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C h a p t e r 8. An Equilibrium Business-Cycle Model. Cyclical Behavior of Real GDP—Recessions and Booms. Real GDP = trend real GDP + cyclical part of real GDP Cyclical part of real GDP Coming from the business cycle Short-term economic fluctuations.

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C h a p t e r 8

An Equilibrium Business-Cycle Model

Macroeconomics Chapter 8

cyclical behavior of real gdp recessions and booms
Cyclical Behavior of Real GDP—Recessions and Booms
  • Real GDP =

trend real GDP + cyclical part of real GDP

  • Cyclical part of real GDP
    • Coming from the business cycle
    • Short-term economic fluctuations.

Macroeconomics Chapter 8

an equilibrium business cycle model
An Equilibrium Business-Cycle Model

Macroeconomics Chapter 8

an equilibrium business cycle model1
An Equilibrium Business-Cycle Model
  • Conceptual Issues
    • Assuming that these fluctuations reflect shocks to the economy.
      • Change in level of technology
        • Y= A·F( K, L)
      • An increase in A means that the economy is more productive.
      • A decrease in A means that the economy is less productive.

Macroeconomics Chapter 8

an equilibrium business cycle model2
An Equilibrium Business-Cycle Model
  • Uses equilibrium conditions to determine how the shocks affect real GDP, Y, and other macroeconomic variables, such as consumption, C, investment, I, and the quantity of labor input, L.
      • RBC model
      • Finn Kydland & Edward Prescott (2004 Nobel Laureates)

Macroeconomics Chapter 8

an equilibrium business cycle model3
An Equilibrium Business-Cycle Model
  • The Model
    • Y= A·F( K, L)
      • the capital stock, K, as fixed in the short run,
      • the labor input, L, is fixed.
    • Changes in Y will reflect only changes in A.
      • When A rises, Y rises,
      • When A falls, Y falls.

Macroeconomics Chapter 8

an equilibrium business cycle model4
An Equilibrium Business-Cycle Model
  • The Model
    • The marginal product of labor and the real wage rate
      • An increase in the technology level, A, raises the marginal product of labor, MPL, for given inputs of capital, K, and labor, L.

Macroeconomics Chapter 8

an equilibrium business cycle model5
An Equilibrium Business-Cycle Model

Macroeconomics Chapter 8

an equilibrium business cycle model6
An Equilibrium Business-Cycle Model

Macroeconomics Chapter 8

an equilibrium business cycle model7
An Equilibrium Business-Cycle Model
  • The Model
    • Marginal product of capital, real rental price, and the interest rate
      • An increase in the technology level, A, raises the marginal product of capital, MPK, for given inputs of capital, K, and labor, L

Macroeconomics Chapter 8

an equilibrium business cycle model8
An Equilibrium Business-Cycle Model

Macroeconomics Chapter 8

an equilibrium business cycle model9
An Equilibrium Business-Cycle Model

Macroeconomics Chapter 8

an equilibrium business cycle model10
An Equilibrium Business-Cycle Model
  • Marginal product of capital, real rental price, and the interest rate
    • i = R/P − δ
    • i = MPK(evaluated at given K and L) − δ
  • The model predicts that an economic boom will have a relatively high interest rate, whereas a recession will have a relatively low interest rate.

Macroeconomics Chapter 8

an equilibrium business cycle model11
An Equilibrium Business-Cycle Model
  • Consumption, saving, and investment
    • Aggregate household budget constraint
      • Given the markets for bonds, labor, and capital services clear:
    • C + ∆K = Y − δ K

Macroeconomics Chapter 8

an equilibrium business cycle model12
An Equilibrium Business-Cycle Model
  • C+∆K = A ·F( K, L) −δ K
    • depreciation, δK, is fixed in the short run,
    • An increase in A raises real GDP for given K and L, we see that a rise in A raises overall real income.

Macroeconomics Chapter 8

an equilibrium business cycle model13
An Equilibrium Business-Cycle Model
  • Consumption, saving, and investment
    • income effect:

The increase in real income motivates

households to raise current consumption and

future consumption.

    • Intertemporal-substitution effect:

The increase in the interest rate tends to

reduce current consumption.

    • The net change depends on whether the income effect is stronger or weaker than the intertemporal-substitution effect.

Macroeconomics Chapter 8

an equilibrium business cycle model14
An Equilibrium Business-Cycle Model
  • Consumption, saving, and investment
    • Assume that the change in A is permanent.
      • the increases in real income tend also to be permanent.
    • The propensity to consume out of higher income would be close to one.
    • When the increase in A is permanent, current consumption will rise. However, as long as the intertemporal-substitution operates at all, the increase in current consumption will be less than the increase in real GDP.

Macroeconomics Chapter 8

an equilibrium business cycle model15
An Equilibrium Business-Cycle Model
  • Consumption, saving, and investment
    • Since current consumption, C, rises, but by less than the increase in real GDP, Y. Therefore, net investment, ∆K, must increase - the increase in real GDP shows up partly as more C and partly as more K.
    • Since net investment, K, equals real saving, this result is consistent with our finding that real saving increased.

Macroeconomics Chapter 8

matching the theory with the facts
Matching the Theory with the Facts
  • Consumption and Investment
    • When a variable fluctuates in the same direction as real GDP that variable is procyclical.
      • A procyclical variable moves in the same direction as the business cycle—it tends to be high relative to its trend in a boom and low relative to its trend in a recession.

Macroeconomics Chapter 8

matching the theory with the facts1
Matching the Theory with the Facts
  • Consumption and Investment
    • A variable that fluctuates in the opposite direction from real GDP is countercyclical.
    • One that has little tendency to move in a particular direction during a business cycle is acyclical.

Macroeconomics Chapter 8

matching the theory with the facts2
Matching the Theory with the Facts

Macroeconomics Chapter 8

matching the theory with the facts3
Matching the Theory with the Facts

Macroeconomics Chapter 8

matching the theory with the facts4
Matching the Theory with the Facts
  • Consumption and Investment
    • Permanent shifts in the technology level, A, match up with some of the empirical patterns
      • Increases in A generate economic booms, where real GDP increases, consumption and investment increases.
      • Decreases in A create recessions, where real GDP, consumption, and investment all decline.

Macroeconomics Chapter 8

matching the theory with the facts5
Matching the Theory with the Facts
  • The Real Wage Rate
    • The model predicts that the real wage rate, w/P, will be relatively high in booms and relatively low in recessions.

Macroeconomics Chapter 8

matching the theory with the facts6
Matching the Theory with the Facts

Macroeconomics Chapter 8

matching the theory with the facts7
Matching the Theory with the Facts
  • The Real Rental Price
    • The model predicts that the real rental price of capital, R/P, will be relatively high in booms and relatively low in recessions.

Macroeconomics Chapter 8

matching the theory with the facts8
Matching the Theory with the Facts

Macroeconomics Chapter 8

matching the theory with the facts9
Matching the Theory with the Facts
  • The Interest Rate
    • The model predicts that booms will have a high interest rate, i, whereas recessions will have a low interest rate.

Macroeconomics Chapter 8

temporary changes in the technology level
Temporary Changes in the Technology Level
  • A decrease in A due toa harvest failure or a general strike would be temporary.
  • To allow for these cases, we now assume that the change in A is temporary.

Macroeconomics Chapter 8

temporary changes in the technology level1
Temporary Changes in the Technology Level
  • If A increases temporarily, real GDP, A ·F (K, L), still rises for fixed values of K and L.
  • The marginal product of capital, MPK, and the interest rate, i, also rise as before.
  • The intertemporal-substitution effect from the higher i still motivates households to reduce current consumption, C, and raise current real saving.

Macroeconomics Chapter 8

temporary changes in the technology level2
Temporary Changes in the Technology Level
  • The model therefore predicts that economic boom would feature high real GDP and investment.
    • Consumption would rise by a small amount.
  • A recession would have low real GDP and investment.
    • Consumption would decline by a modest amount.

Macroeconomics Chapter 8

variations in labor input
Variations in Labor Input
  • Labor Supply
    • More labor supplied means less leisure time for the family.
    • Assume that households also like more leisure time.
    • As with consumption and saving, the choice of Lsinvolves substitution and income effects.

Macroeconomics Chapter 8

variations in labor input1
Variations in Labor Input
  • The substitution effect for leisure and consumption
    • If the household chooses to work one more hour and thereby have one less hour of leisure, the extra w/P of real wage income pays for w/P more units of consumption.
    • Therefore, the household can substitute one less hour of leisure for w/P more units of consumption.

Macroeconomics Chapter 8

variations in labor input2
Variations in Labor Input
  • The substitution effect for leisure and consumption
    • If w/P rises, the household gets a better deal by working more because it gets more consumption for each extra hour worked. Since the deal is better, we predict that the household responds to a higher w/P by working more.

Macroeconomics Chapter 8

variations in labor input3
Variations in Labor Input
  • The substitution effect for leisure and consumption
    • A higher real wage rate, w/P, raises the quantity of labor supplied, Ls

Macroeconomics Chapter 8

variations in labor input4
Variations in Labor Input
  • Income effects on labor supply
    • A higher w/P means higher real wage income, (w/P)·Ls
    • Household spends the extra income on consumption and leisure time.
    • A higher w/P leads to a smaller quantity of labor supplied, Ls.

Macroeconomics Chapter 8

variations in labor input5
Variations in Labor Input
  • Income effects on labor supply
    • Resolve the ambiguity by considering whether the income effect is strong or weak
    • C1 + C2/(1+i1) + C3/[( 1+i1)·(1+i2) ] + ···

= (1 + i0)·(B0/P+K0) +

(w/P)1·Ls1+(w/P)2·Ls2/(1+i1) +

(w/P)3·Ls3 /[(1+i1)·(1+i2)]+ ···

Macroeconomics Chapter 8

variations in labor input6
Variations in Labor Input
  • Income effects on labor supply
    • A permanent increase in real wage rates results in a large income effect.
    • If the change in year 1’s real wage rate, (w/P)1, is temporary, the income effect is small.
    • The income effect will be weaker than the substitution effect.

Macroeconomics Chapter 8

variations in labor input7
Variations in Labor Input
  • Intertemporal-substitution effects on labor supply
    • C1 + C2/(1+i1) + C3/[( 1+i1)·(1+i2) ] + ···

= ( 1 + i0)·(B0/P+K0) +

(w/P)1·Ls1+(w/P)2·Ls2/(1+i1) +

(w/P)3·Ls3 /[(1+i1)·(1+i2)]

+ ···

Macroeconomics Chapter 8

variations in labor input8
Variations in Labor Input
  • Intertemporal-substitution effects on labor supply.
    • If the interest rate, i1, rises, a unit of year2’s real wage income, (w/P)2·Ls2, becomes less valuable as a present value compared to a unit of year1’s real wage income, (w/P)1·Ls 1.
    • We therefore predict that the household would increase Ls1 and decrease Ls2as the interest rate increases.

Macroeconomics Chapter 8

variations in labor input9
Variations in Labor Input

Macroeconomics Chapter 8

variations in labor input10
Variations in Labor Input
  • Fluctuations in Labor Input
    • Measures of labor input are procyclical: they move in the same direction as real GDP during booms and recessions.
      • Employment
      • Total hours worked

Macroeconomics Chapter 8

variations in labor input11
Variations in Labor Input

Macroeconomics Chapter 8

variations in labor input12
Variations in Labor Input
  • The cyclical behavior of labor input: theory
    • Increase in A will lead to:
      • The real wage rate increases
      • Labor inputs increase.

Macroeconomics Chapter 8

variations in labor input13
Variations in Labor Input

Macroeconomics Chapter 8

variations in labor input14
Variations in Labor Input
  • The cyclical behavior of labor productivity
    • Measures of labor productivity,
      • Y/L, is real GDP per worker,
      • Real GDP per worker-hour.
      • Labor productivity turns out to be procyclical in both cases.

Macroeconomics Chapter 8

extra labor supply model
Extra:labor supply model
  • For simplicity: the household has only one member and he lives only for one period and has no initial wealth.
  • FOC:

Macroeconomics Chapter 8

extra labor supply model1
Extra:labor supply model
  • Intuition:

In one period, the income and substitution effects of a change in the wage offset each other.

Macroeconomics Chapter 8

extra labor supply model2
Extra:labor supply model

Two periods:

FOC:

Macroeconomics Chapter 8

extra labor supply model3
Extra:labor supply model

Intuition: intertemporal substitution in labor supply

Macroeconomics Chapter 8

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