9/10/2017. National Income: Where it Comes From and Where it Goes (in the long-run) Introduction. The Neoclassical model

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1 Chapter 3 - The Long-run Model National Income: Where it Comes From and Where it Goes (in the long-run) Introduction In chapter 2 we defined and measured some key macroeconomic variables. Now we start building theories about what determines these key variables. In the next couple lectures we will build up theories that we think hold in the long run, when prices are flexible and markets clear. Called Classical theory or Neoclassical. The Neoclassical model Is a general equilibrium model: Involves multiple markets each with own supply and demand Price in each market adjusts to make quantity demanded equal quantity supplied. 1

2 Neoclassical model The macroeconomy involves three types of markets: 1. Goods (and services) Market 2. Factors Market, needed to produce goods and services we focus on labor and capital. 3. Financial Market Are also three types of agents in an economy: 1. Households 2. Firms 3. Government Neoclassical model Agents interact in markets, where they may be demander in one market and supplier in another 1) Goods market: Supply: firms produce the goods and services Demand: by households for consumption, government spending, and other firms demand them for investment Neoclassical model 2) Labor market (factors of production) Supply: Households sell their labor services. Demand: Firms hire labor to produce the goods. 3) Financial market Supply: households supply private savings: income less consumption Demand: firms borrow funds for investment; government borrows funds to finance expenditures. slide 5 2

3 Neoclassical model We will develop a set of equations to characterize supply and demand in these markets Then use algebra to solve these equations, and see how they interact to establish a general equilibrium. slide 6 Objectives what determines the economy s total output/income in the long-run. how the prices of the factors of production are determined how total income is distributed what determines the demand for goods and services how equilibrium in the goods market is achieved Outline of the long-run model A closed economy, market-clearing model Supply side factor markets (supply, demand, price) determination of output/income Demand side determinants of C, I, and G Equilibrium factor market goods market financial market (loanable funds market) 3

4 Start with the supply side -production Factors of Production K = capital: physical 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 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%) What happens to output, Y 2 = F (K 2, L 2 )? 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 What about: 2 2 F( K, L) KL F( K, L) K L 4

5 Assumptions 1. Technology is fixed. 2. The economy s supplies of capital and labor are fixed at K K and L L Determining GDP in the Long-run Output is determined by the fixed factor supplies and the fixed state of technology: Y F( K, L) Determining GDP in the Long-run Output is determined by the fixed factor supplies and the fixed state of technology: Y F( K, L) We just determined total output(y), course is over! 5

6 The distribution of national income (Y) Equilibrium in the factor market: Who gets Y? determined by factor prices, the price a firms pay for a unit of the factor of production Nominal wage rate (W) = price of L Nominal rental rate (R) = price of K Recall from chapter 2: the value of output equals the value of income. The income is paid to the workers, capital owners, land owners, and so forth. We now explore a simple theory of income distribution. Notation W R P = nominal wage = nominal rental rate = price of output W /P = real wage (measured in units of output) R /P = real rental rate Real wage Think about units: W = $/hour P = $/good W/P = ($/hour) / ($/good) = goods/hour The amount of purchasing power, measured in units of goods, that firms pay per unit of work Work at Starbucks: W = $10/hour, P = $2 per cup. W/P = 5 cups of coffee per hour. 6

7 How factor prices are determined Factor prices are determined by supply and demand in factor markets. We assume supply of each factor is fixed. K K and L L What about demand? Its not fixed! 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 cost does not exceed the benefit. cost = real wage benefit = marginal product of labor(how many cups of coffee they can produce). Marginal product of labor (MPL ) 7

8 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 11? 2 21? ? 5 45? 6 51? 7 56? 8 60? MPL and the production function Y output F ( K, L) 1 MPL 1 MPL As more labor is added, MPL 1 MPL Slope of the production function equals MPL L labor Diminishing marginal returns As a factor input is increased, its marginal product falls (other things equal). Intuition: If L increases while holding K fixed => machines per worker falls. => worker productivity falls. 8

9 NOW YOU TRY: Identifying Diminishing Marginal 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 L Y MPL 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? Firm hires 6 workers. The added cost of the 7 th worker > added benefit. 0 0 n.a Production Function Example Labor Capital

10 MPL and the demand for labor W/P, units of output Real wage Each firm hires labor up to the point where MPL = W/P. MPL = Labor Demand Quantity of labor demanded Units of labor, L Example: deriving labor demand Y K L MPL 05. K L Labor demand is where this equals real wage: The equilibrium real wage W/P, Units of output equilibrium real wage L Labor supply A The real wage adjusts to equate labor demand with supply. MPL, Labor demand Units of labor, L 10

11 Increase in supply of labor reduces the real wage. W/P labor supply Real wage A L B MPL, Labor demand Units of labor, L Determining the rental rate We have just seen that MPL = W/P. The same logic shows that MPK = R/P: diminishing returns to capital: MPK as K The MPK curve is the firm s demand curve for renting capital. Firms maximize profits by choosing K such that MPK = R/P. The equilibrium real rental rate Units of output Supply of capital The real rental rate adjusts to equate demand for capital with supply. equilibrium R/P K MPK=demand for capital Units of capital, K 11

12 The Neoclassical Theory of Distribution states that each factor input is paid its marginal product a good starting point for thinking about income distribution How income is distributed to L and K W total labor income = L P R total capital income = K P MPL L MPK K If production function has constant returns to scale, then Y MPL L MPK K national income labor income capital income The ratio of labor income to total income in the U.S., Labor s share of total income Labor s share of income is approximately Labor s share constant of income over time. is (Thus, approximately capital s constant share is, over too.) time. (Thus, capital s share is, too.)

13 The Cobb-Douglas Production Function The Cobb-Douglas production function has constant factor shares: The Cobb-Douglas production function is: where A represents the level of technology. Y 1 AK L = capital s share of total income 1- = labor s share of total income, capital income = MPK x K = Y labor income = MPL x L = (1 )Y The Cobb-Douglas Production Function Each factor s marginal product is proportional to its average product: MPK AK L K (1 ) Y MPL (1 ) AK L L 1 1 Y Labor productivity and wages Theory: wages depend on labor productivity U.S. data: period productivity growth real wage growth % 1.8% % 2.7% % 1.2% % 2.0% 13

14 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 & services Components of aggregate demand: C = consumer demand for g & s I = demand for investment goods G = government demand for g & s (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. MPC must be between 0 and 1. 14

15 The consumption function C C (Y T ) 1 MPC The slope of the consumption function is the MPC. Y T Consumption function cont. Suppose consumption function: C= Y MPC = 0.75 For extra dollar of income, spend 0.75 dollars consumption Marginal propensity to save (MPS) = 1-MPC slide 43 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 15

16 The investment function r 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: C ( Y T ) I ( r ) G Aggregate supply: Y F ( K, L) Equilibrium: Y = C ( Y T ) I ( r ) G One equation, one unknown. The real interest rate (r) adjusts to equate demand with supply. 16

17 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 Demand for funds: Investment The demand for loanable funds comes from investment: Firms borrow to finance spending on plant & equipment, new office buildings, etc. Consumers borrow to buy new houses. depends negatively on r, the price of loanable funds (cost of borrowing). Loanable funds demand curve r The investment curve is also the demand curve for loanable funds. I (r ) I 17

18 Supply of funds: Saving The supply of loanable funds comes from saving: Households use their saving to make bank deposits, purchase bonds and other assets. These funds become available to firms to borrow to finance investment spending. The government may also contribute to saving if it does not spend all the tax revenue it receives. 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 Types of saving private saving (s p ) = (Y T ) C Public (gov t) saving (s g ) = T G national saving, S = s p + s g = (Y T ) C + T G = Y C G 18

19 Notation: = change in a variable For any variable X, X = the change in X is the Greek (uppercase) letter Delta Examples: If L = 1 and K = 0, then Y = MPL. Y More generally, if K = 0, then MPL. L (Y T ) = Y T, so C = MPC ( Y T ) = MPC Y MPC T NOW YOU TRY: Calculate the change in saving Suppose MPC = 0.8 and MPL = 20. For each of the following, compute S : a. G = 100 b. T = 100 c. Y = 100 d. L = 10 Answers S Y C G Y 0.8( Y T ) G a. S 100 b. S g note: S S S 0.2 Y 0.8 T G g S T G p S Y T C Y T MPC Y T p

20 Budget surpluses and deficits If T > G, budget surplus = (T G ) = public saving. If T < G, budget deficit = (G T ) and public saving is negative. If T = G, balanced budget, public saving = 0. The U.S. government finances its deficit by issuing Treasury bonds i.e., borrowing. U.S. Federal Government Surplus/Deficit, , as a percent of GDP 10% 5% 0% -5% -10% YFSGDA188S -15% -20% -25% -30% U.S. Federal Government Debt, % 120% 100% 80% 60% Fact: In the early 1990s, about 18 cents of every tax dollar went to pay interest on the debt. (In 2007, it was about 10 cents) FDEGDQ188S 40% 20% 0%

21 Loanable funds supply curve r S Y C ( Y T ) G National saving does not depend on r, so the supply curve is vertical. S, I Loanable funds market equilibrium r S Y C ( Y T ) G Equilibrium real interest rate I (r ) Equilibrium level of investment S, I The special role of r r adjusts to equilibrate the goods market and the loanable funds market simultaneously: Thus, 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) Eq m in L.F. market Eq m in goods market 21

22 Algebra example Suppose an economy characterized by: Factors market supply: labor supply= 2500 Capital stock supply=2500 Goods market supply: Production function: Y = 2K.5 L.5 Goods market demand: Consumption function: C = (Y-T) Investment function: I = r G=1000, T = 1000 Algebra example continued Given the exogenous variables (Y, G, T), find the equilibrium values of the endogenous variables (r, C, I) Find r using the goods market equilibrium condition: Y = C + I + G 5000 = ( ) r = r -250 = -5000r so r = 0.05 And I = *(0.05) = 750 C = ( ) = 3250 To master a model, be sure to know: 1. Which of its variables are endogenous and which are exogenous. 2. For each curve in the diagram, know: a. definition b. intuition for slope c. all the things that can shift the curve 3. Use the model to analyze the effects of each item in 2c. 22

23 Mastering the loanable funds model Things that shift the saving curve public saving fiscal policy: changes in G or T private saving preferences tax laws that affect saving 401(k) IRA CASE STUDY: The Reagan deficits Reagan policies during early 1980s: increases in defense spending: G > 0 big tax cuts: T < 0 Both policies reduce national saving: S Y C ( Y T ) G G S T C S CASE STUDY: The Reagan deficits 1. The increase in the deficit reduces saving r S 2 S 1 2. which causes the real interest rate to rise r 2 r 1 3. which reduces the level of investment. I 2 I 1 I (r ) S, I 23

24 Are the data consistent with these results? variable 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. Mastering the loanable funds model, continued Things that shift the investment curve: some technological innovations to take advantage some innovations, firms must buy new investment goods tax laws that affect investment e.g., investment tax credit An increase in investment demand r S raises the interest rate. But the equilibrium level of investment cannot increase because the supply of loanable funds is fixed. r 2 r 1 An increase in desired investment I 2 I 1 S, I 24

25 Saving and the interest rate Why might saving depend on r? How would the results of an increase in investment demand be different? Would r rise as much? Would the equilibrium value of I change? An increase in investment demand when saving depends on r An increase in investment demand raises r, which induces an increase in the quantity of saving, which allows I to increase. r r 2 r 1 I 1 I 2 S( r) I(r) 2 I(r) S, I Chapter Summary Total output in the long-run is determined by: the economy s quantities of capital and labor the level of technology Competitive firms hire each factor until its marginal product equals its price. If the production function has constant returns to scale, then labor income plus capital income equals total income (output). 25

26 Chapter Summary A closed economy s output is used for: consumption investment government spending The real interest rate adjusts to equate the demand for and supply of: goods and services loanable funds 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. 26