Macroeconomics II Lecture 5 Chapter 10. A Real ...
Macroeconomics II Lecture 5 Krzysztof Makarski Fall 2010
Chapter 10. A Real Intertemporal Model with Investment
Intro
Now we build a two period model of the real side of the economy - this will be the base for further analysis and will be used rst for the RBC and the new Keynesian theory. The Representative Consumer
The Representative Consumer - optimal choice
We combine the work-leisure choice with the intertemporal consumption choice. The representative consumer has h units of time in each period and divides this time between work and leisure in each period. Let w denote the real wage in current period, w the real wage in future period, and r the real interest rate. The consumer pays lump sum taxes to the government of T in the current period and T in the future period. Her choice is to choose the current consumption C , future consumption C , leisure in the current and future period l and l to make herself as well of as possible given her budget constraint. The consumer's current budget constraint is C + S = w (h − l ) + π − T (10.1) the consumer's future budget constraint is C = w (h − l ) + π − T + (1 + r)S (10.2) Substituting for S from (10.1) into (10.2) and rearranging we get w (h − l ) + π − T C = w (h − l ) + π − T + (10.3) C + 1+r 1+r The representative consumer's problem is to choose (C , C , l , l ) to make herself as well o as possible given the budget constraint. Since the consumer's choice is four-dimensional we cannot depict it on a graph, but we can describe the consumer's choice in terms of three marginal conditions (we have looked at in Chapters 4 and 8): • current consumption-leisure choice M RS =w (10.4) • intertemporal consumption choice M RS =w (10.5) • future consumption-leisure choice M RS =1+r (10.6) 1
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Current Labor Supply
Increases when the current real wage increases. Recall from Chapter 4 that the impact of the real wage on the choice depends on the relative strength on the income and the substitution eect. Here we assume that the substitution eect is stronger, thus the increase in the real wage will increase labor supply. • Increases when the real interest rate increases. Consumer not only substitutes consumption intertemporally, but also substitutes intertemporally leisure. We assume that in the case of the increase of the real interest rate the substitution eect is larger than the income eect, thus when the real interest rate increases the consumer will consume less current leisure and more future leisure. So since current leisure goes up, current labor supply goes down. • Decreases when the lifetime wealth increases. Since both leisure and consumption goods are normal consumption of both increases when wealth increases. • Current Labor Supply Schedule Thus we can show the relationship between current real wage and current labor supply, see Figure 10.1. On this current labor supply schedule we can also show the eect of the increase in the real wage, see Figure 10.2 and the eect of the increase in the lifetime wealth, see Figure 10.3 •
Current Demand for Consumption Goods
Current income. Recall from Chapter 8 the relationship between current income and current consumption, Figure 10.4. • Real Interest Rate Eects We assume that the substitution eect dominates the income eect, thus when the real interest rate increases, current consumption will decrease, Figure 10.5. • Lifetime Wealth Eect. Since both leisure and consumption goods are normal consumption of both increases when wealth increases, Figure 10.6. Example of the change in lifetime wealth is a decrease of the present value of taxes. •
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Figure 10.1 The Representative Consumer’s Current Labor Supply Curve
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return Figure 10.2 An Increase in the Real Interest Rate Shifts the Current Labor Supply Curve to the Right
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Figure 10.3 Effects of an Increase in Lifetime Wealth
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return Figure 10.4 The Representative Consumer’s Current Demand for Consumption Goods Increases with Income
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Figure 10.5 An Increase in the Real Interest Rate from r1 to r2 Shifts the Demand for Consumption Goods Down
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return Figure 10.6 An Increase in Lifetime Wealth Shifts the Demand for Consumption Goods Up
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The Representative Firm
Firm's choice
Firm Choices: • Current Production In the current period the representative rm produces output according to the following production function Y = z F (K , N ) (10.7) • Future Production In the future period output is produced according to Y = z F (K , N ) (10.8) • Investment and Capital As in the Solow model we assume that the future capital stock is given by K = (1 − d)K + I (10.9) where d− depreciation rate and I − investment Since at the end of the future period there is (1 − d)K capital left, for simplicity, we assume that it is converted into consumption goods. 1
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Pro ts and Current Labor Demand • •
Current Pro ts Current pro ts are
(10.10)
π1 = Y1 − w1 N1 − I1
Future Pro ts Future pro ts are
(9.11) • The Present Value of Pro ts Pro ts are paid out to the shareholders of the rm as dividend income in each period. There is one shareholder in this economy - representative consumer, and the rm acts in the interest of this shareholder. This implies that the rm maximizes the present value of the consumers dividend income (which serves to maximize the lifetime wealth of the consumer), the rm then maximizes π (9.12) V =π + 1+r by choosing current labor demand N , future labor demand N and current investment I . • Current Employment Choice As in Chapter 4 the rm hires current labor until the current marginal product of labor equals the current real wage π2 = Y2 − w2 N2 + (1 − d)K2
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M PN = w
and the demand curve for labor in the current period is identical to the marginal product of labor, Figure 10.7 As in Chapter 4 the labor demand increases with total factor productivity z or with the initial capital stock K , Figure 10.8.
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Figure 10.7 The Demand Curve for Current Labor Is the Representative Firm’s Marginal Product of Labor Schedule
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Figure 10.8 The Current Demand Curve for Labor Shifts Due to Changes in Current Total Factor Productivity z and in the Current Capital Stock K
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The Investment Decision
The choice of investment by the representative rm involves equating the marginal cost of investment with the marginal bene t of investment. • The Marginal Cost of Investment Let M C(I) denote marginal cost of investment, then M C(I) = 1 (10.13) The marginal cost of investment is for the rm is what it gives up, in terms of the present value of pro ts, V . By investing one unit of capital in the current period it cannot sell, thus it decreases the present value of pro ts by 1. • The Marginal Bene t of Investment The marginal bene t of investment, denoted by M B(I) is what one extra unit of investment adds to the present value of pro ts. Notice all the bene ts come in terms of future pro ts π . One unit of investment, will increase capital tomorrow by one unit. And the additional output in the future period is equal to the future's marginal product of capital M P plus an additional (1 − d) units of remaining at the end of the future period. Thus one unit of investment increases future pro ts by M P + 1 − d, in calculating the marginal bene t of investment we have to discount the future gains, thus MP + 1 − d (10.14) M B(I) = 1+r • The Optimal Investment Rule The rm invests until M B(I) = M C(I) MP + 1 − d =1 (10.15) 1+r or after rearranging MP − d = r (10.16) which says that the future net marginal product of capital is equal to the interest rate. Thus the real interest rate represents the opportunity cost of investing in the representative rm. • The Optimal Investment Schedule The optimal investment schedule is the rm's future period net marginal product of capital, Figure 10.9 Also, the optimal investment schedule changes due to the following factors increases when future total factor productivity increases increases when current capital stock decreases Those changes are presented in Figure 10.10 Example: r = 5%, see Table 10.1. 2
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Investment with Asymmetric Information and the Financial Crisis •
What if a bank is not able to distinguish good and bad rms (as discussed in Chapter 9), than there will be spread. Denote r as a lending rate and if x is a default premium we will have L
and thus •
rL = r + x M PK2 − d − x = r
An increase in default premium would (if banks perceive that bad borrowers have become more prevalent) lower investments, which can be represented as a shift of an optimal investment schedule, see Figure 10.11 8
Figure 10.9 Optimal Investment Schedule for the Representative Firm
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Figure 10.10 The Optimal Investment Schedule Shifts to the Right if Current Capital Decreases or Future Total Factor Productivity Is Expected to Increase
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Table 10.1 Data for Christine’s Orchard
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return Figure 10.11 The Effect of an Increased Default Premium on a Firm’s Optimal Investment Schedule
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[PoFC] Investment and the Interest Rate Spread
Negatively correlated. • Particularly during recent nancial crisis, see Figure 10.12 and Figure 10.13 •
Government
Government
The government must satisfy its present-value budget constraint G1 +
G2 T2 = T1 + 1+r 1+r
(9.17)
Competitive Equilibrium
The Current Labor Market and the Output Supply Curve
Equilibrium in the labor market for the given real interest rate. In the labor market the real wage and employment is determined. Employment in equilibrium determines output (given the capital stock), from the production function, see Figure 10.14 • Slope of Output SupplyReal Interest Rate Eects Next suppose that the real interest rate increases from r to r , this increases labor supply, labor supply curve shifts right, this increases equilibrium employment from N to N , and output from Y to Y . Thus output increases when the real interest rate increases, see Figure 10.15 • Shifts in Output Supply Government spending Decrease in lifetime wealth increases labor supply, thus labor demand curve shifts to the right. It leads to the shift of output supply curve to the right, see Figure 10.16. An example of a decrease of lifetime wealth is the increase in government spending (which will increase taxes today or in the future). Current Total Factor Productivity (or current capital stock) An increase in total factor productivity increases labor demand, thus labor demand curve shifts, it leads nally to the shift of the output supply curve, see Figure 10.17. •
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Figure 10.12 Investment and the Interest Rate Spread
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return Figure 10.13 Scatter Plot: Investment vs. Interest Rate Spread
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Figure 10.14 Determination of Equilibrium in the Labor Market Given the Real Interest Rate r
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return Figure 10.15 Construction of the Output Supply Curve
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Figure 10.16 An Increase in Current or Future Government s Spending Shifts the Y Curve
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return Figure 10.17 An Increase in Current Total Factor Productivity s Shifts the Y Curve
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The Current Goods Market and the Output Demand Curve •
Now we turn to the goods market. The equilibrium condition in the goods market is
(10.19) In Figure 10.18 we show the total demand for goods (the right hand side of the equation (10.19)) as a function of current income. The demand for current consumption goods is determined by the intersection of the C (r) + I (r) + G curve with the 45 line. • Construction of Output DemandReal Interest Rate Eects The next step is to derive the output demand curve. Suppose that the real interest rate goes up from r to r , this increases output demand, the C (r) + I (r) + G curve shifts down, thus quantity of goods demanded falls, see Figure 10.19 • Shifts in Output Demand Curve Increase in government expenditure from G to G , then the C (r) + I (r) + G curve shifts up. Since the interest rate does not change this means that the output demand curve shifts to the right, see Figure 10.20. Also the following factors increase demand, and thus shift the C (r) + I (r) + G curve up and thus shift the output demand curve to the right. decrease in the present value of taxes (increases consumption) increase in future income (increases consumption) increase in future total factor productivity (then investment increase) decrease in the current capital stock (then investment increase) Y1 = C1d (r) + I1d (r) + G1
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The Complete Real Intertemporal Model
We have all building blocks for our real intertemporal model. Model is presented in Figure 10.21 which presents market clearing in the labor market (panel (a)), and in the goods market (panel (b)). • Next we perform experiments to see how changes in exogenous variables changes the equilibrium in our economy.
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A Temporary Increase in Government Purchases
Direct eect of an increase in G
See Figure 10.22, AB is equal to BF (45 line). • The vertical distance DF between lines is equal to ∆G − M P C∆G = (1 − M P C) ∆G, where ∆G is an increase in demand due to higher gov. expenditure and M P C∆G is a decline in current consumption from a fall in current wealth by ∆G due to higher future taxes (Ricardian equivalence must hold) = M P C or = M P C (assume • Increase in income by AB increases consumption by DB thus M P C is constant). Substituting = M P C and solving gives ∆Y = ∆G. return
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Figure 10.18 The Demand for Current Goods
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return Figure 10.19 Construction of the Output Demand Curve
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Figure 10.20 The Output Demand Curve Shifts to the Right if Current Government Spending Increases
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return Figure 10.21 The Complete Real Intertemporal Model
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A Temporary Increase in Government Purchases
Impact Eects As government spending go up, present value of taxes goes up, thus consumers decrease consumption of both leisure and consumption goods, thus labor supply goes up (N curve shifts right). Furthermore we know that a decrease in consumption of consumption goods (recall M P C < 1) the demand for current consumption goods falls by less than government purchases rise. Therefore the total demand for goods must rise (so Y curve shifts right). See Figure 10.22 and Figure 10.23 Labor Supply goes up (G goes up, thus taxes will go up, thus wealth goes down). Output Supply goes up (since Labor Supply shifts). Output Demand goes up (see above). • Equilibrium Eects Goods Market: Y %, r % Labor Market: N %, w & The Composition of Output: C &, I & ∗ Government multiplier: Since - as shown ealier - Y shifts by exactly ∆G nally income due to increase in the interest rate - increses by less then the initial increase in G, thus the gov. multplier is smaller than 1. ∗ Notice that an initial decline in consumption equal to M P C∆G - as shown ealier - is not oset by an increase in consumption due to an increse in income, since income goes up by less than ∆G and thus consumption - due to increase in income goes up by less than M P C∆G, so overall consumption falls. ∗ Notice that in equilibrium the interest rate increased, which decreased investment.
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Gov Multiplier
Its value is debated. New classicals (Barro) argue it's less than 1, while Keynesians (Ch. Romer) claim it's larger than one. • Romer's estimate is based on models not immune to Lucas critique (not based on micro foundations) • In our model multiplier generally is smaller than one, but can get higher with: government spending nanced with borrowing when Ricardian equivalence does not hold (e.g. consumers are credit constrained). decline in lifetime wealth (due to higher future taxes) increases labor supply atter Y curve (high response of labor supply to changes in the interest rate) First two points are more likely during a credit crunch. • To have a fully developed new Keynesian argument we need the fully developed new Keynesian model (soon). •
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Figure 10.22 The Effect of an Increase in G on the Total Demand for Goods
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return1return2 Figure 10.23 A Temporary Increase in Government Purchases
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An Increase in Current Total Factor Productivity
An Increase in Current Total Factor Productivity
Impact Eects, See Figure 10.25 Labor Demand (since M P goes up) Output Supply (since labor demand shifts) • Equilibrium Eects Note: as the interest rate goes up (see panel b. on Figure 10.25) the labor supply curve shifts left (see panel a. on Figure 10.25) Goods Market: Y %, r & Labor Market: N ? (likely increases),w % The Composition of Output: C %, I % (since output goes up and the interest rate goes down) •
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An Increase in Future Total Factor Productivity
An Increase in Future Total Factor Productivity
Impact Eects, see Figure 10.26 Output Demand (since investments go up) • Equilibrium Eects Goods Market: Y %, r % Labor Market: N %, w & The Composition of Output: C &, I % •
An Increase in Credit Market Uncertainty:
Asymmetric Information and the
Financial Crisis
An Increase in Credit Market Uncertainty
Source: Asymmetric Information and the Financial Crisis; focus on rms. • An increase in credit market uncertainty leads to an increase in credit rate spreads, thus given any initial lending rate (or central bank interest rate) borrowing rates for rms go up, thus the investments go down, Y curve shifts left. The rest is like for the negative supply shock. • Impact Eects, see Figure 10.28 Labor Supply Output Demand • Equilibrium Eects Goods Market: Y &, r & Labor Market: N &, w % The Composition of Output: C %, I & •
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Figure 10.25 The Equilibrium Effects of an Increase in Current Total Factor Productivity
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return Figure 10.26 The Equilibrium Effects of an Increase in Future Total Factor Productivity
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Summary
Derived a Complete Real Model of the Economy labor market goods market • Performed experiments with eects of dierent shocks. government expenditure (gov. multiplier) current TFP shock future TFP shock •
Reading
Williamson, Chapter 10.
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Figure 10.28 The Effect of an Increase in Credit Market Risk
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Chapter 10. A Real Intertemporal Model with Investment
Intro
Now we build a two period model of the real side of the economy - this will be the base for further analysis and will be used rst for the RBC and the new Keynesian theory. The Representative Consumer
The Representative Consumer - optimal choice
We combine the work-leisure choice with the intertemporal consumption choice. The representative consumer has h units of time in each period and divides this time between work and leisure in each period. Let w denote the real wage in current period, w the real wage in future period, and r the real interest rate. The consumer pays lump sum taxes to the government of T in the current period and T in the future period. Her choice is to choose the current consumption C , future consumption C , leisure in the current and future period l and l to make herself as well of as possible given her budget constraint. The consumer's current budget constraint is C + S = w (h − l ) + π − T (10.1) the consumer's future budget constraint is C = w (h − l ) + π − T + (1 + r)S (10.2) Substituting for S from (10.1) into (10.2) and rearranging we get w (h − l ) + π − T C = w (h − l ) + π − T + (10.3) C + 1+r 1+r The representative consumer's problem is to choose (C , C , l , l ) to make herself as well o as possible given the budget constraint. Since the consumer's choice is four-dimensional we cannot depict it on a graph, but we can describe the consumer's choice in terms of three marginal conditions (we have looked at in Chapters 4 and 8): • current consumption-leisure choice M RS =w (10.4) • intertemporal consumption choice M RS =w (10.5) • future consumption-leisure choice M RS =1+r (10.6) 1
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Current Labor Supply
Increases when the current real wage increases. Recall from Chapter 4 that the impact of the real wage on the choice depends on the relative strength on the income and the substitution eect. Here we assume that the substitution eect is stronger, thus the increase in the real wage will increase labor supply. • Increases when the real interest rate increases. Consumer not only substitutes consumption intertemporally, but also substitutes intertemporally leisure. We assume that in the case of the increase of the real interest rate the substitution eect is larger than the income eect, thus when the real interest rate increases the consumer will consume less current leisure and more future leisure. So since current leisure goes up, current labor supply goes down. • Decreases when the lifetime wealth increases. Since both leisure and consumption goods are normal consumption of both increases when wealth increases. • Current Labor Supply Schedule Thus we can show the relationship between current real wage and current labor supply, see Figure 10.1. On this current labor supply schedule we can also show the eect of the increase in the real wage, see Figure 10.2 and the eect of the increase in the lifetime wealth, see Figure 10.3 •
Current Demand for Consumption Goods
Current income. Recall from Chapter 8 the relationship between current income and current consumption, Figure 10.4. • Real Interest Rate Eects We assume that the substitution eect dominates the income eect, thus when the real interest rate increases, current consumption will decrease, Figure 10.5. • Lifetime Wealth Eect. Since both leisure and consumption goods are normal consumption of both increases when wealth increases, Figure 10.6. Example of the change in lifetime wealth is a decrease of the present value of taxes. •
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Figure 10.1 The Representative Consumer’s Current Labor Supply Curve
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return Figure 10.2 An Increase in the Real Interest Rate Shifts the Current Labor Supply Curve to the Right
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Figure 10.3 Effects of an Increase in Lifetime Wealth
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return Figure 10.4 The Representative Consumer’s Current Demand for Consumption Goods Increases with Income
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Figure 10.5 An Increase in the Real Interest Rate from r1 to r2 Shifts the Demand for Consumption Goods Down
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return Figure 10.6 An Increase in Lifetime Wealth Shifts the Demand for Consumption Goods Up
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The Representative Firm
Firm's choice
Firm Choices: • Current Production In the current period the representative rm produces output according to the following production function Y = z F (K , N ) (10.7) • Future Production In the future period output is produced according to Y = z F (K , N ) (10.8) • Investment and Capital As in the Solow model we assume that the future capital stock is given by K = (1 − d)K + I (10.9) where d− depreciation rate and I − investment Since at the end of the future period there is (1 − d)K capital left, for simplicity, we assume that it is converted into consumption goods. 1
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Pro ts and Current Labor Demand • •
Current Pro ts Current pro ts are
(10.10)
π1 = Y1 − w1 N1 − I1
Future Pro ts Future pro ts are
(9.11) • The Present Value of Pro ts Pro ts are paid out to the shareholders of the rm as dividend income in each period. There is one shareholder in this economy - representative consumer, and the rm acts in the interest of this shareholder. This implies that the rm maximizes the present value of the consumers dividend income (which serves to maximize the lifetime wealth of the consumer), the rm then maximizes π (9.12) V =π + 1+r by choosing current labor demand N , future labor demand N and current investment I . • Current Employment Choice As in Chapter 4 the rm hires current labor until the current marginal product of labor equals the current real wage π2 = Y2 − w2 N2 + (1 − d)K2
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M PN = w
and the demand curve for labor in the current period is identical to the marginal product of labor, Figure 10.7 As in Chapter 4 the labor demand increases with total factor productivity z or with the initial capital stock K , Figure 10.8.
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Figure 10.7 The Demand Curve for Current Labor Is the Representative Firm’s Marginal Product of Labor Schedule
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return
Figure 10.8 The Current Demand Curve for Labor Shifts Due to Changes in Current Total Factor Productivity z and in the Current Capital Stock K
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The Investment Decision
The choice of investment by the representative rm involves equating the marginal cost of investment with the marginal bene t of investment. • The Marginal Cost of Investment Let M C(I) denote marginal cost of investment, then M C(I) = 1 (10.13) The marginal cost of investment is for the rm is what it gives up, in terms of the present value of pro ts, V . By investing one unit of capital in the current period it cannot sell, thus it decreases the present value of pro ts by 1. • The Marginal Bene t of Investment The marginal bene t of investment, denoted by M B(I) is what one extra unit of investment adds to the present value of pro ts. Notice all the bene ts come in terms of future pro ts π . One unit of investment, will increase capital tomorrow by one unit. And the additional output in the future period is equal to the future's marginal product of capital M P plus an additional (1 − d) units of remaining at the end of the future period. Thus one unit of investment increases future pro ts by M P + 1 − d, in calculating the marginal bene t of investment we have to discount the future gains, thus MP + 1 − d (10.14) M B(I) = 1+r • The Optimal Investment Rule The rm invests until M B(I) = M C(I) MP + 1 − d =1 (10.15) 1+r or after rearranging MP − d = r (10.16) which says that the future net marginal product of capital is equal to the interest rate. Thus the real interest rate represents the opportunity cost of investing in the representative rm. • The Optimal Investment Schedule The optimal investment schedule is the rm's future period net marginal product of capital, Figure 10.9 Also, the optimal investment schedule changes due to the following factors increases when future total factor productivity increases increases when current capital stock decreases Those changes are presented in Figure 10.10 Example: r = 5%, see Table 10.1. 2
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Investment with Asymmetric Information and the Financial Crisis •
What if a bank is not able to distinguish good and bad rms (as discussed in Chapter 9), than there will be spread. Denote r as a lending rate and if x is a default premium we will have L
and thus •
rL = r + x M PK2 − d − x = r
An increase in default premium would (if banks perceive that bad borrowers have become more prevalent) lower investments, which can be represented as a shift of an optimal investment schedule, see Figure 10.11 8
Figure 10.9 Optimal Investment Schedule for the Representative Firm
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return
Figure 10.10 The Optimal Investment Schedule Shifts to the Right if Current Capital Decreases or Future Total Factor Productivity Is Expected to Increase
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return 9
Table 10.1 Data for Christine’s Orchard
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return Figure 10.11 The Effect of an Increased Default Premium on a Firm’s Optimal Investment Schedule
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return 10
[PoFC] Investment and the Interest Rate Spread
Negatively correlated. • Particularly during recent nancial crisis, see Figure 10.12 and Figure 10.13 •
Government
Government
The government must satisfy its present-value budget constraint G1 +
G2 T2 = T1 + 1+r 1+r
(9.17)
Competitive Equilibrium
The Current Labor Market and the Output Supply Curve
Equilibrium in the labor market for the given real interest rate. In the labor market the real wage and employment is determined. Employment in equilibrium determines output (given the capital stock), from the production function, see Figure 10.14 • Slope of Output SupplyReal Interest Rate Eects Next suppose that the real interest rate increases from r to r , this increases labor supply, labor supply curve shifts right, this increases equilibrium employment from N to N , and output from Y to Y . Thus output increases when the real interest rate increases, see Figure 10.15 • Shifts in Output Supply Government spending Decrease in lifetime wealth increases labor supply, thus labor demand curve shifts to the right. It leads to the shift of output supply curve to the right, see Figure 10.16. An example of a decrease of lifetime wealth is the increase in government spending (which will increase taxes today or in the future). Current Total Factor Productivity (or current capital stock) An increase in total factor productivity increases labor demand, thus labor demand curve shifts, it leads nally to the shift of the output supply curve, see Figure 10.17. •
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Figure 10.12 Investment and the Interest Rate Spread
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return Figure 10.13 Scatter Plot: Investment vs. Interest Rate Spread
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return 12
Figure 10.14 Determination of Equilibrium in the Labor Market Given the Real Interest Rate r
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return Figure 10.15 Construction of the Output Supply Curve
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Figure 10.16 An Increase in Current or Future Government s Spending Shifts the Y Curve
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return Figure 10.17 An Increase in Current Total Factor Productivity s Shifts the Y Curve
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The Current Goods Market and the Output Demand Curve •
Now we turn to the goods market. The equilibrium condition in the goods market is
(10.19) In Figure 10.18 we show the total demand for goods (the right hand side of the equation (10.19)) as a function of current income. The demand for current consumption goods is determined by the intersection of the C (r) + I (r) + G curve with the 45 line. • Construction of Output DemandReal Interest Rate Eects The next step is to derive the output demand curve. Suppose that the real interest rate goes up from r to r , this increases output demand, the C (r) + I (r) + G curve shifts down, thus quantity of goods demanded falls, see Figure 10.19 • Shifts in Output Demand Curve Increase in government expenditure from G to G , then the C (r) + I (r) + G curve shifts up. Since the interest rate does not change this means that the output demand curve shifts to the right, see Figure 10.20. Also the following factors increase demand, and thus shift the C (r) + I (r) + G curve up and thus shift the output demand curve to the right. decrease in the present value of taxes (increases consumption) increase in future income (increases consumption) increase in future total factor productivity (then investment increase) decrease in the current capital stock (then investment increase) Y1 = C1d (r) + I1d (r) + G1
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The Complete Real Intertemporal Model
We have all building blocks for our real intertemporal model. Model is presented in Figure 10.21 which presents market clearing in the labor market (panel (a)), and in the goods market (panel (b)). • Next we perform experiments to see how changes in exogenous variables changes the equilibrium in our economy.
•
A Temporary Increase in Government Purchases
Direct eect of an increase in G
See Figure 10.22, AB is equal to BF (45 line). • The vertical distance DF between lines is equal to ∆G − M P C∆G = (1 − M P C) ∆G, where ∆G is an increase in demand due to higher gov. expenditure and M P C∆G is a decline in current consumption from a fall in current wealth by ∆G due to higher future taxes (Ricardian equivalence must hold) = M P C or = M P C (assume • Increase in income by AB increases consumption by DB thus M P C is constant). Substituting = M P C and solving gives ∆Y = ∆G. return
•
o
∆Y −(1−M P C)∆G ∆Y
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DB AB
AB−DF AB
Figure 10.18 The Demand for Current Goods
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return Figure 10.19 Construction of the Output Demand Curve
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Figure 10.20 The Output Demand Curve Shifts to the Right if Current Government Spending Increases
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return Figure 10.21 The Complete Real Intertemporal Model
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A Temporary Increase in Government Purchases
Impact Eects As government spending go up, present value of taxes goes up, thus consumers decrease consumption of both leisure and consumption goods, thus labor supply goes up (N curve shifts right). Furthermore we know that a decrease in consumption of consumption goods (recall M P C < 1) the demand for current consumption goods falls by less than government purchases rise. Therefore the total demand for goods must rise (so Y curve shifts right). See Figure 10.22 and Figure 10.23 Labor Supply goes up (G goes up, thus taxes will go up, thus wealth goes down). Output Supply goes up (since Labor Supply shifts). Output Demand goes up (see above). • Equilibrium Eects Goods Market: Y %, r % Labor Market: N %, w & The Composition of Output: C &, I & ∗ Government multiplier: Since - as shown ealier - Y shifts by exactly ∆G nally income due to increase in the interest rate - increses by less then the initial increase in G, thus the gov. multplier is smaller than 1. ∗ Notice that an initial decline in consumption equal to M P C∆G - as shown ealier - is not oset by an increase in consumption due to an increse in income, since income goes up by less than ∆G and thus consumption - due to increase in income goes up by less than M P C∆G, so overall consumption falls. ∗ Notice that in equilibrium the interest rate increased, which decreased investment.
•
s
d
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Gov Multiplier
Its value is debated. New classicals (Barro) argue it's less than 1, while Keynesians (Ch. Romer) claim it's larger than one. • Romer's estimate is based on models not immune to Lucas critique (not based on micro foundations) • In our model multiplier generally is smaller than one, but can get higher with: government spending nanced with borrowing when Ricardian equivalence does not hold (e.g. consumers are credit constrained). decline in lifetime wealth (due to higher future taxes) increases labor supply atter Y curve (high response of labor supply to changes in the interest rate) First two points are more likely during a credit crunch. • To have a fully developed new Keynesian argument we need the fully developed new Keynesian model (soon). •
s
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Figure 10.22 The Effect of an Increase in G on the Total Demand for Goods
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return1return2 Figure 10.23 A Temporary Increase in Government Purchases
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An Increase in Current Total Factor Productivity
An Increase in Current Total Factor Productivity
Impact Eects, See Figure 10.25 Labor Demand (since M P goes up) Output Supply (since labor demand shifts) • Equilibrium Eects Note: as the interest rate goes up (see panel b. on Figure 10.25) the labor supply curve shifts left (see panel a. on Figure 10.25) Goods Market: Y %, r & Labor Market: N ? (likely increases),w % The Composition of Output: C %, I % (since output goes up and the interest rate goes down) •
N
An Increase in Future Total Factor Productivity
An Increase in Future Total Factor Productivity
Impact Eects, see Figure 10.26 Output Demand (since investments go up) • Equilibrium Eects Goods Market: Y %, r % Labor Market: N %, w & The Composition of Output: C &, I % •
An Increase in Credit Market Uncertainty:
Asymmetric Information and the
Financial Crisis
An Increase in Credit Market Uncertainty
Source: Asymmetric Information and the Financial Crisis; focus on rms. • An increase in credit market uncertainty leads to an increase in credit rate spreads, thus given any initial lending rate (or central bank interest rate) borrowing rates for rms go up, thus the investments go down, Y curve shifts left. The rest is like for the negative supply shock. • Impact Eects, see Figure 10.28 Labor Supply Output Demand • Equilibrium Eects Goods Market: Y &, r & Labor Market: N &, w % The Composition of Output: C %, I & •
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Figure 10.25 The Equilibrium Effects of an Increase in Current Total Factor Productivity
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return Figure 10.26 The Equilibrium Effects of an Increase in Future Total Factor Productivity
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Summary
Derived a Complete Real Model of the Economy labor market goods market • Performed experiments with eects of dierent shocks. government expenditure (gov. multiplier) current TFP shock future TFP shock •
Reading
Williamson, Chapter 10.
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Figure 10.28 The Effect of an Increase in Credit Market Risk
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