Outline of model. Factors of production 1/23/2013. The production function: Y = F(K,L) ECON 3010 Intermediate Macroeconomics

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1 ECON 3010 Intermediate Macroeconomics Chapter 3 National Income: Where It Comes From and Where It Goes Outline of model A closed economy, market-clearing model Supply side factors of production determination of output/income Demand side determinants of C, I, and G Equilibrium goods market loanable funds market Factors of production K = capital: tools, machines, and structures used in production L = labor: the physical and mental efforts of workers The production function: Y = F(K,L) shows how much output (Y ) the economy can produce from K units of capital and L units of labor reflects the economy s level of technology exhibits constant returns to scale 1

2 Returns to scale: a review Initially Y 1 = F (K 1, L 1 ) Scale all inputs by the same factor z: K 2 = zk 1 and L 2 = zl 1 (e.g., if z = 1.2, then all inputs are increased by 20%) Returns to scale: Example 1 F ( K, L) K L F ( zk, zl) ( zk )( zl) 2 z K L What happens to output, Y 2 = F (K 2, L 2 )? z 2 K L If constant returns to scale, Y 2 = zy 1 If increasing returns to scale, Y 2 > zy 1 If decreasing returns to scale, Y 2 < zy 1 z K L z F ( K, L) constant returns to scale for any z > 0 NOW YOU TRY Returns to scale Assumptions Determine whether each of these production functions has constant, decreasing, or increasing returns to scale: 1. Technology is fixed. 2. The economy s supplies of capital and labor are fixed at (a) (b) F ( K, L) K L F ( K, L) K L 2 K K and L L 6 2

3 Determining GDP The distribution of national income Output is determined by the fixed factor supplies and the fixed state of technology: Y F ( K, L ) determined by factor prices, the prices per unit firms pay for the factors of production wage = price of L rental rate = price of K Notation How factor prices are determined W = nominal wage R = nominal rental rate P = price of output W /P = real wage (measured in units of output) R /P = real rental rate Factor prices determined by supply and demand in factor markets. Recall: Supply of each factor is fixed. What about demand? 3

4 Demand for labor Assume markets are competitive: each firm takes W, R, and P as given. Basic idea: A firm hires each unit of labor if the benefit exceeds the cost. cost = real wage benefit = marginal product of labor Marginal product of labor (MPL ) definition: The extra output the firm can produce using an additional unit of labor (holding other inputs fixed): MPL = F (K, L +1) F (K, L) NOW YOU TRY Compute & graph MPL a. Determine MPL at each value of L. b. Graph the production function. c. Graph the MPL curve with MPL on the vertical axis and L on the horizontal axis. L Y MPL 0 0 n.a. 1 10? 2 19? ? 5 40? 6 45? 7 49? 8 52? 9 54? 10 55? ANSWERS Compute & graph MPL MPL (units of output) Marginal Product of Labor Labor (L)

5 Y output MPL and the production function 1 As more labor is added, MPL MPL 1 MPL 1 MPL Slope of the production function equals MPL F ( K, L ) L labor Diminishing marginal returns As an input is increased, its marginal product falls (other things equal). Intuition: Suppose L while holding K fixed fewer machines per worker lower worker productivity NOW YOU TRY Identifying Diminishing Returns Which of these production functions have diminishing marginal returns to labor? a) F ( K, L) 2K 15L b) F ( K, L) KL c) F ( K, L) 2 K 15 L NOW YOU TRY MPL and labor demand Suppose W/P = 6. If L = 3, should firm hire more or less labor? Why? If L = 7, should firm hire more or less labor? Why? L Y MPL 0 0 n.a

6 MPL and the demand for labor The equilibrium real wage Units of output Real wage Each firm hires labor up to the point where MPL = W/P. Units of output Labor supply The real wage adjusts to equate labor demand with supply. Quantity of labor demanded MPL, Labor demand Units of labor, L equilibrium real wage L MPL, Labor demand Units of labor, L The equilibrium real rental rate Units of output Supply of capital The real rental rate adjusts to equate demand for capital with supply. The Neoclassical Theory of Distribution states that each factor input is paid its marginal product equilibrium R/P K MPK, demand for capital Units of capital, K a good starting point for thinking about income distribution 6

7 How income is distributed to L and K total labor income = total capital income = W L P R K P MPL L MPK K If the production function has constant returns to scale, then national income Y M P L L M P K K labor income capital income Labor s share of total income The ratio of U.S. labor income to total income Labor s share of income is approximately constant over time. (Thus, capital s share is too.) The Cobb-Douglas Production Function The Cobb-Douglas production function is: 1 Y A K L where A represents the level of technology. The Cobb-Douglas production function has constant factor shares: = (MPK K)/Y = capital s share of income (1 ) = (MPL L)/Y = labor s share of income Labor productivity and wages Theory: wages depend on labor productivity U.S. data: period productivity growth real wage growth % 1.9% % 2.8% % 1.2% % 2.2% 7

8 Outline of model A closed economy, market-clearing model Supply side DONE factor markets (supply, demand, price) DONE determination of output/income Demand side Next determinants of C, I, and G Equilibrium goods market loanable funds market Demand for goods and services Components of aggregate demand: C = consumer demand for goods & services I = demand for investment goods G = government demand for goods & services (closed economy: no NX ) Consumption, C def: Disposable income is total income minus total taxes: Y T. Consumption function: C = C (Y T ) Shows that (Y T ) C def: Marginal propensity to consume (MPC) is the change in C when disposable income increases by one dollar. C The consumption function 1 MPC C (Y T ) The slope of the consumption function is the MPC. Y T 8

9 Investment, I The investment function is I = I (r ) where r denotes the real interest rate, the nominal interest rate corrected for inflation. The real interest rate is the cost of borrowing the opportunity cost of using one s own funds to finance investment spending So, r I r The investment function Spending on investment goods depends negatively on the real interest rate. I (r ) I Government spending, G G = govt spending on goods and services G excludes transfer payments (e.g., Social Security benefits, unemployment insurance benefits) Assume government spending and total taxes are exogenous: G G and T T The market for goods & services Aggregate demand: Aggregate supply: Equilibrium: C ( Y T ) I ( r ) G Y F ( K, L ) Y = C ( Y T ) I ( r ) G The real interest rate adjusts to equate demand with supply. 9

10 The loanable funds market A simple supply demand model of the financial system. One asset: loanable funds demand for funds: investment supply of funds: price of funds: saving real interest rate r Loanable funds demand curve The investment curve is also the demand curve for loanable funds. I (r ) I Types of saving private saving = (Y T ) C public saving = T G national saving, S = private saving + public saving = (Y T ) C + T G = Y C G Budget surpluses and deficits If T > G, budget surplus = (T G ) and public saving is positive. If T < G, budget deficit = (G T ) and public saving is negative. If T = G, balanced budget and public saving is zero. The U.S. government finances its deficit by issuing Treasury bonds i.e., borrowing. 10

11 percent of GDP percent of GDP 1/23/ U.S. Federal Government Surplus/Deficit, U.S. Federal Government Debt, National saving does not depend on r, so the supply curve is vertical. Loanable funds supply curve r S Y C ( Y T ) G Equilibrium real interest rate Loanable funds market equilibrium r S Y C ( Y T ) G S, I Equilibrium level of investment I (r ) S, I 11

12 The special role of r r adjusts to equilibrate the goods market and the loanable funds market simultaneously: If L.F. market in equilibrium, then Y C G = I Add (C +G ) to both sides to get Y = C + I + G (goods market eq m) Thus, CASE STUDY: The Reagan deficits 1. The increase in the deficit reduces saving 2. which causes the real interest rate to rise r r 2 r 1 S 2 S 1 Eq m in L.F. market Eq m in goods market 3. which reduces the level of investment. I 2 I 1 I (r ) S, I Are the data consistent with these results? 1970s 1980s T G S r I T G, S, and I are expressed as a percent of GDP All figures are averages over the decade shown. An increase in investment demand raises the interest rate. But the equilibrium level of investment cannot increase because the supply of loanable funds is fixed. r r 2 r 1 S An increase in desired investment I 2 I 1 S, I 12

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