Chapter 3 — The Long-run Model National Income

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.

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

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)

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 = z. K 1 and L 2 = z. L 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 = z. Y 1 § If increasing returns to scale, Y 2 > z. Y 1 § If decreasing returns to scale, Y 2 < z. Y 1 § What about:

Assumptions 1. Technology is fixed. 2. The economy’s supplies of capital and labor are fixed at

Determining GDP – in the Long-run Output is determined by the fixed factor supplies and the fixed state of technology:

Determining GDP – in the Long-run Output is determined by the fixed factor supplies and the fixed state of technology: We just determined total output(Y), course is over!

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 = nominal wage R = nominal rental rate P = 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.

How factor prices are determined § Factor prices are determined by supply and demand in factor markets. § We assume supply of each factor is fixed. § 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 ) §

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 0 1 2 3 4 5 6 7 8 Y 0 11 21 30 38 45 51 56 60 MPL n. a. ? ? 9 ? ? ?

MPL and the production function Y output 1 MPL As more labor is added, MPL 1 MPL 1 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.

NOW YOU TRY: Identifying Diminishing Marginal Returns § Which of these production functions have diminishing marginal returns to labor?

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? § Firm hires 6 workers. The added cost of the 7 th worker > added benefit. L 0 1 2 3 4 5 6 7 8 Y 0 11 21 30 38 45 51 56 60 MPL n. a. 11 10 9 8 7 6 5 4

Production Function Example Labor 1 Capital 2 3 1 10 17 23 2 12 20 27 3 13 22 30

MPL and the demand for labor W/P, units of output Each firm hires labor up to the point where MPL = W/P. Real wage MPL = Labor Demand Units of labor, L Quantity of labor demanded

Example: deriving labor demand §

The equilibrium real wage W/P, Units of output Labor supply The real wage adjusts to equate labor demand with supply. A equilibrium real wage MPL, Labor demand Units of labor, L

Increase in supply of labor reduces the real wage. W/P Real wage A 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 equilibrium R/P Supply of capital The real rental rate adjusts to equate demand for capital with supply. MPK=demand for capital Units of capital, K

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 total labor income = total capital income = If production function has constant returns to scale, then national income labor income capital income

The ratio of labor income to total income in the U. S. , 1960 -2010 1 Labor’s share of 0. 9 total 0. 8 income 0. 7 0. 6 0. 5 0. 4 0. 3 0. 2 0. 1 Labor’s share of income is approximately constant over time. (Thus, capital’s share is, too. ) 0 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

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. = 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:

Labor productivity and wages § Theory: wages depend on labor productivity § U. S. data: period productivity growth real wage growth 1960 -2013 2. 1% 1. 8% 1960 -1973 2. 9% 2. 7% 1973 -1995 1. 5% 1. 2% 1995 -2013 2. 3% 2. 0%

Outline of model A closed economy, market-clearing model Supply side DONE q factor markets (supply, demand, price) DONE q determination of output/income Demand side Next q determinants of C, I, and G Equilibrium q goods market q 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.

The consumption function C C (Y –T ) MPC 1 The slope of the consumption function is the MPC. Y–T

Consumption function cont. Suppose consumption function: C=10 + 0. 75 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

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:

The market for goods & services § Aggregate demand: § Aggregate supply: § Equilibrium: One equation, one unknown. The real interest rate (r) adjusts to equate demand with supply.

The loanable funds market § A simple supply-demand model of the financial system. § One asset: “loanable funds” § demand for funds: investment § supply of funds: saving § “price” of funds: 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

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 (sp) = (Y –T ) – C § Public (gov’t) saving (sg) = T – G § national saving, S = sp + sg = (Y –T ) – C + T – G = Y – C – G

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. More generally, if K = 0, then § (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

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, 1940 -2007, as a percent of GDP 10% 5% 0% -5% -10% http: //research. stlouisfed. org/fred 2/series/F YFSGDA 188 S -15% -20% -25% -30% 1940 1950 1960 1970 1980 1990 2000 2010

U. S. Federal Government Debt, 1940 -2007 140% Fact: In the early 1990 s, about 18 cents of every tax dollar went to pay interest on the debt. (In 2007, it was about 10 cents) 120% 100% 80% http: //research. stlouisfed. org/fred 2/series/G FDEGDQ 188 S 60% 40% 20% 0% 1940 1950 1960 1970 1980 1990 2000 2010

Loanable funds supply curve r National saving does not depend on r, so the supply curve is vertical. S, I

Loanable funds market equilibrium r 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: 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, Eq’m in L. F. market Eq’m in goods market

Algebra example Suppose an economy characterized by: § Factors market supply: § labor supply= 2500 § Capital stock supply=2500 § Goods market supply: § Production function: Y = 2 K. 5 L. 5 § Goods market demand: § Consumption function: C = 250 + 0. 75(Y-T) § Investment function: I = 1000 – 5000 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 = 250 + 0. 75(5000 -1000) +1000 -5000 r + 1000 5000 = 5250 – 5000 r -250 = -5000 r so r = 0. 05 And I = 1000 – 5000*(0. 05) = 750 C = 250 + 0. 75(5000 - 1000) = 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 2 c.

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 1980 s: § increases in defense spending: G > 0 § big tax cuts: T < 0 § Both policies reduce national saving:

CASE STUDY: The Reagan deficits 1. The increase in the deficit reduces saving… 2. …which causes the real interest rate to rise… 3. …which reduces the level of investment. r r 2 r 1 I (r ) I 2 I 1 S, I

Are the data consistent with these results? variable 1970 s 1980 s T – G – 2. 2 – 3. 9 S 19. 6 17. 4 r 1. 1 6. 3 I 19. 9 19. 4 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 …raises the interest rate. r 2 An increase in desired investment… r 1 But the equilibrium level of investment cannot increase because the supply of loanable funds is fixed. I 1 I 2 S, I

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(r)2 I(r) I 1 I 2 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).

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.