces unorganized competitive firms that demand labor.

Review: Maximization of Total RevenueAssume a monopoly that faces a downward-sloping demand curve.Assume that the inverse demand-curve is: P=10-Q MR = 10 – Q*2

Total revenue, P*Q, is maximized along the Demand-curve at the quantity where MR=0. This occurs when

Optimal price: ,

The union faces the aggregate demand curve for labor. We assume that the firms are not organized into an employment organization that bargains over wages with the union. Firms are assumed to be perfectly competitive. The assumed problem of the union is to choose the point (real wage and the employment) on the aggregate demand curve for labor that maximizes labor income: real wage*employment.(An somewhat modified union objective would be to maximize labor income subject to the constraint that more employment implies that leisure are foregone. The cost of foregone leisure is reflected by the labor supply curve.)

In wage negotiations in Sweden there is an employer organization (who may act as an monopsonist) and a union.

OPTIONAL (=not necessary to read) Numerical Example: I The competitive outcome: Competitive firms and no union.Assume:Assume a perfectly competitive firm in the short run (=K is fixed):

Real profits=TR-TC

The profit-maximizing level of employment, , is given by:

MR( )=MC( ) In the competitive equilibrium:

,

II A union facing competitive demand for laborThe union wants to maximize (W/P)*L subject to the constraint that the union must choose a point on the (inverse) labor demand curve: Thus, the union chooses L (and thereby W/P) to maximize . The optimal labor supply is given by : ,

,

Labor income is higher and profits are lower relative to the competitive case (I). (Note: A competitive firm can make a profit in the short run.)

Exercise: Calculate the (structural) unemployment. That is, the number of people that would like to work when the real wage = 35 minus the actual employment.

III A single buyer of labor (monopsonist) facing unorganized workersA monoponist chooses the point on the labor supply curve that maximizes profits. The real wage the monopsonist has to pay is dependent on the number of workers it hires.The problem of the monopsonist is to choose L (and thereby Y) and W/P in order to maximize real profits: The constraint is that the monopsonist must choose a point on the (inverse) labor supply curve: Inserting the constraint into the profit function:

The profit-maximizing level of employment, , is found by the equation

.

Solving for : , the optimal real wage:W/P*L=5000,

=35000-12500-5000=17500. Highest profits and lowest labor income of the cases I-III.

Case II and III are depicted in figure above.The graphs are: 1.The inverse competitive demand curve for labor:W/P=70-0.1*L2. The marginal revenue curve associated to this demand curve:MR=70-0.2*L3. The inverse competitive labor supply curve: W/P=L/50

In wage negotiations between a monopsonist (an employer organization) and a union we expect an outcome somewhere in between case II and case III. Where exactly should depend on the relative strengths of these organizations.

Recall that unions in Europe are blamed for high unemployment.

GROWTH ACCOUNTING (TILLVÄXTBOKFÖRING)Mathematics: Percentage Changes in Economics.

Expressing levels into growth rates; that is, into percentage changes:

Rule 1. If y(t) = x(t)*z(t), then .

Ex.: Total Revenue (TR) = Price(P)*Quantity(Q) If P is raised by 10 % and sold quantity (Q) thereby decreases by 5%, then TR increases by 5 %.

Rule 2. If y(t) = x(t)/z(t), then .

Ex.: GNP per capita (y) = GNP(Y)/Population(Pop) If GNP (Y) increases by 5 % and the population increases by 3 % , then GNP per capita increases by 2 %.

Rule 3. If , then .

Rule 4. If ,

then

thus the growth rate of Y equals:(1) The growth rate of totalfactorproductivity.(2) The contribution of physical capital.(3) The contribution of labor.

Question addressed by so-called growth accounting (Mankiw, ch. 8, app.)growth accounting: How big share of the growth rate of the GDP can be attributed to changes in capital, to changes in the labor input and to changes in total factor productivity?

For developed countries we have good data on and ,

We have not direct data on as A captures the influence on Y of many different factors

on Y. E.g. taxes, climate for business, educational level of work force, infrastructure, social capital etc.Under perfect competion, , is the share of national income that is capital income, and (1-) is the share of national income that is labor income. We have data on labor income and national income. Thereby, we get an estimate of .

Example:Year Y A K L2005 100 ? 300 10002006 103 ? 306 1010

and

0.03 = + 0.3*0.02 + 0.7*0.01

= 0.03 – 0.006 – 0.007 = 0.017.

0.017/0.03 = 0.57 : 57 percent of the growth rate of Y can be attributed to an increase in A. 0.006/0.03 = 0.2: 20 percent can be attributed to an increase in K.0.007/0.03 = 0.23: 23 procent can be attributed to an increase in L.

We have not explained why K, L and A changes over time.We have only been engaged in accounting.The neoclassical growth model explains why K and thereby Y increase. (A and L are exogenously given in this model; that is, they are determined outside the model.)

The growth rate of output equals the growth rate of aggregate demand, which can be split up as follows:

NATIONAL INCOME ACCOUNTING II: National Saving, Domestic Investment, the trade balance and the current account balance.Swedish: Nationalräkenskaper II: Nationellt finansiellt sparande, inhemska investeringar, handelsbalansen och bytesbalansen.

Assume a closed economy: GNP = GDP = C + I + G“income measure” = “production measure” = C + G + I

S = GNP – C – G = I National saving (= income – (private consumption + government spending on goods and services)) = gross private investmentIn Swedish: Nationellt realt sparande.

Most often but not in the Mankiw textbook G is split up into GC and GI; that is, G = GC + GI.

GNP = C + I + GC + GI

S = GNP – C – GC = I + GI

National saving (= income – consumption (private and public)) = private and public gross investment.

From now on we use the definition of national saving by Mankiw.

Disaggregating national saving into private and public saving:Model assumption: T = net taxes (= government tax revenues – government transfer expenditures). Thus, although in the real world there are many taxes, we lump them all together. If T > 0, then government tax revenues > government transfer expenditures. This is typically the case in the real world as taxes apart from paying for transfers also pays for G.

GNP – T = private disposable income.

Often it is assumed that net taxes are positively related to income: T is procyclical; tax revenues increases and transfer expenditures decreases in a boom (when Y increases relative to potential GDP where the unemployment rate is at its natural rate). In a recession, when Y is below potential Y, tax revenues fall and transfer expenditures increases due to higher expenditures for the unemployed. The fact that net taxes tend to fall in a recession and rise in booms is an so-called automatic stabilizator of the market economy. Lower net taxes in a recession implies that disposable income fall less than income which may mean that private consumption which constitute half of aggregate demand fall less.It is often assumed Taxes = t*GDP, where t is a proportional tax rate, e.g. 0.4 (that is, 40 percent). With this formulation government tax revenues increase when GDP increases. In a recession tax revenues tend to decrease and transfer expenditures tend to increase (e.g. unemployment benefits), decreasing public saving. In a boom the opposite happens, tax revenues high and transfer expenditures low, increasing public saving.

S = GNP – C – G = I National Saving (S) = I

S = GNP – C – G + T – T = I

S = (GNP – T – C) + (T – G) = I

National Saving (S) = private saving + public financial saving = I

Public saving = government income (government tax revenues) - total government expenditures (= government transfer expenditures + government spending on final goods and services, GC+GI) = government budget surplusIn Swedish: Offentliga sektorns finansiella sparande =offentliga sektorns budgetöverskott.

The open economy: THE TRADE BALANCE AND THE CURRENT ACCOUNT

GDP (Y) = C + I + G + NX (=Exports – Imports)

NX = GDP – (C+I+G) = Domestic output – domestic spending/absorbtion

If domestic output exceeds domestic spending, exports are larger than imports. In other words, the trade balance, NX, is positive.In Swedish: NX = handelsbalans

National Saving and the current account balance: GNP = GDP + net factor income from abroad (NFI) = C + I + G + NX + NFI

S = GNP – C – G = I + NX + NFI

where NX + NFI = current account balance

national saving = private domestic investment + current account balanceIn Swedish: Nationellt realt sparande = inhemska privata investeringar + bytesbalansen.

The current account balance is often called net foreign investment. Saving is either invested domestically or abroad. Assume that NFI = 0, and NX>0. This means that the value of exports is bigger than the value of imports, which means that foreign countries become indebted towards us and that our foreign assets thereby are increased. Hence, the term net foreign investment is explained.

To be exact, one should also account for net transfers from abroad when calculating national saving:

GNP + net transfers from abroad (NFTr) = C + I + G + NX + NFI + NFTr

S = GNP + NFTr – C – G = I + NX + NFI + NFTr

where NX + NFI + NFTr = current account balance (net foreign investment)

national saving (S) = private domestic investment + current account balance

If NFI and NFTr are relatively stable over time, changes in national saving (S) and in domestic investment (I) are reflected in the trade balance (NX).If national saving exceeds private domestic investment, the current account is positive. As mentioned most often (but not in Mankiw) G is split up into GC and GI:

S = GNP + NFTr – C – GC = I + GI + NX + NFI + NFTr

national saving (S) = private and public domestic investment + current account balance (net foreign investment)

Back to Mankiw’s formulation and disaggregating national saving (S) into private and public saving: S = GNP + NFTr – C – G + T – T = I + NX + NFI + NFTr

(GNP + NFTr – T – C) + (T – G) = I + NX + NFI + NFTr

(private saving) + (public saving) = private domestic investment + current account balance (net foreign investment)

Application: “Twin Deficits”. A government budget deficit, G-T>0, generates a current account deficit if private saving and domestic private investment (I) are constant.E.g. if military spending increases due to the Iraqi war, G (T-G) NX if private saving, I, NFI, and NFTr are constant.

Summary:National Saving = GNP + NFTr – (C+G) = I + NX + NFI + NFTrwhere NX + NFI + NTr = current account balance

ECONOMIC GROWTHAim to explain why the standard of living (GDP/GNP per capita) changes over time. Main text: Mankiw, Ch. 7-8.Math: Growth rate = Percentage Change

, e.g. = 0.02, that is, 2 % .

where = income per capita year 0, = income per capita year 1.

= growth rate/percentage change between year 0 and year1.

Analogously: ,

At a constant yearly percentage change (growth rate) income year 3 is:

where r = constant yearly growth rate/percentage change.

After t years and a constant growth rate income per capita equals: , where t = number of years.

Exercise: If GDP per capita (in 1995 prices) in 1995 and in 2000 was 194 and 222 thousands, what is the average annual growth rate during this 5-year period?

Graphical representation of the exponential function: . Let and r = 0.03:

If r increases, steeper slope. If y0 increases, the curve shifts upwards.Students do not have to know logarithms:Alternative graphical representation of the function:

ln( ) = ln( ) ln( ) = ln( ) + ln( )

ln( ) = ln( ) +

This is the equation for a straight line: y = a + If r is a small number < 0.1

Formula: How many years does it take to double y at different growth rates?

ln(2) = ln( )

ln(2) = ln(2)/r t t ln(2)/r

If r = 0.05 t 14 years. If r = 0.015 t 46 years.

THE SOLOW GROWTH MODEL:Aim to explain the development over time of K and Y, k=K/L, and y=Y/L.

In the model the growth rate of the technological level, , and the growth rate of the numbers of workers, , are exogenous variables. In the model everyone is a worker. Thus, the number of workers = population.Thus, they are determined outside the model.

As , and are assumed to be exogenous variables, the model is about the accumulation of physical capital, and its effects on k, Y, and y.

To simplify we start by assuming: . Thus, the level of A and L are assumed to be constant over time.

Assumption (A1): The production function:, where 0 < < 1.

Expressing production in terms of per worker (labor productivity):

Labor productivity depends on:* Totalfaktorproductivity, A. If A Y/L * Physical capital per worker, K/L. If K/L Y/L

Note: (1- )* Labor productivity (Y/L) = MPL (= W/P)

Thus, the level of A and L are assumed to be constant over time.As L is assumed to be constant we can assume L=1. Small letters indicate that variables are expressed in terms of per worker.

In figure: A=1,2, and =0.5 .

Slope of the curve above is MPK=dY/dK.Note: L is assumed to be a constant; for example, L=1 K=k

More complicated proof which is optional:

[ , which is MPK:

MPK= ]

Assumption (A2): A constant share of income is saved (= a constant share of production is invested).

Goods market equilibrium condition: We assume a closed economy without a government sector: G=NX=0 S=Y-C=I National saving equals gross investment.

It is easy to augment the model so it includes a government sector as well as exports and imports we do this on the C-level.

(A2): , where s is the share of income that is saved.

Note1: Y=GDP=GNPNote2: s is not saving per worker even though s is a small letter.

Moreover,

In figure: s=0.3, A=1, and =0.5. The vertical distance between the curves for production per worker, and investment per worker is consumption per worker. Assumption (A3): where is net investment, I = gross investment, and = depreciation of capital per period. is the depreciation rate, which is between 0 and 1; e.g. 0.05. (That is, 5 %). If

, then If , then ; If , then .Expressing (A3) in terms of per worker:

Derivation optional:[

Using k = K/L , where =0 by assumption.

]

In figure:

The whole model:(A1): , the production function(A2): investment = saving (equilibrium condition) where saving is constant share of income.(A3): , The time path of the capital stock per worker

A-level students need not know mathematical derivation below:The whole model can be reduced to one equation:Inserting (A1) and (A2) into (A3):

The long-run equilibrium (steady state) value for k, , occurs when .That is, when gross investment equals depreciation

Solving for k in equilibrium:

What is the long-run equilibrium value of y, ?

If s or A and .

If the economy is not in its equilibrium, it converges over time towards the equilibrium because if k< , then i> , and if k> , then i< . See figure below.Showing the equilibrium in the Solow diagram:

In figure: A=1, s=0.3, , and =0.5.

The transition to equilibrium: a numerical exampleStarting below the equilibrium: The initial value of k: k(year=1)=4.00. Assume also: A=1, s=0.3, , and =0.5.year k

1 4.00 2.00 1.4 0.6 0.4 0.2 0.049 0.05 0.02452 4.2 2.049 1.435 0.615 0.420 0.195 0.047 0.046 0.02293 4.395 2.096 1.467 0.629 0.440 0.189 0.045 0.043 0.0214 4.584 2.141 1.499 0.642 0.458 0.184 0.043 0.040 0.0205 4.768 2.184 1.529 0.655 0.477 0.178…

9 3 2.1 0.9 0.9 0 0 0 0The equilibrium values of k and y are calculated by using the formulas:

,

How to fill out the Table based on an initial value and assumed parameter values: A=1, s=0.3, , and =0.5.Start by filling out the column for k based on the formula:

If k(year=1)=4, A=1, s=0.3, , and =0.5.

, , etc.After the values of k has been filled out, all other values of other variables (columns) can be calculated.

Graphical description of transition to equilibrium when economy start below and above the equilibrium ln( )=1.1:(1) k(t=1)=4, y (t=1)=2 , and ln(y (t=1)=2)=0.69 (2) k(t=1)=14, y (t=1)=3.74 , and ln(y (t=1)=2)=1.32

According to model:The growth rates of k and y are higher the lower k and y are. This explains why the slope of the curves for lny becomes flatter and flatter when lny approaches its equilibrium. Recall that the slope of lny is the growth rate of y. If two economies share the same equilibrium; that is, have the same parameter values on A, s (as well as on and ) but differ with respect to initial values, then the economy with lower k and y experience higher growth rates of k and y than the economy with higher k and y. the model says that y (and k) of these two economies converge over time. In other words, the model says that y over time converge across economies if the economies share the same equilibrium value of y).

Main lesson of empirical work on growth:Real per capita income tends over time to converge across economies, which are similar with respect to “institutions”.An economy with an initially relatively low real income per capita has on average a higher growth rate of real income per capita than an economy with an initially relatively high real income per capita if “institutions” are similar. Ex.: EU-countries and regions within countries.

Evidence from the OECD-countries (the currently rich countries)

Sample includes: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Greece, Iceland, Ireland, Italy, Japan, Netherlands, New Zealand, Norway Portugal, Spain, Sweden, Switzerland, United Kingdom and USA.

Initially poor countries grow faster in terms of real GDP per capita during the period 1960-2000 than initially rich countries. The correlation between the average annual growth rate of real GDP per capita between 1960 and 2000 and real GDP per capita in 1960 = - 0.89

Evidence from the 24 Swedish Regions, 1911-1993

Regions that were relatively poor in terms of real income per capita in 1911, on average had a higher growth rate of real income per capita.Higher growth rates in poor regions caused relative differences in real per capita income to diminish across the Swedish Regions between 1

911 and 1993.

The dispersion is lower for real per capita income when it is adjusted for regional differences in cost of living as counties with high unadjusted real per capita incomes tend to have cost of

living.

Per capita Income adjusted and unadjusted for cost of living

Värmland moves to top category of per capita income when regional differences in cost of living are accounted for in 1993

Per capita income (p.c.i) is in 1980 prices

The empirical evidence on convergence in real per capita income across the Swedish regions is consistent with the predications of the textbook model:Low real per capita income

Little capital (physical + human) per worker,low wages, high rates of return to capital capital per worker production per worker income per capita Also factor mobility tends to contribute to convergence:Low wages and high returns to capital out-migration, and foreign investment capital per worker production per worker

Evidence from the countries of the world

Sample includes 80 countries.

No convergence in real GDP per capita across the countries of the world. The correlation between the average annual growth rate of real GDP per capita between 1960 and 2000 and real GDP per capita in 1960 = + 0.14.

Is lack of convergence in GDP per capita for the countries of the world, evidence against the model? NO!

The model says that if countries have the same equilibrium, the poorer country should grow faster in terms of y and k than the country that is richer in terms of y and k.

But if countries differ with respect to equilibrium, that is, with respect to values on A, s (as well as on and ), the poorer economy need, according to model, not grow faster than the initially richer economy.Africa is poor because it has a low equilibrium.Example that a rich country can grow faster than a poor countryCountry A (Poor Country): A=1, s=0.2, , and =0.5 : ,Assumed initial values of k and y: 4 and 2. Country A’s growth rate of y=0

Country B (Rich Country): A=1, s=0.3, , and =0.5 : ,Assumed initial values of k and y: 5 and 2.24.

Country B’s growth rate of y is positive.

The short and long run effects of an increase of L (e.g. due to immigration)

A one-time increase of L:L(t=0)<L(t=1)= L(t=2)= L(t=3)= L(t=4) At time 1: K/L and Y/L, At time 2 and onwards: K/L and Y/L If the economy initially is in its equilibrium, it will over time revert to the initial equilibrium as gross investment exceeds depreciation of capital.

In figure: A=1, s=0.3, , and =0.5, K(0)=900, L(0)=100 and L(1)=200.The long run values of k and y are unchanged. However, adjustment takes a long time so migration plays a role for y during a long time according to model.What happens to the long run values of Y and K?

Size of economy increases when L increases.Example: increases from 3*100= 300 to 3*200=600, and increases from 9*100=900 to 9*200=1800.

In case of a pandemic, L decreases, the results are the opposite.

The effect of an increase in A

Old value: A=1, s=0.3, , and =0.5 and .New value: A=1.5 ,

The transition to the new long run equilibrium

Long-run growth of the number of workersBefore we assumed: L(0)=L(1)=L(2)=L(3)Now we assume : where n is the constant growth rate of the number of workers; e.g. 0.01.

Assumption A4. L(0)<L(1)<L(2)<L(3)

To keep k constant gross investment (I) now needs to compensate not only for depreciation of capital to keep k constant but also for the fact that the number of workers increases over time:(A3):

Derivation below optional:

[

Using k = K/L , where by assumption.

]

The whole model:(A1): , the production function(A2): investment = saving (equilibrium condition) where saving is constant share of income.(A3)+(A4): , The time path of the capital stock per worker

A-level students need not know mathematical derivation below:The whole model can be reduced to one equation:Inserting (A1) and (A2) into (A3)+(A4):

The long-run equilibrium

The long-run equilibrium (steady state) value for k, , occurs when .That is, when gross investment equals “depreciation”

Solving for k in equilibrium:

What is the long-run equilibrium value of y, ?

If n and .

The transition to the equilibriumIf the economy initially is in equilibrium and n the economy moves over time to the new lower equilibrium because when i< k:

In figure: A=1, s=0.3, , =0.5 and n=0 and 0.05.(1) when n=0 and .(2) when n=0.05 and .

The growth rates of aggregate variables:

In the steady-state:

Factor prices: In the model: C + I = Y = capital income + labor income= MPL*L+MPK*K= (W/P)*L + (r+ )Kr= real return on physical capital.Note: There is only one good in the Solow model, which is consumed or invested. If it is invested it is an asset which yields a return. K is the only asset in the economy. There exist no bonds, shares or money in the model.

Expressing the equilibrium condition above in terms of per worker: c + i=y=(W/P) + (r+ )k(1) W/P=MPL=(2) If k W/P and r In poor and rich countries K/L is low and high, respectively.

Factor mobility across economiesIf the value of A is the same in poor and rich countries, the real return on capital is higher in poor countries. As a result, we expect capital to move from rich to poor countries, increasing K/L in poor countries and lowering K/L in rich countries. Thereby, mobility of capital contributes to convergence in K/L between rich and poor economies. We expect L to move the opposite way because W/P is higher in rich countries. Mobility of L increases K/L in poor countries and decreases K/L in rich countries. Thereby, it also contributes to convergence in K/L between rich and poor countries.

Why do capital not flow to Africa? In other words, why are not large investments taking place in some African countries? Answer: Because A is low, which means that MPK=r+d is not so high.This can be seen in Solow-diagram. (Allow countries to differ w.r.t. A.)

In other words, if A is the same across countries (which it is not). (assume g=0).K will move from richer countries with low r (due to high k) to poorer countries where r is high due to low k. Thereby k and y will tend to equalize across countries. Nowadays, rich EU-countries invest capital or move production to new EU-countries or to CHINA or India. L will move the opposite way, from low-wage countries to high wage countries, which also contributes to equalize real wages, r and k across countries.Workers move from new EU-countries to old EU-countries where real wages are higher.

Specific example: assume two countries that are the same with respect to the parameters: A, n, d, and alfa, but one country has a higher saving rate than the other. Assume that these countries are in their respective equilibria. Allowing for factor mobility across countries equalizes the real wage, the real return to capital, k and y across countries.

The new equilibrium will be joint for the two countries and is determined by a weighted average of the saving rates in the 2 countries, where the weights are given by the size of the populations in the two countries.

Capital to labor (k) ratio is low in developing countries. As a result, one would expect a high real rate of return on investment in those countries. Why then do not a lot of investment (construction of new factories, etc.) take place in many of these countries? Answer: There is a lot of corruption, which makes the actual rate of return much lower; that is, after the investor have paid off a lot of government official, there might not be so much money left. A is low. There might also be a political risk. Investors might risk that some bandits take over the factories, like in Zimbabve.

Important Exercise: Derive the equilibrium expressions for the real wage and for the real return on capital; that is, express the real wage and the real return to capital as functions of the exogenous variables: s, A, n, the depreciation rate and alfa.

Golden rule is optional reading for A-level students:The golden rule level of capital:The level of capital that maximizes consumption per worker in equilibriumConsumption per worker is the distance between the curve for labor productivity () and the curve for depreciation of capital per worker: (n+d)k. This distance is maximized at the level of k where the slopes of these two curves are the same:

Solving the equation for k yields the answer.A government that wants to maximize consumption per worker should choose the saving rate (s) so that this level of capital is achieved.An economy can save too much. That is, by decreasing the saving rate per capita consumption can increase in the steady state.

Adding realism in the model: continuing technological progressThere is technological progress if new production techniques arise due to innovations such as the computer, engine, electricity, etc.

Model assumption: (A5): ,

[optional reading: ]where g =rate of technological progress is exogenously assumed.[Optional reading: The model is here formulated in continuous time which means that time changes continuously. Previously the model was in discrete time which means that the time is in periods. If the model were in discrete time: .]

Only technological progress can explain long run increases in the living standard= GDP per capita = Y/L=y

Growth rates in the long-run equilibrium:

Before: , Now:

, , ,

Technological progress is exogenousAs the rate of technological progress is unexplained by the SOLOW model (that is, exogenous), adding g to the model does not add any more economic insights than the version of the model with g=0.For this reason and because it is simpler we will focus on the version of the model where g=0. Keep however in mind that technological progress makes the model more realistic because in the real world y typically increases over time due to new production techniques; that is, due to innovations.

What happens if the economy is off its equilibrium growth path?

When the economy approaches its equilibrium growth path, the growth rate of y deviates from the long-run growth rate (g). If an economy starts out below (above) the equilibrium growth path, the growth rate of y is higher (lower) than g. Holding constant the equilibrium growth path that is holding constant A(0), s, n, g, d and alfa, a lower y means a higher growth rate of y.

What happens to the growth rate and to the equilibrium growth path if the saving rate increases (or institutions improve or population growth )?

If s increases, the equilibrium shifts upwards, and the growth rate of y is higher than the long run growth rate during to the transition to the new equilibrium growth path.

Factors that impact GDP per capita in the real world:

POP = Population. If GDP per hour (=labor productivity) increases or the hours worked per employed increases or the number of employed as a share of population increases, then GDP per person increases.In other words, get each worker to produce more or get more people in production, then GDP per person increases.Production per employed (= the first 2 terms on the left hand side of the equation above) is in macromodels is GDP per worker, Y/L.

GDP (or GNP) per capita as a measure of the standard of living The income distributionGDP per capita (=average income) can be a poor indicator of the income of the average citizen; that is, of the median income.The median is the person in the middle of the income distribution.

The income distribution is typically assymmetric: median income < average income the more unequal income distribution the greater difference between median and average income and a larger proportion of the population tends to have an income below the average income. An extreme example:Country Equal. 10 individuals each with an income of 5000. The median and mean income is 5000. Country Unequal. 9 individuals each has an income of 2000.One individual has an income of 32000.Average income is 5000. Median income is 2000.GDP per capita as an indicator of “human development/happiness”We have concluded that average income per capita may be a poor indicator of the income of the average person; that is, of the median person.

What is the relationship between income per capita and other indicators of “welfare/happiness”? We want (but cannot) measure is happiness/utility:U = U (y, x1, x2, x3, x4,…)Where y = income per capita, x1=literacy rate, x2=assess to clean water, x3= infant mortality rate, x4=life expectancy, etc.

2 views: 1. The correlation between income per capita and other variables (x1,x2,x3,x4,..) which we believe impact the welfare of people is high.Therefore, it is sufficient to study determinants to income per capita.2.The correlation is not necessarily high.

The UN (UNDP’s) “Human Development Index” has 3 components:1. Life expectancy. 2. Educational level (e.g. literacy rate).2. Income per capita.

According to this index Sweden’s is a top 5 whereas with respect to income per capita Sweden is only top 20.

Problem of Household surveys that ask “Are you happy?” is that the meaning of the word happy may differ across cultures.We are rich now but are we happier?

The importance of relative position.Harvard-students were asked what alternative they preferred:

a) USD 50000/year whereas others get half.b) USD 100000/year whereas others get the double.

Source: The economist, Aug. 9, 2003.

Some characteristics of poor countriesLarge agricultural sector. They have a comparative advantage with respect to labor-intensive production as they have a lot of labor but only a little capital (physical and human).Demography: Young populations, many kids per woman.

In the Solow-model there is one type of asset; physical capital, in this chapter and in the Keynesian model there are also financial assets: money, bonds, and equities or stocks.

Chapter 4 (and 18): MONEY SUPPLY AND INFLATION IN THE LONG RUN

4.1There are 4 main kinds of assets in the economy: money, bonds, equities orstocks, and real assets.

MONEY The money stock consists of assets that can be immediately used for making paymentsMoney includes currency (notes and coins) and also deposits on which checks can be written.

The Functions of money are to serve as : 1. A Medium of exchange 2. A Unit of account. 3. A Store of value (=An asset).

There are different measures of money that vary with respect to liquidity:By liquidity we mean how easy it is to transform money into goods and services.M1= currency (=notes and coins), salary- and check accounts, travellers’ checks.M2 = M1 + saving deposits. Etc. M2 is less liquid than M1.

Notes and coins are sometimes called the monetary base (MB).

Without a medium of exchange we have a barter economy (=bytesekonomi).Today that would be inefficient.

BONDS (from Dornbusch and Fischer)A bond is a promise by a borrower to pay the lender a certain amount (the principal) at a specified date (the maturity date of the bond) and in the meantime to pay a given amount of interest per year. Thus we might have a bond, issued by the Swedish Debt Office, that pays 10000 on June 1, 2012, and until that time pays 8 percent per year, or 800 kronor per year. Bonds are issued by many types of borrowers – the government, municipalities, corporations. The interest rates on bonds issued by different borrowers reflect the differing risk of defaults. Default occurs when a borrower is unable to meet the commitment to pay interest or principal.

EQUITIES OR STOCKS (from Dornbusch and Fischer)Equities or stocks are claims to a share of the profits in an enterprise. For example, a share in Ericsson entitles the owner to a share of the profits of that corporation. The shareholder or stockholder receives the return on equity in two forms. Most firms pay regular dividends, which means that stockholders receive a certain amount of dollars for each share they own. Firms may also decide not to distribute profits to the stockholders, but rather retain them and reinvest them and reinvest these profits by adding to their stock machines and buildings/structures. When this occurs, the shares become more valuable since they now represent claims on the profits from a larger capital stock. Therefore, the price of the stock in the market will rise, and stockholders make capital gains. A capital gain is an increase, per period of time, in the price of an asset. Of course, when the outlook for a corporation turns sour, stock prices can fall and stockholders make capital losses. Thus the return on stocks or the yield to a holder of a stock is equal to the dividend (as a percentage of price) plus the capital gain.

Example: Suppose that a stock in 2006 trades for 15 kronor. In 2007 the stock pays a dividend of 0.75 kronor and the stock price increases to 16.50 kronor. What is the yield on the

stock? The yield per year is equal to 15 percent, which is the dividend as a percent of initial price (5 percent = (0.75/15)*100) plus 10 percent, which is the 1.50 kronor capital gain as percent of initial price. Alternatively, 2.25/15*100 = 15 percent.

REAL ASSETSReal assets, or tangible assets are machines, land, and structures owned by corporations, and the consumer durables (cars, washing machines, stereos etc) and houses owned by households. These assets carry a return that differs from one asset to another. Owner-occupied houses provide a return to owners who enjoy living in them and not paying monthly rent; the machines a firm owns contribute to producing output and thus making profits. The assets are called real to distinguish them from financial assets (money, stocks, bonds).

The value of equities and bonds held by individuals cannot be added to tangible wealth to get the total wealth of individuals. The reason is that the equities and bonds they hold are claims on part of the tangible wealth, that part held by corporations. The equity share gives an individual a part ownership in the factory and machinery.

4.2 IN MACROMODELS:In macroeconomics, to make things manageble, we lump financial assets into two categories. On one side we have money, with the specific characteristic that it is the only asset that serves as a means of payment. On the other hand we have all other financial assets. Because money offers the convenience of being a means of payment, it carries a lower return than other financial assets, but that differential depends on the relative supplies of financial assets. As we soon will see, when the central bank reduces the money stock and increases the supply of other financial assets (we say “bonds”), the yield on other financial assets increases.

To sum up: 2 types of financial assets: money and interest-bearing assets (“bonds”).A bond is a promise to pay to its holder certain agreed-upon amounts of money at specified dates in the future. For example, a borrower sells a bond in exchange for a given amount of money today, say 100 kronor, and promises to pay a fixed amount, say, 6 percent, each year to the person who owns the bond; an to repay the full 100 kronor (the principal) after some fixedd period of time, such as 3 years, or perhaps longer. In this example, the interest rate is 6 percent, for that is the percentage of the amount borrowed that the borrower pays each year.

4.3 THE WEALTH CONSTRAINTAt any given point in time, an individual has to decide how to allocate his or her financial wealth between alternative assets. The wealth budget constraint in the asset markets states that the real money demand, the quantity of nominal money divided by the price level, which we denote L, plus the demand for real money bond holdings, which we denote DB, must add up to the real financial wealth of the individual. Real financial wealth is, of course, simply nominal wealth WN divided by the price level, P:L+DB=WN/P.

Note that the wealth budget constraint implies, given an individual’s real wealth, that a decision to hold more real balances is also a decision to hold less real wealth in the form of bonds.

The total amount of real financial wealth in the economy consists of the real money supply and of real bonds in existence. Thus, total real financial wealth is equal to:WN/P=M/P+SBWhere M is the nominal money supply and SB is the real value of the supply of bonds.Thus, L+DB=WN/P=M/P+SB(L-M/P)+(DB-SB)=0.

Thus, the wealth budget constrain implies that when the money market is in equilibrium (L=M/P), the bond market, too, is in equilibrium (DB=SB). Similarly, when there is excess demand in the money market, so that L>M/P, there is an excess supply of bonds; DB<SB. We can therefore fully discuss the assets markets by concentrating on the money market.

SIMPLIFICATION IN MODELSIn our macromodels the central bank controls the money supply.The central bank directly controls the amount of currency and indirectly the amount of bank deposits (M2) through reserve requirements, and through the interest rate bank pays to the central bank if they borrow from the central bank.

The Bank Sector creates moneyAssume that Money supply (M) = monetary base (MB) + bank deposits.Assume that the central bank increases the currency by 100 millions, through an open-market operation; that is, the central bank buys government bonds and pays with newly printed notes and coins. We assume that the public increases their bank deposits by 100 as a result. If the reserve-requirement for banks is 10 %, the banks can increase their lending by 90 million to people who needs to make investments, or buy houses. If we assume that the seller of the investment goods (for example new machines) or the sellers of the houses deposits the 90 millions in the bank system, the money supply increases by an additional 90 millions. The banks can now increases their lending further; by 0.9*90=81 millions to people that needs to money to invest in stocks, physical capital, home-owned houses, etc. The sellers of these goods and assets therefore receive 81 millions, which we assume are deposited in the banks. Thus, bank deposits increase by an additional 81 millions, and the banks can therefore increase their lending further; by 0.9*81 millions to people that needs to money to invest in stocks, physical capital, home-owned houses, etc. We summarize:

Period 0 The bank deposits increase by 100 and banks increase their lending by 0.9*100=90Period 1: The bank deposits increase by 90, and banks increase their lending by 0.9*90=81.Period 2: The bank deposits increase by 81, and banks increase their lending by 0.9*81.Period 3: The bank deposits increase by 0.9*81, and banks increase their lending by 0.9*0.9*81. Etc.Thus ∆M = ∆MB + ∆bank deposits = 100 + 90 + 81 + 0.9*81 + …More generally, ∆M = ∆MB(1+ (1-rr) + (1-rr)*(1-rr) + (1-rr)*(1-rr)*(1-rr) + ….Where r is reserve requirement, which is determined by central bank.As profit-maximizing banks should not want to have excess reserves, the central banks indirectly controls the money supply.Using the formula for the sum of a geometric series (see below):M=MB/rr.Thus, if reserve-requirements is 0.1, the money supply is 10 times higher than MB. What is a bank run?

The central bank is the bank of the banks. Private banks can borrow from the central bank. The central bank sets the interest rate the private banks have to pay on their loans. This interest rate together with the currency and reserve requirement are factors that impact the money supply. When the central bank increases the supply of money it usually buys government bonds from the public and pays with newly printed currency.

If the money supply increases through an open-market operation the supply of bonds decreases, then the interest rate goes down, and the price of outstanding bonds increases. An open market operation implies that the government buys outstanding bonds with newly printed money.When the interest rate goes down also stock prices tend to increase.

The quantity theory for money:The quantity equation:M*V=P*Y

M=nominal money supplyV= income velocity of money. It is the number of times a dollar is used for purchases of newly produced goods and services during a year.P = price level. Y= real GDP. Note: P*Y= GDP in current prices.Note that this equation is an identity, which means that it holds for sure.

The quantity theory for money:Assumptions: 1.The factors of production and the production function determine real GDP:

The quantity theory for money is a theory for the long run as it assumes that the level of Y is independent of M.2. Velocity is constant.

Thus, changes in M translate into changes in P.

We can write the quantity equation in percentage terms:∆M/M + ∆V/V = ∆P/P + ∆Y/Y

Ex. 1: If ∆V/V and ∆Y/Y are zero, and money supply increases by 10 percent, what is the rate of inflation: 10 + 0 = = ∆P/P + 0 . Thus, inflation is 10 percent as a result.

Ex. 2:If ∆V/V = 0 and ∆Y/Y=3, and money supply increases by 10 percent, what is the rate of inflation:10 % + 0 = inflation + 3Thus, inflation is 7 percent according to this theory.

Ex. 3:If ∆V/V = 0 and ∆Y/Y=3, and the central bank has an inflation target of 2 percent by how much should it increase the money supply to obtain this target?∆M/M + 0 = 2 + 3 = 5 percent.

The demand for money in real terms:The demand for money in terms of how many goods and services that your money can buy:

,where k is positive constant.

If k is large people hold a lot of dollars in relation to income.

The real money demand function shows that when real income increases, the real money demand increases as well. This is because when your income increases then your consumption increases which means that you need more money to pay for your increased purchases.

Relation between money market equilibrium and the quantity theory of money: Equilibrium in the money (and bond) market:Real Money Supply = Real money demand

, k>0

If k=1/V, then

, which is the quantity equation.

Thus, the quantity equation shows the equilibrium in the money market when real money demand = k*Y.

The Fischer effect:In the Keynesian model in the long run the real interest rate (r) is determined bySaving (r)=Investment (r) for a closed economy.For a small open economy, the real interest rate (r) is determined byWorld Saving (r)=World Investment (r)

The real interest rate, r= rate the bank pays (nominal interest rate, i)–Inflation. The Fischer equation: i=r+inflation.

The Fisher effect says as the real interest rate is determined by real factors in the long run(S=I(r)), inflation increases the nominal interest rate one-for-one.

From the quantity theory of money we find out the inflation rate in the long run,And from the Fisher equation we find out the nominal interest rate.Ex.: If Velocity is constant, and the growth rate of real GDP is 2 percent,And the growth rate of the money supply is 8 percent, and the real interest rate is 3 percent, what is the inflation rate according to the quantity theory of money and what is the nominal interest rate according to the fischer equation?

Modifying the Fischer equation. Making it more realistic.Assume: nominal interest rate is set before actual inflation for the period is known. Thus, i is assumed to be a fixed rate, when you take the bank loan or when you deposit your money in the bank. i= expected r + expected inflationThus, the expected real interest rate r is determined by S(r)=I(r).The nominal interest rate moves one-for-one with changes in expected inflation.

Making the real money demand function more realistic:When you have bills and coins in your pocket you give up interest that this money could have generated. The nominal interest rate is the cost of holding money, which should impact your real money demand. Thus:

The figure shows that the real demand for money depends negatively on the nominal interest rate and positively on the real income, Y.More on this demand function for real money in Chapter 10.[If real money demand depends on the nominal interest rate = r + inflation,Then velocity should depend on inflation as well.A higher inflation and thereby a higher nominal interest rate, a higher velocity.Example: Assume L(i, Y) = f(i)*Y, if nominal interest rate f(i) Money market equilibrium implies: M/P=f(i)*YM*(1/f(i)) = P*Y. M*V(i) = P*Y.if nominal interest rate (i) f(i) , V(i) .]

The costs of inflation:If inflation is expected the people have adjusted, so the only cost is shoe-leather inflation as you go to the money machine more often because of the higher nominal interest rate. Also restaurants want to reprint menus more often, which is a cost. If actual inflation is higher than the extected then the real actual interest rate is lower than the expected at a given bank interest rate, which means that savers loose and borrowers gain. Also your real wage becomes lower than expected.

Hyperinflation is more than 50 percent per month.

r

M/p,PPP

M/pPPP/PP

M/P

L(r,Y1))'L

((r,Y)

r1

r2

Summary:In the classical model = Keynesian model in the long run (=flexible prices) changes in nominal money supply do not impact real variables such as real GDP and the real interest rate, and employment.

Bonds In more detail (from Varian, 6th edition): Perhaps use explanation from dornbusch.Bonds are basically a way to borrow money. The borrower – the agent who issues the bond – promises to pay a fixed number of dollars x (the coupon) each period until a certain date T (the maturity date), at which point the borrower will pay an amount F (the face value) to the holder of the bond. Thus, the payment stream of a bond looks like (x,x,x,x,x,,,,F). If the interest rate (i) is constant, the present value of such a bond is easy to compute. It is given by

For someone to be willing to buy a bond the rate of return (interest rate) must be at least as high as the rates of returns (interest rates) on assets of similar risk. Governments bonds for countries like Sweden are relatively safe. Assume the coupon is 10 kr and the face value is 1000 kr, then the interest rate is 10 percent:

Note that the present value (PV) of an issued bond will decline if the interest rate increases. Why? When the interest rate goes up the price now for 1 dollar delivered in the future goes down. So the future payments of the bond will be worth less now. There is a large and developed secondary market for bonds. That is, a market where outstanding bonds are traded daily. The market value of outstanding bonds will fluctuate as the interest rate fluctuates since the present value of the stream of payments represented by the bond will change.

An interesting special kind of a bond is a bond that makes payments forever. These are called concols or perpetuities. Suppose that we consider a consol that promises to pay $x dollars a year forever. To compute the value of this consol we have to compute the infinite sum:

The trick to computing this is to factor out 1/(1+i) to get

But the term in the brackets is just x plus the present value! Substituting and solving for PV:

PV=x/i.

For a consol it is easy to see how increasing the interest rate reduces the value of a bond. Suppose, for example, that a consol is issued when the interest rate is 10 percent. Then if it promises to pay 10 dollars a year, forever, it will be worth 100 dollars now – since 100 dollars would generate 10 dollars a year in interest income. NOW, suppose that the interest rate goes up to 20 percent. The value of the consol must fall to 50 dollars, since it only takes 50 dollars to earn 10 dollars a year at a 20 percent interest rate. The formula for the consol can be used to calculate an approximate value of a long term bond.

BUSINESS CYCLE ANALYSIS:THE KEYNESIAN AND CLASSICAL MODELSThe Keynesian model in the long run (when prices are flexible) = Classical model.COMPONENTS OF AGGREGATE DEMAND: What determines aggregate demand (AD) for goods and services?AD = C+I+G

MPC = marginal propensity to consume shows by how much C increases when the households’ disposable income, Y-T, increases by one unit.

We assume that

Thus, if Y-T increases by 1 dollar, C increases by less than 1 dollar as some of the increase in disposable income is saved.

The saving functionHouseholds use their disposable income to C and to saving (S) :Y-T= C+S.

C = C(Y- T) C = C(YC = C(Y-- T) T)

consumptionconsumptionspending byspending byhouseholdshouseholds

consumptionconsumptionspending byspending byhouseholdshouseholds

dependsdependsonon

dependsdependsonon

disposabledisposableincome income

disposabledisposableincome income

C

Y-T

The slope of the consumption function is the MPC.

C

Y-T

The slope of the consumption function is the MPC.

A richer private consumption functionIn many textbooks the Keynesian private consumption function is:

, where t=proportional tax rate; eg. t=0.4. TR=transfers to households, unemployment benefits, child allowances, sick benefits, etc.This consumption which is more realistic, the households’ tax payments, t*Y, is related to income, Y.

Realistically, current consumption may depend not only on Current disposable income but also on expected future disposable income, Wealth, and on the interest rate. For example, we expect if wealth .Many textbooks assume that a higher real interest rate increases private saving, S, and lowers private consumption at a given level of Y-T.

The investment functionLägg in lite mer här från lärobok om investeringsbeslutet.

Real interest rate (r) nominal interest rate (i)– inflation rate ( )

The nominal interest rate is the bank interest rate.

The Exact formula:

Realinterestrate, r

Quantity of investment, I

Realinterestrate, r

Quantity of investment, I

Investment function, I(r)Investment function, I(r)

The investment function relates the quantity of investment I to the realinterest rate r. Investment depends on the real interest rate because theinterest rate is the cost of borrowing. The investment function slopesdownward; when the interest rate rises, fewer investment projects are profitable.

The investment function relates the quantity of investment I to the realinterest rate r. Investment depends on the real interest rate because theinterest rate is the cost of borrowing. The investment function slopesdownward; when the interest rate rises, fewer investment projects are profitable.

Often we assume a linear investment function: , where d>0

- We expect the intercept, , increases if firms’ expectations about the future improves.

The government sector:T=net taxes = tax revenues – transfers to households.G = GC + GIT and G are assumed to be fixed; determined outside the model:

THE FOREIGN EXCHANGE MARKET

When e(Yen/$) increases, the dollar becomes stronger, appreciates, which implies that american goods become more expensive relative Japanese goods.When e(Yen/$) increases American goods become more expensive in Yen: , where P($) is the domestic price level. When e(Yen/$) increases Japanese goods become cheaper in dollars:

.

Explaining slopes of D- and S-curves: More expensive american goods means a lower foreign demand for american goods, and thereby a lower demand for US dollars, and higher domestic (=American)e demand for japanese goods, and therefore a higher supply of US dollars.

Note: The exchange rate is to a large extent determined by financial flows due to financial investments rather than due to the trade of goods and services. That is, the demand and supply of foreign currency are determined mainly by interest differentials on financial investments.

D$ shifts rightward and increases the nominal exchange rate, e. This is known as appreciation of the dollar.Be1 Be1

e

Dollar Value of Transactions

D$

Ae0

S$

$

e

Dollar Value of Transactions

D$

Ae0

S$

$

e

Dollar Value of Transactions

D$

Ae0

S$

$

Suppose that there is an increase in the demand for U.S. goods andservices. How will this affect the nominal exchange rate?

Events which decrease the demand for the dollar, and thus decrease e would be a depreciation of the dollar.

D$ D$

The real exchange rate is often called terms of trade.The relation between the real ( ) and nominal exchange rate (e):

A higher real exchange rate means that domestic goods and services become more expensive relative to foreign goods and services in the same currency.

Example: Nominal exchange rate (e)=120 yen/$. Price of car in the us, Ford = 10,000 $, Price of car in Japan, Toyota = 2,400,000 yen

Real exchange rate =

We get one half of a Japanese car per American car.

If e(yen/$) increases to 240, we get one Japanese car per American car.The American car has become more expensive!

Model assumption: Exports , Imports NX=(Exports-Imports)

Purchasing power parity (PPP) implies:

PPP and the law of one price implies:

NX()

Net Exports, NX

Real exchangerate,

The law of one price applied to the international marketplace suggests thatnet exports are highly sensitive to smallmovements in the real exchange rate.This high sensitivity is reflected herewith a very flat net-exports schedule.

S-I

The inflation and depreciation of the nominal exchange rate:

If

If inflation is higher in Japan than it is in the US, then the dollar appreciates ,e(yen/dollar), and the yen depreciates.

The law of one price applied on financial returns in different countries Bond yields in different countries must have the same expected rate of return in the same currency because of arbitrage. Uncovered interest rate parity:

The left-hand side of the equation tells you how much you have after one year if you invest one dollar in a bank in your home country USA. tells you how much you have in Yen after one year if you invest the dollar in a bank in Japan. The right-hand side of the equation shows the expected return of saving in Japan after one year in $. is the expected exchange rate in a year. Students need not know derivation below:

. Divide by :

. Subtract 1 from both sides:

. For small values of :

.

If nominal interest rate = 1percent in the U.S.A. And 5 percent in Japan. Do you expect the dollar to appreciate or depreciate? We expect To decrease by 4 %. That is, we the dollar to appreciate by 4 percent. INTRODUCTION TO AND SUMMARY OF THE KEYNESIAN MODEL IN THE SHORT AND THE LONG RUN

In the short run actual GDP, Y, may be lower or higher or equal to potential GDP, .

Aim of the Keynesian model in the short run is to explain short-run fluctuations in production around a long-run trend. The short-run supply curve is assumed to be horizontal. Thus, in this model aggregate demand determines output at a fixed price level. Actual Output can be below or above the full-employment GDP, . K is fixed more or less. By more or less I mean that some part of the fixed stock of physical capital can be unused in a recession.

In the long run nominal variables such as the nominal money supply only impact nominal variables such as the price level. Nominal money supply do not impact real variables such as real GDP, employment, unemployment, the real interest rate, etc.In the short run, however, nominal money supply may impact real variables such as real GDP. In the short run the money and goods market interact and jointly determine the level of real variables such as real GDP.

The closed economy with its own currency:Aggregate demand, AD= C(Y-T) + I(r)+G is measured on the horizontal axis, and the price level (P) on the vertical axis:

Why does aggregate demand, AD= C(Y-T) + I(r)+G, depends negatively on P?When P M/Pr I(r), AD= (C(Y-T) + I(r)+G)

In many textbooks, it is assumed that C(Y-T) also depends negatively on the real interest rate, r, which provides one additonal reason why the AD-curve depends negatively on P.What factors increases AD at a given price level; that is, shifts the AD-curve to the right?*Expansionary monetary policy by the Central Bank:If M (M/P) nominal interest (=real interest rate when P is constant) I(r) , AD= (C(Y-T) + I(r)+G) at a given level of P.

P

Y

LRAS

YY = F (K,L)

P0

AD=C(Y-T)+I(r)+G1AD=C(Y-T)+I(r)+G2A

BC

SRAS

When the short-run supply curve is horizontal, when AD Y C(Y-T) .In the new short run equilibrium: r is lower, I,Y, and C are higher than before.

*Expansionary fiscal policy by the political authorities:If G (or T) AD= (C(Y-T) + I(r)+G) at a given price level. When the short-run supply curve is horizontal, when AD Y C(Y-T) , the demand for real money, L(r,Y) r I.In the new short run equilibrium: r is higher, I is lower, G, C, and Y higher than before. See figure above.

Other factors that shifts the AD-curve to the right:If C at a given Y-T due to e.g. higher expected future disposable income, Y-T.If I at a given r due to e.g. improved expectations about the future.(If L(r,Y) (= velocity) at a given i and Y, lowers the nominal interest rate and thereby increases private investment, I.)

Conclusion: An increase in aggregate demand increases income, Y in the short run.

The small open economy (in which r=r*) with its own currency:

Why does aggregate demand, AD = (C(Y-T)+I(r*) + G + NX(real exchange rate)), depends negatively on P?If P the real exchange rate: which lowers exports and increases imports: NX , AD = (C(Y-T)+I(r*) + G + NX(real exchange rate)) Also: If P M/P r so that r>r* instantaneously financial investments in domestic country turns more profitable demand for the domestic currency the nominal exchange rate, e, appreciates (e) NX, AD = (C(Y-T)+I(r*) + G + NX(( ))

Factors that increase AD at a given price level; that is, shifts the AD-curve to the right:If M (M/P) and [if L(r,Y) (= velocity) for given r and Y] r so that r<r* financial investments in domestic country turns less profitable demand for the domestic currency the nominal exchange rate, e, depreciates (e) NX, AD = (C(Y-T)+I(r*) + G + NX(( )) Fiscal policy (G, T) does not shift the AD-curve for a small open economy:

If G (or T or C(Y-T) at a given Y-T or I at a given r=r*) r so that r>r* financial investments in domestic country turns more profitable demand for the domestic currency the nominal exchange rate, e, appreciates (e)

NX, AD = (C(Y-T)+I(r*) + G + NX(( )) ]

In the long run:When actual Y>full employment (=potential) Y; that is; when actual employment is above full employment, and actual unemployment is above the natural rate of unemployment at point B in diagram, nominal wages and prices increase, which shifts the short-run aggregate supply-curve upwards. (The SRAS-curve is equivalent to the MC-curve in microeconomics.) A higher price level decreases the real money supply (M/P), which increases the interest rate and thereby lowers private investment, I, for the closed economy. For the small open economy a higher domestic price level, increases the real exchange rate, and thereby lowers net exports, NX.

In the long run the economy is back at the full-employment output but at a higher price level.

Example: A fall in aggregate demand

PP

YY

LRASLRAS

YY

ADAD

SRASSRAS

ADAD''

AABB

CC

A reduction in aggregate demand, due e.g. to an increase of private saving, C(Y-T) at a given Y-T, results in unemployment above the natural rate (=employment below full employment) in the short run. The new short-run equilibrium is at point B. Over time employment below full employment decreases nominal wages and prices, which increases aggregate demand because a lower price level increases real money supply (M/P), which lowers the interest rate and thereby stimulates private investment, I, for the closed economy. For the small open economy a lower domestic price level, decreases the real exchange rate, and thereby stimulates net exports, NX.

In the long run the economy back at full employment.At the new long-run equilibrium (point C) the price level is lower than at the old long-run equilibrium.

Keynes said that it may take a long time for nominal wages and prices to fall. As a result, it might be motivated with expansionary monetary (M) or fiscal policy (G, T) to increase employment and production.

Example: An adverse aggregate supply shock

PP

YY

LRASLRAS

YY

ADAD

SRASSRASADAD''AA

BB SRASSRAS''

Think of the short-run aggregate supply-curve (SRAS) as being equivalent to the marginal cost-curve, MC-curve, in microeconomics:

Increases in input prices, e.g. higher nominal wages, or higher oil prices, increase production cost at a given level of production; that is, shifts the SRAS-curve upwards.

The new short-run equilibrium is at point B.The price level is higher and Y is lower than before.An event with higher prices and lower production is called stagflation.

In the long run:

Over time employment below the full-employment level decreases nominal wages and prices, which shifts the SRAS-curve shifts back.In the long run the economy is back in its old long-run equilibrium.

Keynes said that it may take a long time for nominal wages and prices to fall. As a result, it might be motivated with expansionary monetary (M) or fiscal policy (G, T) to increase employment and production.

THE KEYNESIAN MODEL MORE IN DEPTH: The simple Keynesian model for a closed economy witout its own currency:Assumption: The short-run supply curve is horizontal (= P is fixed), which implies that aggregate demand alone determines output.The model also assumes that the real interest rate is fixed; and that planned investment is an exogenous variable. The money market plays no explicit role here.

The model is thus relevant for small economies without monetary authorities that are not or far from full-employment. If economies are at full-employment government spending cannot increase aggregate production. For example: the model is relevant for small municipalities within Sweden or small countries within the Euro-area or small states within the US states. If they are big, expansionary fiscal policies might increase the real interest rate.

The model how income Y is determined for given levels of the exogenous variables: government purchases (G), net taxes (T) and planned investment, I (planned). Actual expenditure (Y) is the amount households, firms, and the government spends on newly produced goods and services (GDP). Planned expeditures is the amount households, firms and the government would like to spend on newly produced goods and services. The economy is in equilibrium when Actual expenditures (Y) = Planned expeditures (E)

Actual expenditures (Y) = Planned expenditures (E) + involuntary inventory investment (positive or negative).

Actual investment = I(planned) + involuntary inventory investment (which is zero, negative or positive).

Planned Expenditure (E) =

where Y=GDP=GNP= households’ income before tax and transfers(as we assume that NFI=VAT=depreciation of capital=0). Note that: .

If we rewrite the equation above:

Y, E

Income, Output, Y

Actual Expenditure, Y=E

Planned Expenditure,E = C(Y-T)+ I(pl.) + G

Y2 Y1Y*

, where 0<MPC<1.

How is the equilibrium achieved?

At Y2 planned expenditures (E) > actual expenditures (Y) involuntary depletion of inventories, > I (actual) firms increase production, Y

At Y1 planned expenditures (E) < actual expenditures (Y) involuntary inventory build-up, < I (actual) firms decrease production, Y

The goods market Equilibrium implies: Y = E

The effect on Y of increased government spending (G):

An increase in government purchases of G raises planned expenditures (E) by that amount for any given level of income (Y): the E-schedule shifts up. The equilibrium moves from A to B and income rises. Note that the increase in income Y exceeds the increase in government purchases G. Thus, fiscal policy has a multiplied effect on income. This is because a higher income increases private consumption, C(Y-T).Y=C(Y-T) + G.

The multiplier process:

Y, E

Income, Output, Y

Actual Expenditure, Y=E

Planned Expenditure,E = C(Y-T) + I(pl.) + G0

Y1Y*

GA

B

If government spending (G) increase by 1 $, you might expect equilibrium output (Y*) to also rise by 1$. But it does not:Initially planned expenditures (E) increases by G, and income increases. A higher income increases consumption (and thereby planned expenditures) by MPC*G, which raises Y again. This second increase in income of MPC*G again raises consumption, this time by MPC*(MPC*G), which again raises income and so on.

The change in equilibrium Y is:

Using the expression for the sum of an infinite series:

>1 because 0<MPC<1. E.g., MPC=0.8

This is the government spending multiplier, which is 5 if MPC equals 0.8.The multiplier effect operates fully if the factors of production are not fully utilized; that is, when the short-run aggregate supply curve is horizontal.

The tax multiplier: The effect of lower net taxes on Y

A decrease in net taxes, T<0, raises planned expenditures (E) by that amount for any given level of income (Y). The equilibrium moves from A to B and income rises. Note that the decrease in income Y exceeds the initial decrease in net taxes T. Thus, tax policies have a multiplied effect on income when the short-run supply curve is horizontal. The multiplier process:If net taxes (T) are decreased by 1 $, you might expect equilibrium output (Y*) to rise by 1$*MPC. But it does not:Initially private consumption and planned expenditures (E) increases by –MPC*T, and income increases by this amount. A higher income increases consumption (and thereby planned expenditures) by MPC*(- MPC*T) in the next round, which raises Y again. This second increase in income of MPC*(- MPC*T) again raises consumption, this time by MPC* MPC*(- MPC*T) , which again raises income and so on.

The change in equilibrium Y is:

Using the expression for the sum of an infinite series:

>1 because 0<MPC<1.

. This is the tax multiplier.

NOTE: A tax reduction of 1 dollar increases Y less than a dollar increase of G because the consumer uses the increase in disposable income both to consumption (which increases aggregate demand and therefore Y) and to saving (which does not have an effect on aggregate demand and hence no effect on Y).

Y, E

Income, Output, Y

Actual Expenditure, Y=E

Planned Expenditure,E = C(Y-T0) + I(pl.) + G

Y1Y*

AB

-MPC*T

Solving for equilibrium Y mathematically and deriving multipliers mathematically:

Goods market Equilibrium: Y = E

Rewriting somewhat:

This is one equation with one unknown variable (one endogenous variable): Y.

is equilibrium Y, the value of Y which implies equilibrium in the goods market.The solution implies that the unknown/endogenous variable, Y, is expressed as a function of the exogenous variables.

What happens to equilibrium Y when the exogenous variables change?

The government spending multiplier

If

The tax multiplier is:

The balanced budget multiplier:Question: How much does Y increase if G and T increases by the same amount?If T is increased by the same amount that G increases, the government budget does not worsen.

A balanced budget implies:

Thus, the balanced-budget multiplier equals one.

Accounting for a foreign sector:Some of the demand of the production of a municipality comes from abroad.Here we assume that X is an exogenous variable, whereas imports depends on the economy’s income. (By the same reasoning exports should depend on the income in the rest of the world.) Moreover, both exports and imports should depend on the real exchange rate.If the economy has no currency of its own: exports and imports should depend on the relative prices. In sum:

Exports = F(world income, ; ))

Note: if the economy lacks its own currency: e=1.A higher “world” income should increase the exports of newly produced goods and services.A higher price level relative to the price level in the rest of the world should decrease exports.

Imports = G(Y; )

A higher income, Y, should increase imports.A higher real exchange rate should increase imports.

Simplifying assumptions:

Exports, , is assumed to be exogenously given.Imports is assumed to depend on income: M=m*Y, where m is assumed to be a positive constant, e.g. m=0.1. m is called the marginal propensity to import, which says if income, Y, increases by 10 million, then imports increase by m millions. If m=0.1 then imports increase by 1 million.

Equilibrium in the goods market implies that Y=E

Assuming our specific consumption function:

This is one equation with one unknown variable (one endogenous variable): Y.

is equilibrium Y, the value of Y which implies equilibrium in the goods market.

The solution implies that the unknown/endogenous variable, Y, is expressed as a function of the exogenous variables.

What happens to equilibrium Y when the exogenous variables change?

The government spending multiplier

If

Note: The multiplier is lower as some of the increased demand for goods and services when Y increases falls on imported goods and services.

Deriving multipliers mathematically for a more elaborate private consumption function:

Assume now the following private consumption function:

Equilibrium in the goods market implies that Y=E, when we assume our new specific consumption function:

This is one equation with one unknown variable (one endogenous variable): Y.

is equilibrium Y, the value of Y which implies equilibrium in the goods market.

The solution implies that the unknown/endogenous variable, Y, is expressed as a function of the exogenous variables.

What happens to equilibrium Y when the exogenous variables change?

The government spending multiplier

If

Note: The multiplier is lower as some of the increased income, Y, increases taxes.Before a million increases of income, Y, increased disposable income, Y-T, by 1 million.Now a million increase of income, Y, increases disposable income by (1-t)*(1 million).

BACK TO OUR ORIGINAL SPECIFICATION OF CONSUMPTION FUNCTION:

Summary: Factors that increase the equilibrium income (Y):

Planned expenditures(E) at a given level of Y:If C(Y-T) at a given level of Y, e.g. if . Also if wealth (the stock market), or expected future income or preferences become more impatient, we expect C(Y-T) at a given level of Y-T.If (pl.) due to improved expectations about the future, and if G.

If assuming a linear consumption function:

If , or MPC (when Y-T>0) , or , C(Y-T) at a given level of Y.

Thus: If , or MPC (when Y-T>0), or , or (pl.), or E at a given level of Y so that E>Y at the old equilibrium Y Y .

The effect of Y on private saving:

Households use their disposable income to saving and consumption:

Thus, the private-saving function (S) is

Because with this saving function S+C equals Y-T.

MAIN LESSON IN THIS MODEL: If government spending increases by 1 dollar, aggregate demand and output may increase by more than 1 dollar.Leftist parties talk often about multipliers, when they want a larger government sector.They rarely mention that increased G may decrease I and NX.

THE AD-CURVE in the PY-diagram is drawn under the assumption that Y=E, which means that actual investment = I (planned).

Why is aggregate demand, AD= C(Y-T) + I(r)+G, higher when P is lower?For Closed economy with its own currency:when P M/Pr I(r) ,AD= (C(Y-T) + I(r)+G).

For small open economy (r=r*) with its own currency: If P the real exchange rate: NX , AD = (C(Y-T)+I(r*) + G + NX(real exchange rate))

Also: If P M/P r so that r<r* instantaneously financial investments in domestic country turns less profitable demand for the domestic currency the nominal exchange rate, e, depreciates (e) NX, AD = (C(Y-T)+I(r*) + G + NX(( ))

Y, E

Income, Output, Y

Actual Expenditure, Y=E

Planned Expenditure,E = C(Y-T) + I(r0) + G

Y1Y*

A

B

P

Output (Y)

AD

THE KEYNESIAN MODEL MORE IN DEPTH CONTINUED:INTRODUCING THE MONEY AND BOND MARKETIf the closed economy has its own currency and a central bank, the model below is relevant. Now we have 2 markets: the goods market and the money (and bond) market, which interact: A higher income (Y) increases the real money demand which results in a higher interest rate (= real interest rate when M/P is fixed), which lowers I(planned): Our equilibrium requires both these markets to be in equilibrium.

Assumptions: Short run: P is fixed. K is fixed more or less.2 markets:Equilibrium in the goods market: Y=E=C(Y-T)+I(r)+G..Equilibrium in the money market: M/P = L(r,Y)Real interest rate (r)=nominal interest rate (i) – inflation rate = nominal interest rate

Note1: since P is assumed to be constant, the inflation rate is 0, and the real interest rate equals the nominal interest rate.Note2: We now assume that planned investment depends on the real interest rate: I(r).Equation system with the endogenous variables: Y, r, I(r), C(Y-T).Exogenous variables determined outside the model:M determined by the central bank.G, T are determined by the government.P is fixed in the short run.

In the long run actual Y = full employment Y. P increases as long as actual Y>full-employment Y: the short-run aggregate supply curve (SRAS) shifts upwards.

P decreases as long as actual Y<full-employment: the SRAS-curve shifts downwards.

Analysis of expansionary fiscal policy: that is, a higher G or a lower T.The short and long-run effects on increased government spending (G)

If G AD= (C(Y-T) + I(r)+G) at given level of YWhen AD Y the real money demand, L(r,Y) r I.In the new short run equilibrium (B): r is higher, I is lower, G, C, and Y higher than before.

Y increases by less than because private investment falls (“is crowded

out”) due to a higher interest rate.

Y, E

Income, Output, Y

Actual Expenditure, Y=E

Planned Expenditure,E = C(Y-T) + I(r0) + G0

Y1Y*

AB

P

Y

LRAS

YY = F (K,L)

P0

AD=C(Y-T)+I(r)+G0AD=C(Y-T)+I(r)+G1A

BC

SRAS

G+

Variable Old short-and long-runEquilibrium (A)

New short-runEquilibrium (B)

New long-run equilibrium (C)

G G0 <G1 = G1Y Y0 < Y1 Y2=Y0Interest rate R0 <R1 <r2I I0 >I1 >I2C C(Y0-T) <C(Y1-T) C(Y0-T)P P0 =P1 <P2National saving S0=I0 >S1=I1 >S2=I2

The long run effect .In the long run: the price level increases when Y is larger than the full-employment Y. A higher price lever lowers M/P which increases the real interest rate, and lowers private investment even more.

NOTE that in the long run I decreases by the same amount that G increased becausein the long run actual output equals full employment or potential output.

i

M/pPPP

M/pPPP/PP

M/P

L(i,Y1))'L(i,Y0

) ((r,Y)

i

i

The short and long-run effects of lower net taxes (T):

If T AD= (C(Y-T) + I(r)+G) at given level of YWhen AD Y the real money demand, L(r,Y) r I.In the new short run equilibrium (B): r is higher, I is lower, C, and Y are higher than before.

Y increases by less than because private investment falls (“is crowded

out”) due to a higher interest rate.

Y, E

Income, Output, Y

Actual Expenditure, Y=E

Planned Expenditure,E = C(Y-T0) + I(r0) + G

Y1Y*

AB

P

Y

LRAS

YY = F (K,L)

P0

AD=C(Y-T0)+I(r)+G

AD=C(Y-T1)+I(r)+G

AB

C

SRAS

MPC*+

Variable Old short-and long-runEquilibrium (A)

New short-runEquilibrium (B)

New long-run equilibrium (C)

T T0 >T1 = T1Y Y0 < Y1 Y2=Y0Interest rate R0 <R1 <r2I I0 >I1 >I2C C(Y0-T0) <C(Y1-T1) C(Y0-T1)P P0 =P1 <P2National saving S0=I0 >S1=I1 >S2=I2

The long run effect .In the long run: the price level increases when Y is larger than the full-employment Y. A higher price lever lowers M/P which increases the real interest rate, and lowers private investment even more.

NOTE that in the long run I decreases by the same amount that C increased becausein the long run actual output equals full employment output.

i

M/pPPP

M/pPPP/PP

M/P

L(i,Y1))'L(i,Y0

) ((r,Y)

i

i

Shortand long run effects of expansionary monetary policyAssume that nominal money supply (M) is increased: Note that the picture shows the opposite, a lower nominal money supply.Recall that the price level (P) is assumed to be constant in the short run.

r

M/PM/P

Supplyr

M/PM/P

Supply

Demand, L (r,Y)Demand, L (r,Y)

Supply'Supply'

If M (M/P) nominal interest (=real interest rate when P is constant) I(r) , AD= (C(Y-T) + I(r)+G) at a given level of P, which increases Y, which increases real money demand; which pushes up the interest somewhat.

Y, E

Income, Output, Y

Actual Expenditure, Y=E

Planned Expenditure,E = C(Y-T) + I(r0) + G

Y1Y*

AB

+

Variable Old short-and long-runEquilibrium (A)

New short-runEquilibrium (B)

New long-run equilibrium (C)

Y Y0 < Y1 Y2=Y0Interest rate R0 >R1 r2=r0I I0 <I1 I2=I0C C(Y0-T) <C(Y1-T) C(Y0-T)P P0 =P1 <P2M/P M0/P0 <M1/P0 M0/P0

In the long run P increases until M/P becomes identical to M0/P0. Thus,An increased nominal money supply has no effect on real variables in the long run.

P

Y

LRAS

YY = F (K,L)

P0

AD=C(Y-T)+I(r)+GAD=C(Y-T)+I(r)+GA

BC

SRAS

THE CLASSICAL MODEL = THE KEYNESIAN MODEL IN THE LONG RUN (WHEN PRICES ARE FLEXIBLE).CLOSED ECONOMYHow does equilibrium in the goods market occur? Equilibrium in the goods market: Aggregate supply of output (Y) = aggregate demand for output (AD)

where Y=GDP=GNP=national income (as depreciation and indirect taxes are 0).Goods market equilibrium in the long run; that is, when :

Note: r is the only variable not already determined in the last equation. Thus, r plays a key role: it must adjust to ensure that the demand for goods and services equals the supply of newly produced goods and services. The greater the interest rate, the lower level of investment, and thus the lower the aggregate demand for goods and services, and vice versa.The real interest rate brings financial markets into equilibrium, which also leads to equilibrium in the goods market:

To see how the interest rate brings financial markets into equilibrium,substitute the consumption function and the investment function intothe national income accounts identity:

Y - C (Y-T) - G = I(r)Next, note that G and T are fixed by policy and Y is fixed by the factorsof production and the production function: Y - C (Y-T) - G = I(r)

S = I(r)

To see how the interest rate brings financial markets into equilibrium,substitute the consumption function and the investment function intothe national income accounts identity:

Y - C (Y-T) - G = I(r)Next, note that G and T are fixed by policy and Y is fixed by the factorsof production and the production function: Y - C (Y-T) - G = I(r)

S = I(r)

Investment, Saving, I, SDesired Investment, I(r)

Realinterestrate, r

Saving, S

S

Equilibriuminterest

rate

The vertical line represents saving-- the supply of loanable funds. The downward-sloping line represents investment-- the

demand for loanable funds. The intersection determines the

equilibrium interest rate.

The vertical line represents saving-- the supply of loanable funds. The downward-sloping line represents investment-- the

demand for loanable funds. The intersection determines the

equilibrium interest rate.S'S'S'

Investment, Saving, I, SDesired Investment, I(r)

Realinterestrate, r

Saving, S

S Investment, Saving, I, SDesired Investment, I(r)

Realinterestrate, r

Saving, S

S Investment, Saving, I, SDesired Investment, I(r)

Realinterestrate, r

Saving, S

S

A reduction in saving, possibly the result of a change in fiscal policy,shifts the saving schedule to the left.The new equilibrium is the point at which the new saving schedule crossesthe investment schedule. A reductionin saving lowers the amount of investment and raises the interest rate.

A reduction in saving, possibly the result of a change in fiscal policy,shifts the saving schedule to the left.The new equilibrium is the point at which the new saving schedule crossesthe investment schedule. A reductionin saving lowers the amount of investment and raises the interest rate.

A reduction in saving, possibly the result of a change in fiscal policy,shifts the saving schedule to the left.The new equilibrium is the point at which the new saving schedule crossesthe investment schedule. A reductionin saving lowers the amount of investment and raises the interest rate.

A reduction in saving, possibly the result of a change in fiscal policy,shifts the saving schedule to the left.The new equilibrium is the point at which the new saving schedule crossesthe investment schedule. A reductionin saving lowers the amount of investment and raises the interest rate.

Fiscal policy actions are said to crowd out investment.Fiscal policy actions are said to crowd out investment.

If G ,

Private saving, , is unchanged.

Public saving, , decreases.

If T , ,

Private saving increases because Y-T increases more than C increases when T is lowered because 0<MPC <1. Public saving, , decreases.

Summary: Lower taxes (T) or higher public spending (G) decreases public saving and national saving. Thereby, r increases and I decreases.

If private saving increases when the real interest rate increases, this means that private consumption decreases when the real interest rate increases as private saving plus private consumption always equals disposable income; , which is unrelated to the real interest rate in the classical model.

If national saving is unrelated to the real interest rate, a shift in the investment-curve only increases the real interest rate. A higher intercept, , which shifts the investment-curve, , outwards, happens if the firms’ expectations about the future improves.

Summary: If G and T I(r)

Main lesson: Increased government spending or lower net taxes (which implies a higher government budget deficit) increases the real interest rate and thereby lowers private investment to the same extent so that aggregate demand and output are unchanged.

When saving is positively related to the interest rate, as shown by the upward-sloping S(r) curve, a rightward shift in the investment schedule I(r), increases the interest rate and the amount of investment. The higher interest rate induces people to increasesaving, which in turn allows investment to increase.

Investment, Saving, I, S

I1

Realinterestrate, r

S(r)

I2AB

Investment, Saving, I, S

I1

Realinterestrate, r

S(r)

I2AB

I1

Realinterestrate, r

S(r)

I2AB

MATHEMATICAL TREATMENT OF KEYNESIAN MODEL IN SHORT RUN(and of the AD-curve in the PY-diagram.)Assumption: Short run: P is fixed and K is fixed more or less.2 markets:Equilibrium in the goods market: Y=C(Y-T)+I(r)+GEquilibrium in the money market: M/P=L(i,Y)Real interest rate(r) =nominal interest rate (i)-inflation rate=iNote: since P is assumed to be constant, the inflation rate is 0, and the real interest rate equals the nominal interest rate.

Assume now: planned investment depends on the real interest rate: I(r).

Thus, 3 equations and 3 endogenous variables: Y,r,i.

If reducing the equation system to 2 equations:Equilibrium in the goods market: Y=C(Y-T)+I(r)+GEquilibrium in the money market: M/P=L(r,Y)Thus, 2 equations and 2 endogenous variables: Y, r.

Section not required for A-level students:

Equilibrium in the goods market:

Before:

If I depends on r:

where d>0.

Equilibrium in the money market (and bond market):

Solving for equilibrium Y and r means that the endogenous variables Y and r are expressed as functions of the exogenous variables and parameters; that is, as functions of autonomous spending: , , , , and of real money supply, , and of the parameters: MPC, d, e, and f (which all are assumed to be positive).To do so, we substitute the equation for money market equilibrium into the equation for goods market equilibrium:

If , or MPC, or , or , or , or equilibrium Y increases.

NOTE: That the equation above also is the equation for the AD-curve: If P increases AD goes down.

Solving for equilibrium r by inserting the expression for equilibrium Y into the equation for the equation that shows equilibrium in the money market:

which can be simplified:

If , or , or , or , equilibrium r increases. If , equilibrium r decreases.

THE SMALL OPEN ECONOMY (r= ) with its own currency:The short and long run effect of monetary policyIf M (M/P) and [if L(r,Y) (= velocity) for given r and Y] r so that r<r* financial investments in domestic country turns less profitable demand for the domestic currency the nominal exchange rate, e, depreciates (e) NX, AD = (C(Y-T)+I(r*) + G + NX(( ))

Variable Old short-and long-runEquilibrium (A)

New short-runEquilibrium (B)

New long-run equilibrium (C)

Y Y0 < Y1 Y2=Y0Interest rate R0 =R1 =r2=r0I I0 =I1 =I2=i0e E0 >e1 e2=e0C C(Y0-T) <C(Y1-T) C(Y0-T)NX NX0 <nx1 Nx2=nx0P P0 =P1 <P2M/P M0/P0 <M1/P0 M0/P0

Fiscal policy (G, T) does not shift the AD-curve for a small open economy:If G (or T) r so that r>r* financial investments in domestic country turns more profitable demand for the domestic currency the nominal exchange rate, e, appreciates (e) NX, AD = (C(Y-T)+I(r*) + G + NX(( ))

Increased G or increased C(Y-T) due to lower net taxes crowds out net exports completely even in the short run.

More in-depth analysis of the short-run effect for the small open economy: 2 equations: Equilibrium in the goods market: Y = C(Y-T) + I(r*) + G + NX (e)

Equilibrium in the money market: M/P = L(r*,Y)

Assumption 1: r = r*Assumption 2: P($) and are assumed to be constant, which means that only

changes in e change

Thus, e , e ‘e=yen/dollar: e () appreciation (depreciation) of dollar Domestic goods become more expensive (cheaper) in foreign currency (Yen) and foreign goods become cheaper (more expensive) in domestic currency (dollar). Exports, Imports NX

The money market equilibrium condition: , determines the equilibrium level of output (Y). , P and are exogenously given in the model. The only endogenous variable in the LM-equation is Y, which then is determined by the exogenous variables

, and :

Ex.: The money market equilibrium condition:

If M=1000 and P=1, and , where =0.04 1000=Y-100*0.04 Y = 1000 + 4 = 1004

If M=1100 Y = 1100 + 4 = 1104 Given P and , M determines Y.Since M determines Y, fiscal policy (changes in G and T) has no effect on Y.

A monetary expansion in the standard model above:If r : r < not profitable with financial investments in our country: the demand for our currency the currency depreciates: e NX

Monetary policy has a larger impact on Y in small open economy compared to the effect in a closed economy because there is no crowding-out of private investment.

Fiscal Policy(G,T):Changes in G and T do not impact equilibrium Y (because eqb. Y is determined by the equation: :

If e.g. G aggregate demand at a given level of Y.But AD must be unchanged as is fixed.

As and also are fixed, e must increase so that NX by the same amount

that G . That is,

Why does a fiscal expansion increase e?If G aggregate demand at a given exchange rate. When aggregate demand Y real money demand domestic interest rate, r : r > profitable with financial investments in our country the demand for our currency the currency appreciates NX

(In a richer model, fiscal policy impacts Y in the short run:A currency appreciation (e) tends to make the price on imported goods and services cheaper in the domestic currency P because prices on imported goods are included in the consumer price index : Fiscal policy has an effect on Y. *Fixed exchange rates are not included in the course*The large open economy is an average of the closed economy and the small open economy. To find how any policy will impact any variable, find the answer in the 2 extreme cases and take an average.

THE CLASSICAL MODEL = THE KEYNESIAN MODEL IN THE LONG RUNThe small open economy with its own currency

Simplify by assuming that NFI=NTr=0: GDP (Y) = GNP, trade balance = current account balance

Equilibrium in the goods market:

S = GNP – C – G = I + NX

The model below is for a small open economy:For a small open economy: its real interest rate, r, equals the world interest rate,

C = C (Y-T)

I = I (r)

Y = Y = F(K,L)

NX = (Y-C-G) - I or NX = S - I

The economy’s output Y is fixed by thefactors of production and the productionfunction.Consumption is positively related to disposable income (Y-T).Investment is negatively related to thereal interest rate.The national income accounts identity,expressed in terms of saving and investment.

Now substitute our three assumptions from Chapter 3 and the conditionthat the interest rate equals the world interest rate, r*.

NX = (Y-C(Y-T) - G) - I (r*)NX = S - I (r*)

This equation suggests that the trade balance is determined by thedifference between saving and investment at the world interest rate.

S

I(r)

Investment, Saving, I, S

Real interest rate, r*

rclosed

S

I(r)

Investment, Saving, I, S

Real interest rate, r*

rclosed

r*

NX

r*

NX

In a closed economy, r adjusts to equilibrate saving and investment.In a closed economy, r adjusts to equilibrate saving and investment.

In a small open economy, the interest rate is set by worldfinancial markets. The differencebetween saving and investmentdetermines the trade balance.

In a small open economy, the interest rate is set by worldfinancial markets. The differencebetween saving and investmentdetermines the trade balance.

In this case, since r* is above rclosed and saving exceeds investment, there is a trade surplus.

r*'NX

r*'NX

If the world interest rate decreased to r* ', I would exceed S and there would be a trade deficit.

NX()

Net Exports, NX

Real exchangerate,

NX1 Net Exports, NX

Real exchangerate,

NX1 Net Exports, NX

Real exchangerate,

NX1

The fall in saving reduces the supply of dollarsto be exchanged into foreign currency, fromS1-I to S2-I. This shift raises the equilibrium realexchange rate from 1 to 2.

S1-I

The fall in saving reduces the supply of dollarsto be exchanged into foreign currency, fromS1-I to S2-I. This shift raises the equilibrium realexchange rate from 1 to 2.

S1-I

The fall in saving reduces the supply of dollarsto be exchanged into foreign currency, fromS1-I to S2-I. This shift raises the equilibrium realexchange rate from 1 to 2.

S1-I Expansionary fiscal policy at home, such as anincrease in government purchases G or a cut intaxes, reduces national saving.

A reduction in saving reducesthe supply of dollars whichcauses the real exchange rateto rise and causes net exportsto fall.

A reduction in saving reducesthe supply of dollars whichcauses the real exchange rateto rise and causes net exportsto fall.

S2-I

NX2

2

1

NX()

Net Exports, NX

Real exchangerate,

NX2

NX()

Net Exports, NX

Real exchangerate,

NX2 Net Exports, NX

Real exchangerate,

NX2 Net Exports, NX

Real exchangerate,

NX2

The increase in the world interest rate reducesinvestment at home, which in turn raises thesupply of dollars to be exchanged into foreigncurrencies.

S-I (r2*)

The increase in the world interest rate reducesinvestment at home, which in turn raises thesupply of dollars to be exchanged into foreigncurrencies.

S-I (r2*)

The increase in the world interest rate reducesinvestment at home, which in turn raises thesupply of dollars to be exchanged into foreigncurrencies.

S-I (r2*)Expansionary fiscal policy abroad reduces world saving and raises the world interest rate from r1* to r2*.

As a result, the equilibriumreal exchange rate falls from 1 to 2.

NX1

1

2

S-I(r1*)

Summary: If G and T , NX( ),

Main lesson: Increased government spending or lower net taxes (which implies a higher government budget deficit) increases the real exchange rate and thereby lowers net exports (=exports – imports) to the same extent so that aggregate demand and output are unchanged.

THE SHORT-RUN AGGREGATE SUPPLY CURVE WITH A POSITIVE SLOPE:

Labor, L

Y = F(L)

Income, Output, Y

Labor, LL = Ld (W/P)

Y=Y+(P-Pe)

rea l

wa g

e , W

/ P

Inc o

me ,

Ou t

p ut,

YPr

i ce

leve

l, P

An increase in the price level,reduces the real wage for a given

nominal wage, which raises employment and output and

income.

An increase in the price level,reduces the real wage for a given

nominal wage, which raises employment and output and

income.

Labor, L

Y = F(L)

Income, Output, Y

Labor, LL = Ld (W/P)

Y=Y+(P-Pe)

rea l

wa g

e , W

/ Pre

a l w

a ge ,

W/ P

Inc o

me ,

Ou t

p ut,

YPr

i ce

leve

l, P

An increase in the price level,reduces the real wage for a given

nominal wage, which raises employment and output and

income.

An increase in the price level,reduces the real wage for a given

nominal wage, which raises employment and output and

income.

Assume: P0=expected P0.Assume that the AD-curve shifts out:Y if W is fixed, or if the increase in aggregate demand is unexpected. If W in the next period is flexible, workers demand higher nominal wages to compensate for the unexpected fall in the real wage due to the unexpected P. In the new long-run equilibrium: P2 and , where the real wage is identical to the real wage in the old long-run equilibrium.In this long-run equilibrium the actual real wage is equal to the expected real wage.

In the short-run aggregate demand can impact Y if:*Nominal wages are flexible but workers are surprised by P so that W/P L. If W is flexible and workers are not surprised W adjust when P so that Y remains at . In figure above: the economy moves from A to B. * Nominal wages are determined by contracts. This means that even if workers are not surprised when the change in aggregate demand occurs, their real wage changes when P changes.

The SRAS-curve equals the Marginal Cost-curve (MC-curve) in micro when labor is the variable factor of production:

If L for given values of A and K MPL MC

Start at point A; the economy is at full employment Y and the actual price level is P0. Here the actual price level equals the expected price level. Now let’s suppose we increase the price level to P1. Since P (the actual price level) is now greater than Pe (the expected price level) Y will rise above the natural rate, and weslide along the SRAS (Pe=P0) curve to A' . Remember that our new SRAS (Pe=P0) curve is defined by the presence of fixed expectations (in this case at P0). So in terms of the SRAS equation, when P rises to P1, holding Pe constant at P0, Y must rise.

The “long-run” will be defined when the expected price level equals the actual price level. So, as price level expectations adjust, Pe P2, we’ll end up on a new short-run aggregate supply curve, SRAS (Pe=P2) at point B.Hooray! We made it back to LRAS, a situation characterized by perfect information where the actual price level (now P2) equals the expected price level (also, P2).

Y = Y + ( P-Pe) Y = Y + ( P-Pe) Y = Y + ( P-Pe)

Y = Y + (P-Pe)Y = Y + (P-Pe)

Y = Y + ( P- Pe)Y = Y + ( P- Pe)Y = Y + ( P- Pe)

In terms of the SRAS equation, we can see that as Pe catches up with P, that entire “expectations gap” disappears and we end up on the long run aggregate supply curve at full employment where Y = Y. In terms of the SRAS equation, we can see that as Pe catches up with P, that entire “expectations gap” disappears and we end up on the long run aggregate supply curve at full employment where Y = Y.

SRAS (Pe=P2)

BP2A'

Y'

SRAS (Pe=P0)P

Output

AP0

LRAS*

YAD

AD'

P1

SRAS (Pe=P2)

BP2A'

Y'

SRAS (Pe=P0)P

Output

AP0

LRAS*

YAD

AD'

P1

Factors that shifts the SRAS-curve?1. Higher nominal wages increases MC at given level of Y:If W Marginal cost (MC) increases at a given level of YSRAS-curve shift inwards as .The new short-run eqb. implies a higher P and a lower Y. In the long-run W will go down to the original level.

*

In response to an adverse supply shock, the monetary authorities can increase aggregate demand by increasing the nominal money supply to prevent reduction in output. The cost of this policy is a higher price level permanently. In this diagram SRAS is horizontal because I do not have the appropriate figure.

2. A higher labor productivity decreases MC at given level of Y:If A or K at given W Marginal Cost (MC) at a given level of Y because MPL=(1-alpha)*(Y/L) at given L: SRAS-curve and LRAS outwards.Maybe the SRAS-curve shifts more to the right than LRAS because in the long run W adjust upwards.Ex.1: A permanent increase in oil prices impacts energy use and thereby A. Thereby, both the SRAS and the LRAS-curves shift out.A temporary increase in oil prices only shifts the SRAS-curve. Ex.2:Globalisation increased the Y/L because of increased competition.

PP

YY

LRASLRAS

YY

ADAD

SRASSRASADAD''AA

BB

An adverse supply shock pushes up costs and prices. If AD is held constant, the economy moves from point A to point B, leading tostagflation-- a combination of increasing prices and declining output.Eventually, as prices fall, the economy returns to the natural rate at point A.

SRASSRAS''

Deriving the Phillips-curve from the Aggregate Supply Curve:

A more realistic formulation of the SRAS-curve:

Thus, if actual P > than expected P, then actual real wage < expected real wageemployment > full-employment, unemployment < the natural rate of unemployment, actual output > potential output.

Rewrite this equation in percentage terms and relate potential output to the natural rate of unemployment:

,

We have added a term, v, which is a supply chock:v is positive if oil prices go up, and is negative if oil prices go down.

There exists a short-run trade-off between inflation and unemployment. *If inflationary expectations are not rational, e.g. adaptive. Then an increase in aggregate demand and thereby a higher P can lower the real wage and thereby lower unemployment.*If inflation expectations are rational but nominal wages are fixed by nominal wage contracts.

un

Unemployment, u

e +

In the short run, inflation and unemploymentare negatively related. At any point in time, apolicymaker who controls aggregate demandcan choose a combination of inflation andunemployment on this short-run Phillipscurve.

In the short run, inflation and unemploymentare negatively related. At any point in time, apolicymaker who controls aggregate demandcan choose a combination of inflation andunemployment on this short-run Phillipscurve.

The rational expectations school says that monetary and fiscal authorities cannot systematically surprise workers. That is, they cannot systematically use the short-run trade-off between unemployment and inflation.

= -1 n) +

One example of adaptive expectations is that expected inflation equals last years inflation rate.

If the monetary policies can surprise workers and firms, e.g. if inflation expectations are adaptive, unemployment can be lowered below the natural rate in the short run.

Rational expectation school argues that the short-run Phillips curve does not accurately represent the options that policymakers have available. If policy makers are credibly committed to reducing inflation, rational people will understand the commitment and lower their expectations of inflation. Inflation can then come down without a rise in unemployment and fall in output.

Hysteris means that a recession has permanent or long-lasting effect on unemployment. That is, the long-run supply curve is not relevant.Unemployed never come back they become drunks so they will be useless in production in the future.

un

Unemployment, u

LRPC (u=un)

5%

10%

SRPC (e=0%)

SRPC (e=10%)

SRPC (e=5%)un

Unemployment, u

LRPC (u=un)

5%

10%

SRPC (e=0%)

SRPC (e=10%)

SRPC (e=5%)

Unemployment, u

LRPC (u=un)

5%

10%

SRPC (e=0%)

SRPC (e=10%)

SRPC (e=5%)

Unemployment, u

LRPC (u=un)

Unemployment, u

LRPC (u=un)

Unemployment, u

LRPC (u=un)

5%

10%

SRPC (e=0%)

SRPC (e=10%)

SRPC (e=5%)

DD

BB CC

EE

Suppose there is an increase in the rate of growth of the money supply causing LM and AD to shift out resulting in an unexpected increase in inflation. The Phillips curve equation = e – (u-un) + vimplies that the change in inflation misperceptions causes unemployment to decline. So, the economy moves to a point above full employment at point B.

AA

As long as this inflation misperception exists, the economy willremain below its natural rate un at u'.

Let’s start at point A, a point of price stability (=0%) and full employment (u=un).

When the economic agents realize the new level of inflation, they will end up on a new short-run Phillips curve where expected inflation equals the new rate of inflation (5%) at point C, where actual inflation (5%) equals expected inflation (5%).

Remember, each short-run Phillips curve is defined by the presence of fixed expectations.

If the monetary authorities opt to obtain a lower u again, then they will increase the money supply such that is 10%, for example. The economy moves to point D, where actual inflation is 10% but, e is 5%.

When expectations adjust, the economy will land on a new SRPC, at point E, where both and e equal 10%.u'u'

SHOULD STABILIZATION POLICIES BE ACTIVE OR PASSIVE? Stabilization policies consist of fiscal policy (T, G) and by monetary policy (M). The aim is to lower the variation in employment and output that arise in a market economy.

Should the government try to shift AD-curve back with e.g. fiscal policy?

The issue at stake:Should policy-makers use monetary and fiscal policy to stabilize the economy when shocks occur to aggregate demand and to aggregate supply to avoid recessions?

Some say Yes, other say No.

The view on this issue depends on ones belief on whether the politicians have the capacity or the will to stabilize the economy.

Or do they tend to destabilize the economy?: Do politicians increase the economic fluctuations rather than decrease them?

Problems with an active stabilization policy

Problem1: Lags in the implementation and effects of stabilization policies.

PP

YY

LRASLRAS

YY

ADAD

SRASSRAS

ADAD''

AABB

CC

The economy begins in long-run equilibrium at point A. A reductionin aggregate demand, perhaps caused by a decrease in the moneysupply M, moves the economy from point A to point B, where output is below its natural level. As prices fall, the economy recovers from the recession, moving from point B to point C.

The inside lag is the time between a shock to the economy and the policy action responding to that shock. This lag arises because it takes time for policymakers first to recognize that a shock has occurred and then to put appropriate policies into effect.Monetary policy has a short inside lag whereas fiscal policy has a long lag.

The outside lag is the time between a policy action and its influence on the economy. This lag arises because policies do not immediately influence spending, income, and employment.

Automatic stabilizers are fiscal policy without any inside lag.For example, in recessions taxes become lower because they are related to income. Similarly, the unemployment insurance and welfare systems automatically raise transfer payments in a recession.

Thus, if YT (= tax revenues - transfer expenditures)And if YT (= tax revenues - transfer expenditures)Thus, public saving = public budget surplus = (T- ) when Y.

Are fiscal policies expansionary or not?As public saving increase with Y, to find out whether fiscal policy are expansionary one calculate public saving at full-employment Y.If public saving is negative at full-employment Y, fiscal policies are said to be expansionary.

Problem2: Economic Forecasting is difficult and even experts have imperfect knowledge about the functioning of the economy

Problem3: “Established” Historical economic relations can change over time due to changes in the way people form expectations.Thus, it is hard to predict the future on the basis on past empirical relations.

Should monetary and fiscal policies be governed by rules or by discretion?

Policy is conducted by rule if policymakers announce in advance how policy will respond to various situations and commit themselves to this. Policy is conducted by discretion if policymakers are free to act in the way they feel appropriate at the time an event occurs.The debate over rules versus discretion is distinct from the debate over passive versus active policy. Policy can be conducted by rule yet be either passive or active. Ex.: One rule that is an active stabilization policy is the automatic stabilizers. Another rule that is an active stabilization policy is the Taylor rule.Nominal Official Interest Rate = Inflation + 2.0 + 0.5(inflation -2.0)- 0.5*GDP gap

where the GDP gap = (potential output – actual output)/potential output

The view against discretionary policy is that politicians are incompetent and/or are driven by their interest to be reelected, which might cause political business cycles.

Even if politicians are driven by a desire to stabilize the economy rather than favour their own interest, e.g. to be reelected, an argument against discretionary policies is the TIME INCONSISTENCY PROBLEM:

Policy makers announce in advance the policy they will follow in order to influence the expectations of the private decision makers.Later, after the private decision makers have acted on the basis of their expectations, policymakers may be tempted to renege on their announcement.

EX.:1. To encourage research, the government announces that it will give a temporary monopoly to companies that discover new drugs. But, after the drugs have been discovered, the government is tempted to revoke the patent to increase consumer surplus. Of course if it does, next time the government promises a patent researchers might not believe it, and devote less effort to find new drugs than they otherwise would have done.

The time inconsistency problem is the reason behind an inflation target and an independent central bank. Show in the phillipsdiagram.If the central bank does not have a target it may be tempted to exploit the short-run trade-off between unemployment and inflation in order to lower the unemployment rate in the short run. Firms and workers understand this, which leads to higher inflation expectations than would be the case with an inflation target. The end result is higher inflation, and no lower unemployment than the natural rate. If the central bank were not independent but instead run by Politicians the temptation to increase the growth rate of nominal money supply to lower the unemployment rate would be higher because politicians want to be reelected. In the long run the unemployment is at the natural rate.But, the inflation rate will be higher with politicians in charge.

MICROECONOMIC FOUNDATIONS OF CONSUMPTIONAccording to Keynesian theory the private consumption function is:

, Where T=net taxes=taxes – transfersY-T=disposable income Current private consumption depends on current disposable income.More elaborate theories say that current consumption depends not also on expected future disposable income, Wealth, and on the interest rate. For example, we expect an increase in wealth to increase current consumption at a given level of Y-T, which would increase in the equation above.

A Simple Model of Intertemporal Choice over the life-cycle.Assumptions: The individual lives 2 periods.The individual consumes in both periods and also receives incomes in both periods. The incomes are exogenously given.We assume a perfect capital market, which means that the individual can borrow and lend as much as she wants at a given interest rate.The individual receives and leaves no bequest.

Preferences are represented by the utility function: U(C1,C2)where C1=consumption in first period of life, and C2=consumption in second and last period of life. The individual values both goods (C1 and C2). The marginal utility of C1 is diminishing when C1 increases (and C2 is constant), and the marginal utility of C2 is diminishing when C2 increases (and C1 is constant).Diminishing marginal utilities implies that the individual wants to “smooth” consumption rather than consuming a lot in one period and little in the other period. The perfect capital market, which implies that the individual can lend and borrow at a given interest rate, makes consumption “smoothing” possible. A consequence of diminishing marginal utilities is that if income only is received in one period of life, the individual wants to spread this income over both periods of life. If income increases only in one period, the individual wants to spread this increase of income over both periods.

The constraints: (1) S=Y1-C1, (2) C2=(1+r)S+Y2where S = Saving in first period of life (can be negative), r=interest rate, Y1 and Y2 income net of taxes received in period 1 and in period 2. r is the real interest rate net of taxes as before. If capital or interest income is taxed, real interest rate after tax, r= (1-t)*nominal interest rate –inflation= (1-t)*(real interest rate before tax). The proportional tax rate, t, is 0.3 in Sweden.Combining the constraints (1) and (2): C2=(1+r)*(Y1-C1) + Y2The budget constraint in figure above:

Slope of the constraint:

Giving up one unit of C1 means more than one unit of C2 can be consumed because of positive return (interest) on saving. Thus, C1 is “more expensive” than C2.

The budget constraint can also be written:

Present value of life-time consumption = Present value of life-time incomeWhat is a present value? If r=0.05, the present value, x(t), of a value next year, x(t+1): e.g. 105 dollars, is the value you have to deposit in a bank today to receive 105 dollars next year. Thus, x(t)*(1+r)=x(t+1). If there is no uncertainty, and there is a perfect capital market, the individual should be indifferent between receiving 100 dollars today and receiving 105 dollars next year if the interest rate is 5 %. The intertemporal budget constraint above corresponds to our usual budget constraint that has prices in front of the quantities:

Here are the combinations of first-period and second-period consumptionthe consumer can choose. If he chooses a point between A and B, he consumes less than his income in the first period and saves the rest for the second period. If he chooses between A and C, he consumes more thathis income in the first period and borrows to make up the difference.

First-period consumption

Seco

nd-

perio

dco

nsu m

ptio

n Consumer’s budget constraintConsumer’s budget constraint

Saving

BorrowingA

C

B

Horizontal intercept isY1 + Y2/(1+r)

Horizontal intercept isY1 + Y2/(1+r)

Vertical intercept is(1+r)Y1 + Y2

Vertical intercept is(1+r)Y1 + Y2

Y1

Y2

where P1= price of current consumption=1, P2=1/(1+r)=the price of future consumption. P1>P2. Because if giving up one unit of C1, positive interest on savings means more than one unit of C2 can be consumed. Thus, C1 is more expensive than C2.

If either Y1 or Y2 , the budget constraint shifts outwards.

and because of diminishing marginal utilities. The optimal levels of C1 and

C2 depends on the present value of life-time income, :

and

Regardless of whether Y1 or Y2 increase, the consumer spread the increase in

over both periods.

If Y1 ,as the consumer wants to increase consumption in both periods.If Y2 , for the same reason. Thus, if Y2 . This result does not happen in the Keynesian model.

If the interest rate increases, C1 becomes more expensive relative to C2.The substitution effect is that you consume less of the good whose price has increased, , and more of the other good, .

For a saver: If r , a saver becomes richer: the income effect: and .The net effect (substitution + income effect): , ? , S=(Y1- )?

For a borrower:If r , a borrower becomes poorer: the income effect: and .The net effect (substitution + income effect): , S=(Y1- ), ?In aggregate an economy typically saves: r S=(Y1- )?It is often assumed that an increase in r has no or a positive effect on S.

Borrowing constraints: C1 Y1Consider an individual that consumes less than she would like in period 1:If Y1 , . That is, she uses all of the increase in Y1 for C1.

Borrowing constraints are facts of life: They should increase aggregate saving in the economy, but may be an obstacle for small-business that may have profitable investment projects that the banks might not want to lend money to because of imperfect information.The motive for saving in the intertemporal choice model is that the individual wants to smooth consumption over the life-time. If we add uncertainty to the model, people also save

Economists decompose the impact of an increase in the real interestrate on consumption into two effects: an income effect and asubstitution effect. The income effect is the change in consumptionthat results from the movement to a higher indifference curve. Thesubstitution effect is the change in consumption that results from thechange in the relative price of consumption in the two periods.

Economists decompose the impact of an increase in the real interestrate on consumption into two effects: an income effect and asubstitution effect. The income effect is the change in consumptionthat results from the movement to a higher indifference curve. Thesubstitution effect is the change in consumption that results from thechange in the relative price of consumption in the two periods.

First-period consumption

Seco

nd-

perio

dco

nsum

p tio

n

B

IC1IC2

AC

An increase in the interest rate rotates the budget constraint around the point C, where C is (Y1, Y2). The higher interest rate reduces first period consumption (move to point A) and raises second-period consumption (move to point B).

An increase in the interest rate rotates the budget constraint around the point C, where C is (Y1, Y2). The higher interest rate reduces first period consumption (move to point A) and raises second-period consumption (move to point B).

New budgetconstraint

Old budget constraint

Y1

Y2

because future income may be uncertain or because the individual might live longer than expected. This is called precautionary saving.

Modigliani’s life-cycle model, and Friedman’s permanent income hypothesis builds on the microeconomic intertemporal choice model above.

GOVERNMENT DEBT When a government spends more than it collects in taxes, it borrows from the private sector to finance the budget deficit:

Size of government debt and “fiscal sustainability”:

To compare the government debt across countries or over time it should be related to income; that is, to GDP or to GNP.When does Debt/GDP increase?If G-T =0, Debt/GDP increases if the r > growth rate of GDP

Problems in measurement:1.Debt should be measured in real terms2. Government not only has a debt but also assets. The budget procedure that accounts for assets as well as liabilities is called capital budgeting. Under capital budgeting, government borrowing to finance the purchase of a capital good would not raise the deficit.3. The government budgets deficit is countercyclical. It increases in a recession and decreases in a boom. To see whether fiscal policies are expansionary economists often calculate a cyclically-adjusted budget deficit: the government budget deficit at the full-employment output.

The intertemporal budget constraint of the government:

This intertemporal budget constraint implies that the present discounted value of net taxes must cover the present discounted value of government spending plus the initial government debt.

Lower taxes today means higher taxes in the future.Thus, an increased tax burden on future generations.

Do government budget deficits imply a tax burden on future generations?The intertemporal budget constraint of the government shows that the government can redistribute across generations. It shows e.g. that if the government lowers T1,which benefits the current generation, the government must raise future taxes, which hurts “the future generations”. Also spending :G1, G2, benefits different generations.

Some redistribution from present to future generation is optimal if the real incomesOf the future generations will be higher if there is technological growth in the economy;That is, growth in A. If there is growth in A, then Y/L will increase by the same rate in the steady state in the Solow model. Y will increase by the same rate that A increases by If G are constant over time (they won’t), and Ts are constant over the time periods, this would mean that the tax rate of future generations will fall:

T=t1*Y1=t2*Y2=t2*Y3=

where Y1<Y2<Y3<Y4, implies t1>t2>t3>t4 if T should be constant over time.

Lower-letter t is the tax rate.

From utilitarian point of view it would be socially optimal if the tax payments were higher for future generations if their incomes are higher as the utility of income is assumed to be diminshing. Redistribution of income may thus be socially optimal.

The Ricardian view on whether a tax cut can stimulate the economy:A tax cut today will mean higher future taxes for the households so that their present value of life-time income will be unchanged, so private consumption is unchanged. Households only increase their saving in response to a tax cut today. Thus, no effect on Y.

Also an increase in G will have a lower effect on Y as people realize that a higher G will imply higher taxes in the future, so households’ life-time income will go down so households will cut their consumption and increase their saving. Thus, lower effect on Y of an increase of G as people at the same time cut their consumption. Y=C+I+G.

Proponents of the Ricardian view assume that people are rational when making decisions such as choosing how much of their income to consume and how much to save. When the government borrows to pay for current spending, rational consumers look ahead to anticipate the future taxes required to support this debt.

Why the ricardian view might not hold? That is, why a tax cut today may increase current consumption even though future taxes must be higher, leaving the life-time income in present value of the consumers unchanged.1. Short-sighted consumers. 2. Borrowing constraints: The theory says that people want a smooth consumption over time to diminishing marginal utility of consumption at a particular point of time. The Ricardian view is that consumers base their spending not only on current but on their lifetime income, which includes both current and expected future income. Advocates of the traditional view of

government debt argue that current consumption is more important than lifetime income for those consumers who face borrowing constraints, which are limits on how much an individual can borrow from financial institutions.

A person who wants to consume more than his current income must borrow, for example because his current disposable income is low, e.g. for students. If he can’t borrow to finance his current consumption, his current income determines what he can consume, regardless of his future income. In this case, a debt-financed tax cut raises current income and thus consumption, even though future income is lower. 3. Also generations may not be altruistic towards their kids so they do not compensate their kids with a higher bequests to compensate for higher future taxes.

Other questions:Should the government balance the budget in every period?A budget deficit or surplus can help stabilize the economy. A balancedbudget rule would revoke the automatic stabilizing powers of the system of taxes and transfers. When the economy goes into a recession, tax receipts fall, and transfers automatically rise. Although these automatic responses help stabilize the economy, they push the budget into deficit. A strict balanced budget rule would require that the government raise taxes or reduce spending in a recession, but these actions would further depress aggregate demand.

Money supply and budget deficitsOne way to finance a budget deficit is to print more money. Money-financed budget deficits cause inflation, particularly in developing countries.

The Laffer-curve: Tax rates and total tax revenues:Government tax revenues=Tax rate*Y(L(tax rate))

If the tax rate increases tax revenues increases ceteris paribus.However, higher taxes might lower labor supply and thereby production.Laffer pointed out that government revenues actually can actually fall when tax rates are increased.

Government bonds that are indexed with inflation:The return is based on CPI, and when the principal (the price of the bond when it is issued) is repaid by government it is increased by rate of inflation.The interest rate paid on the bonds, therefore, is a real interest rate. Indexed bonds reduce the government’s incentive to produce surprise inflation to reduce the real value of its debt.Optional reading: 2-period model to show the Ricardian view:Assumptions:

(1)

if G>T, the government borrows from the public.

(2)

The government is assumed to “live” 2 periods and balance its budget over these 2 periods.Combining equations (1) and (2):

Present value of income equals present value of consumption.

The consumer maximizes by choosing C1, (and thereby S and C2) subject to the constraints: (1) S=Y1-T1-C1, (2) C2=(1+r)S+Y2-T2where S = Saving in first period of life (can be negative), r=interest rate, Y1-T1 and Y2-T2 net income received in period 1 and in period 2.Combining the constraints (1) and (2):

C2=(1+r)*(Y1-T2-C1) + Y2-T2

If the government decreases T1 to stimulate aggregate demand it must increase T2 due to the government’s intertemporal budget constraint:

because G1 and G2 are assumed to be constant.

How is private consumption (C1) impacted by the decrease of T1?The present value of the life-time income of the consumer is not affected by T1. As a result, C1 is unchanged, and Y1 is unchanged.

What is the effect on private saving of T1?

Private saving increases when T1

What is the effect on public saving? When current net taxes are lowered, public saving decreases.

There is no effect on aggregate saving, the decrease of public saving is fully compensated by an increase in private saving.

As aggregate saving is unchanged, the interest rate is unchanged, and the domestic investment is unchanged. Also C1 and C2 are unchangedwhich means that aggregate demand is not impacted.

A MATHEMATICAL EXAMPLE OF THE LIFE-CYCLE MODEL WITH COBB-DOUGLAS UTILITYThe individual/household chooses C1 (and thereby S and C2) to maximize

, where

If the individual is impatient which is a common assumption: The budget constraint of the individual is:

where r, Y1 and Y2 cannot be affected by the individual (are exogenous).

Note: The solution to the mathematical problem is such that the endogenous (the choice) variables are expressed as functions of the exogenous variables.

If , ; if Y1, if Y2.

If r , ,