Topic 3: National Income: Where it Comes From and Where it Goes (chapter 3) CHAPTER 3 National Income revised 9/21/09 Introduction In the last lecture 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. CHAPTER 3 National Income slide 2 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. CHAPTER 3 National Income slide 3
Neoclassical model The macroeconomy involves three types of markets: 1. Goods (and services) Market 2. Factors Market or Labor market , needed to produce goods and services 3. Financial market Are also three types of agents in an economy: 1. Households 2. Firms 3. Government CHAPTER 3 National Income slide 4 Three Markets Three agents work Labor Market
hiring Financial Market saving Households consumption borrowing Government government spending borrowing Firms production investment Goods Market CHAPTER 3
National Income slide 5 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 Demand: by households for consumption, government spending, and other firms demand them for investment CHAPTER 3 National Income slide 6 Neoclassical model 2) Labor market (factors of production) Supply: Households sell their labor services. Demand: Firms need to 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. CHAPTER 3 National Income slide 7 Neoclassical model We will develop a set of equations to charac-terize supply and demand in these markets Then use algebra to solve these equations together, and see how they interact to establish a general equilibrium. Start with production
CHAPTER 3 National Income slide 8 Three Markets Three agents work Labor Market hiring Financial Market saving Households consumption borrowing Government government
spending borrowing Firms production investment Goods Market CHAPTER 3 National Income slide 9 Part 1: Supply in goods market: Production Supply in the goods market depends on a production function: denoted Y = F (K, L) Where K = capital: tools, machines, and structures used in production L = labor: the physical and mental
efforts of workers CHAPTER 3 National Income slide 10 The production function shows how much output (Y ) the economy can produce from K units of capital and L units of labor. reflects the economys level of technology. Generally, we will assume it exhibits constant returns to scale. CHAPTER 3 National Income slide 11
Returns to scale Initially Y1 = F (K1 , L1 ) Scale all inputs by the same multiple z: K2 = zK1 and L2 = zL1 for z>1 (If z = 1.25, then all inputs increase by 25%) What happens to output, Y2 = F (K2 , L2 ) ? If constant returns to scale, Y2 = zY1 If increasing returns to scale, Y2 > zY1 If decreasing returns to scale, Y2 < zY1 CHAPTER 3 National Income slide 12 Exercise: determine returns to scale Determine whether the following production function has constant, increasing, or
decreasing returns to scale: F (K ,L) 2K 15L CHAPTER 3 National Income slide 13 Exercise: determine returns to scale Does F (zK , zL) zF (K ,L)? Suppose F (K ,L) 2K 15L F (zK , zL) 2 zK 15 zL z (2K 15L) zF (K ,L) Yes, constant returns to scale CHAPTER 3 National Income
slide 14 Assumptions of the model 1. Technology is fixed. 2. The economys supplies of capital and labor are fixed at K K CHAPTER 3 and National Income L L slide 15 Determining GDP Output is determined by the fixed factor supplies and the fixed state
of technology: So we have a simple initial theory of supply in the goods market: Y F (K , L) CHAPTER 3 National Income slide 16 Three Markets Three agents work Labor Market hiring Financial Market saving Households consumption
borrowing Government government spending borrowing Firms production investment Goods Market CHAPTER 3 National Income slide 17 Part 2: Equilibrium in the factors market Equilibrium is where factor supply equals factor demand.
Recall: Supply of factors is fixed. Demand for factors comes from firms. CHAPTER 3 National Income slide 18 Demand in factors market Analyze the decision of a typical firm. It buys labor in the labor market, where price is wage, W. It rents capital in the factors market, at rate R. It uses labor and capital to produce the good, which it sells in the goods market, at price P.
CHAPTER 3 National Income slide 19 Demand in factors market Assume the market is competitive: Each firm is small relative to the market, so its actions do not affect the market prices. It takes prices in markets as given W,R, P. CHAPTER 3 National Income slide 20 Demand in factors market It then chooses the optimal quantity of Labor and capital to maximize its profit. How write profit: Profit
costs = PY = revenue -labor costs -capital - WL - RK = P F(K,L) - WL - RK CHAPTER 3 National Income slide 21 Demand in the factors market Increasing hiring of L will have two effects: 1) Benefit: raise output by some amount 2) Cost: raise labor costs at rate W
To see how much output rises, we need the marginal product of labor (MPL) CHAPTER 3 National Income slide 22 Marginal product of labor (MPL) An approximate definition (used in text) : The extra output the firm can produce using one additional labor (holding other inputs fixed): MPL = F (K, L +1) F (K, L) CHAPTER 3 National Income slide 23 The MPL and the production function
Y output F (K , L) MP 1 L MP 1 L MP L 1 CHAPTER 3 As more labor is added, MPL Slope of the production function equals MPL: rise over run L National Income
labo r slide 24 Diminishing marginal returns As a factor input is increased, its marginal product falls (other things equal). Intuition: L while holding K fixed fewer machines per worker lower productivity CHAPTER 3 National Income slide 25 MPL with calculus We can give a more precise definition of MPL: The rate at which output rises for a small amount
of additional labor (holding other inputs fixed): MPL = [F (K, L +L) F (K, L)] / L whereis delta and represents change Earlier definition assumed that L=1. F (K, L +1) F (K, L) We can consider smaller change in labor. CHAPTER 3 National Income slide 26 MPL as a derivative As we take the limit for small change in L: F (K ,L L) F (K ,L) MPL lim L 0 L fL (K ,L) Which is the definition of the (partial)
derivative of the production function with respect to L, treating K as a constant. This shows the slope of the production function at any particular point, which is what we want. CHAPTER 3 National Income slide 27 The MPL and the production function Y output MPL is slope of the production function (rise over run) F (K , L) F (K, L +L) F (K, L))
L CHAPTER 3 National Income L labo r slide 28 Derivative as marginal product 1 2 2)Y F (L) 3L 3 L Y 9 1
Y 1 2 1 fL 3 L L 2 1 3 2 3 L 2 2 L L: F(L): fL: CHAPTER 3 1 3 1.5 National Income 6 3
1 4 6 0.75 4 9 L 9 9 0.5 slide 29 Return to firm problem: hiring L Firm chooses L to maximize its profit. How will increasing L change profit? profit = revenue - cost = P * MPL - W
If this is: > 0 should hire more < 0 should hire less = 0 hiring right amount CHAPTER 3 National Income slide 30 Firm problem continued So the firms demand for labor is determined by the condition: P *MPL = W Hires more and more L, until MPL falls enough to satisfy the condition. Also may be written: MPL = W/P, where W/P is the real wage CHAPTER 3
National Income slide 31 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 CHAPTER 3 National Income slide 32 Example: deriving labor demand Suppose a production function for all firms in the economy: Y K 0.5L0.5
MPL 0.5K 0.5L 0.5 Labor demand is where this equals real wage: W 0.5 0.5 0.5K L P CHAPTER 3 National Income slide 33 Labor demand continued or rewrite with L as a function of real wage 0.5K 0.5 0.5 L W
P 2 W 0.5K L 2P 1 P 1 K L 0.25 W 2 P demand L 0.25K
W So a rise in wage want to hire less labor; rise in capital stock want to hire more labor 0.5 0.5 CHAPTER 3 2 National Income slide 34 Labor market equilibrium Take this firm as representative, and su m over all firms to derive aggregate labor demand.
Combine with labor supply to find equili brium wage: demand: 0.5K 0.5 demand L 0.5 W P supply: Lsupply L 0.5 W 0.5 equilibrium: 0.5K L
P So rise in labor supply fall in equlibrium real wage CHAPTER 3 National Income slide 35 Three Markets Three agents work Labor Market hiring Financial Market saving Households consumption borrowing
Government government spending borrowing Firms production investment Goods Market CHAPTER 3 National Income slide 36 MPL and the demand for labor Units of output labor supply
Real wag e L CHAPTER 3 National Income Each Each firm firm hires hires labor labor up up to to the the point point where
where MPL MPL = = W/P W/P MPL, Labor demand Units of labor, L slide 37 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 firms demand curve for renting capital. Firms maximize profits by choosing K such that MPK = R/P . CHAPTER 3
National Income slide 38 How income is distributed: We found that if markets are competitive, then factors of production will be paid their marginal contribution to the production process. total labor income = W L P total capital income R K = P CHAPTER 3 National Income
MPL L MPK K slide 39 Eulers theorem: Under our assumptions (constant returns to scale, profit maximization, and competitive markets) total output is divided between the payments to capital and labor, depending on their marginal productivities, with no extra profit over. Y left MPL L MPK K national income CHAPTER 3 labor
income National Income capital income slide 40 Mathematical example Consider a production function with Cobb-Douglas form: Y = AKL1- where A is a constant, representing technology Show this has constant returns to scale: multiply factors by Z: F(ZK,ZY) = A (ZK) (ZL)1- = A Z K Z1- L1- = A Z Z1- K L1- = Z x A K L1- = Z x F(K,L) CHAPTER 3 National Income slide 41
Mathematical example continued Compute marginal products: MPL = (1-) A K L- MPK = A K-1L1- Compute total factor payments: MPL x L + MPK x K = (1-) A K L- x L + A K-1L1- x K = (1-) A K L1- + A K L1- = A K L1- =Y So total factor payments equals total production. CHAPTER 3 National Income slide 42 Three Markets Three agents work Labor Market hiring
Financial Market saving Households consumption borrowing Government government spending borrowing Firms production investment Goods Market CHAPTER 3 National Income
slide 43 Outline of model A closed economy, market-clearing model Goods DONE market: Next Supply side: production Demand side: C, I, and G Factors DONE market DONE Supply side Demand side Loanable funds market Supply side: saving Demand side: borrowing CHAPTER 3
National Income slide 44 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 ) CHAPTER 3 National Income slide 45 Consumption, C def: disposable income is total income minus total taxes: YT Consumption function: C = C (Y T )
Shows that (Y T ) C def: The marginal propensity to consume (MPC) is the increase in C caused by an increase in disposable income. So MPC = derivative of the consumption function with respect to disposable income. MPC must be between 0 and 1. CHAPTER 3 National Income slide 46 The consumption function C C (Y T)
rise r u n The slope of the consumption function is the MPC. YT CHAPTER 3 National Income slide 47 Consumption function cont. Suppose consumption function: C=10 + 0.75Y MPC = 0.75 For extra dollar of income, spend 0.75 dollars consumption Marginal propensity to save = 1MPC
CHAPTER 3 National Income slide 48 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 ones own funds to finance investment spending. So, r I CHAPTER 3 National Income slide 49
The investment function r Spending on investment goods is a downwardsloping function of the real interest rate I (r ) I CHAPTER 3 National Income slide 50 Government spending, G G includes government spending on goods and services. G excludes transfer payments
Assume government spending and total taxes are exogenous: G G CHAPTER 3 and National Income T T slide 51 The market for goods & services Agg. demand: Agg. supply: Equilibrium: C (Y T ) I (r ) G Y F (K , L) Y = C (Y T ) I (r ) G
The The real real interest interest rate rate adjusts adjusts to to equate equate demand demand with with supply. supply. We can get more intuition for how this works by looking at the loanable funds market CHAPTER 3 National Income slide 52 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 CHAPTER 3 National Income slide 53 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 (the cost of
borrowing). CHAPTER 3 National Income slide 54 Loanable funds demand curve r The investment curve is also the demand curve for loanable funds. I (r ) I CHAPTER 3 National Income slide 55
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 of the tax revenue it receives. CHAPTER 3 National Income slide 56 Types of saving private saving (sp) = (Y T ) C government saving (sg) = T G
national saving, S = sp + = (Y T ) C + = CHAPTER 3 Y sg TG C G National Income slide 57
EXERCISE: Calculate the change in saving Suppose MPC = 0.8 For each of the following, compute S : a. G = 100 b. T = 100 CHAPTER 3 National Income slide 58 Answers S Y C G Y 0.8(Y T ) G 0.2 Y 0.8 T G a. S 100 b. S 0.8 100 80 note: S S g S p
S g T G 100 0 100 S p Y T C Y T MPC Y T 0 100 0.8 0 100 100 80 20 CHAPTER 3 National Income slide 59 digression: Budget surpluses and deficits When T > G , budget surplus = (T G ) = public saving When T < G , budget deficit = (G T ) and public saving is negative.
When T = G , budget is balanced and public saving = 0. CHAPTER 3 National Income slide 60 The U.S. Federal Government Budget 44 GDP %%ofofGDP 00 -4-4 (T (T-G -G))as asaa%
% of ofGDP GDP -8-8 -12 -12 1940 1940 1950 1950 CHAPTER 3 1960 1960 1970 1970 National Income
1980 1980 1990 1990 2000 2000 slide 61 The U.S. Federal Government Debt Fun Funfact: fact: In Inthe theearly early1990s, 1990s, nearly nearly18 18cents centsof ofevery everytax
tax dollar dollarwent wentto topay payinterest intereston on the thedebt. debt. 120 120 PercentofofGDP GDP Percent 100 100 80 80 60
60 40 40 20 20 00 1940 1940 CHAPTER 3 1950 1950 1960 1960 1970 1970 National Income 1980 1980
1990 1990 2000 2000 slide 62 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 CHAPTER 3 National Income
slide 63 Loanable funds market equilibrium r S Y C (Y T ) G Equilibrium real interest rate I (r ) Equilibrium level of investment CHAPTER 3 National Income S, I slide 64 The special role of r rr adjusts
adjusts to to equilibrate equilibrate the the goods goods market market and and the the loanable loanable funds funds market market simultaneously: simultaneously: IfIf L.F. L.F. market market in in equilibrium, equilibrium, then then Y Y C C G G =
= II Add Add (C (C +G +G )) to to both both sides sides to to get get Y Y= =C C+ + II + +G G (goods (goods market market eqm) eqm) Eqm in Eqm in Thus, Thus, L.F.
goods market market CHAPTER 3 National Income slide 65 Algebra example Suppose an economy characterized by: Factors market supply: labor supply= 1000 Capital stock supply=1000 Goods market supply: Production function: Y = 3K + 2L Goods market demand: Consumption function: C = 250 + 0.75(Y-T)
Investment function: I = 1000 5000r G=1000, T = 1000 CHAPTER 3 National Income slide 66 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 -5000r + 1000 5000 = 5250 5000r -250 = -5000r so r = 0.05 And I = 1000 5000*(0.05) = 750 C = 250 + 0.75(5000 - 1000) = 3250 CHAPTER 3
National Income slide 67 Mastering the loanable funds model Things that shift the saving curve a. public saving i. fiscal policy: changes in G or T b. private saving i. preferences ii. tax laws that affect saving (401(k), IRA) CHAPTER 3 National Income slide 68 CASE STUDY The Reagan Deficits
Reagan policies during early 1980s: increases in defense spending: G > 0 big tax cuts: T < 0 According to our model, both policies reduce national saving: S Y C (Y T ) G G S CHAPTER 3 National Income T C S slide 69 1. The Reagan deficits, cont. 1. The increase in the deficit reduces saving 2. which causes the real interest
rate to rise r S1 r2 r1 3. which reduces the level of investment. CHAPTER 3 S2 National Income I (r ) I2 I1 S, I
slide 70 Are the data consistent with these results? variable variable TT G G 1970s 1970s 2.2 2.2 1980s 1980s 3.9 3.9 SS rr 19.6 19.6 1.1
1.1 17.4 17.4 6.3 6.3 II 19.9 19.9 19.4 19.4 TG, S, and I are expressed as a percent of GDP All figures are averages over the decade shown. CHAPTER 3 National Income slide 71 Chapter summary
1. Total output is determined by how much capital and labor the economy has the level of technology 2. Competitive firms hire each factor until its marginal product equals its price. 3. If the production function has constant returns to scale, then labor income plus capital income equals total income (output). CHAPTER 3 National Income slide 72 Chapter summary 4. The economys output is used for consumption (which depends on disposable income)
Investment (depends on real interest rate) government spending (exogenous) 5. The real interest rate adjusts to equate the demand for and supply of goods and services loanable funds 6. A decrease in national saving causes the interest rate to rise and investment to fall. CHAPTER 3 National Income slide 73 Friendly quiz #1 Write answers to the following 4 questions on a sheet of paper to hand in (each worth 1 point). 1) Your name 2) Your TAs name (hint: Yi = Monday, Mei = Wednesday)
dy / dx 3) Derive the derivative for y 10 x 4) Does the following production function exhibit constant returns to scale (yes or no)? F (K ,L) 2 K 15 L CHAPTER 3 National Income slide 74 Exercise: determine returns to scale y = 10x1 2 1 1 2 1 dy dx 10 x 5x -1 2 5 2 3)
4) F (zK , zL) 2 zK 15 x zL K 15 L z 2 zF (K ,L) < zF (K ,L) for z >1 no (decreasing returns) CHAPTER 3 National Income
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