In this chapter, you will learn… C H A P T E R 3 . what determines the economy’s total output/income National Income: . how the prices of the factors of production are Where it Comes From determined and Where it Goes . how total income is distributed . what determines the demand for goods and MACROECONOMICS SIXTH EDITION services N. GREGORY MANKIW . how equilibrium in the goods market is achieved PowerPoint® Slides by Ron Cronovich

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Outline of model Factors of production

A closed economy, market-clearing model K = capital: Supply side tools, machines, and structures used in . factor markets (supply, demand, price) production . determination of output/income Demand side L = labor: . determinants of C, I, and G the physical and mental efforts of workers Equilibrium . goods market . loanable funds market

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The production function Returns to scale: A review

Initially Y1 = F (K1 , L1 ) . denoted Y = F(K, L) Scale all inputs by the same factor z: . shows how much output (Y ) the economy can produce from K2 = zK1 and L2 = zL1

K units of capital and L units of labor (e.g., if z = 1.25, then all inputs are increased by 25%)

. reflects the economy’s level of technology What happens to output, Y2 = F (K2, L2 )?

. exhibits constant returns to scale . If constant returns to scale, Y2 = zY1

. If increasing returns to scale, Y2 > zY1

. If decreasing returns to scale, Y2 < zY1

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1 Example 1 Now you try…

F(K,L) = KL . Determine whether constant, decreasing, or increasing returns to scale for each of these F(zK,zL) = (zK)(zL) production functions: 2 = z KL K 2 (a) F(K,L) = L = z2 KL (b) F(K,L) = K + L = z KL constant returns to z F(K,L) = scale for any z > 0

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Answer to part (a) Answer to part (b)

K 2 F(K,L) = F(K,L) = K + L L (zK)2 F(zK,zL) = zK + zL F(zK,zL) = zL = z(K + L) z2K 2 = constant returns to zL = z F(K,L) scale for any z > 0 K 2 = z L constant returns to z F(K,L) = scale for any z > 0 CHAPTER 3 National Income slide 10 CHAPTER 3 National Income slide 11

Assumptions of the model Determining GDP

Technology is fixed. Output is determined by the fixed factor supplies The economy’s supplies of capital and labor and the fixed state of technology: are fixed at Y = F(K, L) K = K and L = L

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2 The distribution of national Notation income

. determined by factor prices, W = nominal wage the prices per unit that firms pay for the R = nominal rental rate factors of production P = price of output . wage = price of L W /P = real wage . rental rate = price of K (measured in units of output)

R /P = real rental rate

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How factor prices are determined Demand for labor

. Factor prices are determined by supply and . Assume markets are competitive: demand in factor markets. each firm takes W, R, and P as given. . Recall: Supply of each factor is fixed. . Basic idea: A firm hires each unit of labor . What about demand? if the cost does not exceed the benefit. . cost = real wage . benefit = marginal product of labor

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Marginal product of labor (MPL ) MPL and the production function Y . definition: output The extra output the firm can produce F (K ,L) using an additional unit of labor MPL 1 (holding other inputs fixed): As more labor is MPL added, MPL ↓

MPL = F (K, L +1) – F (K, L) 1

MPL Slope of the production function equals MPL 1 L labor

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3 Diminishing marginal returns Check your understanding:

. As a factor input is increased, . Which of these production functions have its marginal product falls (other things equal). diminishing marginal returns to labor? Intuition: . a) F(K,L) = 2K + 15L Suppose ↑L while holding K fixed ⇒ fewer machines per worker b) F(K ,L) = KL ⇒ lower worker productivity c) F(K ,L) = 2 K + 15 L

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MPL and the demand for labor The equilibrium real wage

Units of Units of Labor The real wage output Each firm hires labor output supply up to the point where adjusts to equate MPL = W/P. labor demand Real with supply. wage

equilibrium MPL, real wage MPL, Labor Labor demand demand Units of labor, L L Units of labor, L Quantity of labor demanded

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Determining the rental rate The equilibrium real rental rate

Units of We have just seen that MPL = W/P. output Supply of The real rental rate capital adjusts to equate The same logic shows that MPK = R/P : demand for capital . diminishing returns to capital: MPK ↓ as K ↑ with supply.

. The MPK curve is the firm’s demand curve for renting capital. equilibrium R/P MPK, . Firms maximize profits by choosing K demand for capital such that MPK = R/P . K Units of capital, K

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4 The Neoclassical Theory of Distribution How income is distributed: W total labor income = L = MPL ! L . states that each factor input is paid its marginal P product R total capital income = K = MPK ! K P If production function has constant returns to scale, then Y = MPL ! L + MPK ! K

national labor capital income income income

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The ratio of labor income to total The Cobb-Douglas Production income in the U.S. Function

Labor’s 1 . The Cobb-Douglas production function has share constant factor shares: of total 0.8 income α = capital’s share of total income: 0.6 capital income = MPK x K = α Y labor income = MPL x L = (1 – α )Y 0.4 Labor’s share of income is approximately constant over time. . The Cobb-Douglas production function is: 0.2 (Hence, capital’s share is, too.) Y = AK " L1!" 0 where A represents the level of technology. 1960 1970 1980 1990 2000

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The Cobb-Douglas Production Outline of model Function A closed economy, market-clearing model . Each factor’s marginal product is proportional to its average product: Supply side DONE  factor markets (supply, demand, price) " !1 1!" "Y MPK = " AK L = DONE determination of output/income K Demand side " !" (1!" )Y MPL = (1!" ) AK L =  determinants of C, I, and G L Next  Equilibrium  goods market  loanable funds market

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5 Demand for goods & services Consumption, C

. def: Disposable income is total income minus Components of aggregate demand: total taxes: Y – T. C = consumer demand for g & s . Consumption function: C = C (Y – T )

I = demand for investment goods Shows that ↑(Y – T ) ⇒ ↑C G = government demand for g & s . def: Marginal propensity to consume (MPC) (closed economy: no NX ) is the increase in C caused by a one-unit increase in disposable income.

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The consumption function Investment, I

C . The investment function is I = I (r ), where r denotes the real interest rate, C (Y –T ) the nominal interest rate corrected for inflation. . The real interest rate is The slope of the MPC . the cost of borrowing consumption function 1 is the MPC. . the opportunity cost of using one’s own funds to finance investment spending.

Y – T So, ↑r ⇒ ↓I

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The investment function Government spending, G

r Spending on . G = govt spending on goods and services. investment goods depends negatively on . G excludes transfer payments the real interest rate. (e.g., social security benefits, unemployment insurance benefits). . Assume government spending and total taxes are exogenous: I (r ) G = G and T = T I

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6 The market for goods & services The loanable funds market

. Aggregate demand: C (Y !T ) + I (r ) + G . A simple supply-demand model of the financial system. . Aggregate supply: Y = F (K ,L) . One asset: “loanable funds” . demand for funds: investment . Equilibrium: Y = C (Y !T ) + I (r ) + G . supply of funds: saving . “price” of funds: real interest rate . The real interest rate adjusts to equate demand with supply.

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Demand for funds: Investment Loanable funds demand curve

r The demand for loanable funds… The investment . comes from investment: curve is also the Firms borrow to finance spending on plant & demand curve for equipment, new office buildings, etc. loanable funds. Consumers borrow to buy new houses. . depends negatively on r, the “price” of loanable funds I (r ) (cost of borrowing). I

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Supply of funds: Saving Types of saving

. The supply of loanable funds comes from private saving = (Y – T ) – C saving: public saving = T – G . Households use their saving to make bank deposits, purchase bonds and other assets. national saving, S These funds become available to firms to = private saving + public saving borrow to finance investment spending. = (Y –T ) – C + T – G . The government may also contribute to saving = Y – C – G if it does not spend all the tax revenue it receives.

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7 EXERCISE: Answers Calculate the change in saving

Suppose MPC = 0.8 and MPL = 20. !S = !Y " !C " !G = !Y " 0.8(!Y " !T ) " !G For each of the following, compute ΔS : = 0.2 !Y + 0.8 !T " !G a. ΔG = 100 a. !S = " 100

b. ΔT = 100 b. !S = 0.8 "100 = 80 c. ΔY = 100 c. !S = 0.2 "100 = 20 d. ΔL = 10 d. !Y = MPL " !L = 20 "10 = 200, !S = 0.2 " !Y = 0.2 " 200 = 40.

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Loanable funds market Loanable funds supply curve equilibrium r S =Y !C (Y !T ) !G r S =Y !C (Y !T ) !G National saving does not depend on r, so the supply Equilibrium real curve is vertical. interest rate

I (r ) S, I Equilibrium level S, I of investment

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The special role of r Digression: Mastering models

r adjusts to equilibrate the goods market and the To master a model, be sure to know: loanable funds market simultaneously: 1. Which of its variables are endogenous and If L.F. market in equilibrium, then which are exogenous. Y – C – G = I 2. For each curve in the diagram, know Add (C +G ) to both sides to get a. definition Y = C + I + G (goods market eq’m) b. intuition for slope Thus, c. all the things that can shift the curve Eq’m in Eq’m in goods L.F. market ! market 3. Use the model to analyze the effects of each item in 2c.

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8 Mastering the loanable funds CASE STUDY: model The Reagan deficits Things that shift the saving curve . Reagan policies during early 1980s: . public saving . increases in defense spending: ΔG > 0 . fiscal policy: changes in G or T . big tax cuts: ΔT < 0 . private saving . Both policies reduce national saving: . preferences . tax laws that affect saving S =Y !C (Y !T ) !G –401(k) –IRA ! G " # S !T " # C " ! S –replace income tax with consumption tax

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CASE STUDY: Are the data consistent with these results? The Reagan deficits 1. The increase in r S 2 S 1 variable 1970s 1980s the deficit reduces saving… T – G –2.2 –3.9

r2 S 19.6 17.4 2. …which causes the real interest r r 1.1 6.3 rate to rise… 1 I 19.9 19.4

3. …which reduces I (r ) T–G, S, and I are expressed as a percent of GDP the level of I I S, I All figures are averages over the decade shown. investment. 2 1

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Mastering the loanable funds An increase in investment demand model, continued r S Things that shift the investment curve An increase . some technological innovations …raises the interest rate. r in desired . to take advantage of the innovation, 2 investment…

firms must buy new investment goods r1 . tax laws that affect investment But the equilibrium

. investment tax credit level of investment I2 cannot increase I1 because the S, I supply of loanable funds is fixed.

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9 Chapter Summary Chapter Summary

. Total output is determined by . A closed economy’s output is used for . the economy’s quantities of capital and labor . consumption . the level of technology . investment . government spending . Competitive firms hire each factor until its marginal product equals its price. . The real interest rate adjusts to equate the demand for and supply of . If the production function has constant returns to scale, then labor income plus capital income . goods and services equals total income (output). . loanable funds

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Chapter Summary

. A decrease in national saving causes the interest rate to rise and investment to fall. . An increase in investment demand causes the interest rate to rise, but does not affect the equilibrium level of investment if the supply of loanable funds is fixed.

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