1 A closed economy, market-clearing model Outline of modelA closed economy, market-clearing modelSupply sidefactor markets (supply, demand, price)determination of output/incomeDemand sidedeterminants of C, I, and GEquilibriumgoods marketloanable funds market
2 Production Function Y = F (K, L) Input/output relationship reflects the economy’s level of technologyexhibits constant returns to scale
3 Returns to scale: A review Initially Y1 = F (K1 , L1 )Scale all inputs by the same factor z:K2 = zK1 and L2 = zL1(e.g., if z = 1.25, then all inputs are increased by 25%)What happens to output, Y2 = F (K2, L2 )?If constant returns to scale, Y2 = zY1If increasing returns to scale, Y2 > zY1If decreasing returns to scale, Y2 < zY1
4 Assumptions of the model Technology is fixed.The economy’s supplies of capital and labor are fixed at
5 Determining GDPOutput is determined by the fixed factor supplies and the fixed state of technology:
6 The distribution of national income determined by factor prices, the prices per unit that firms pay for the factors of productionwage = price of Lrental rate = price of K
7 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
8 How factor prices are determined Factor prices are determined by supply and demand in factor markets.Recall: Supply of each factor is fixed.What about demand?
9 Demand for laborAssume 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 wagebenefit = marginal product of labor
10 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)
11 Exercise: Compute & graph MPL L Y MPL0 0 n.a.1 10 ?2 19 ?3 27 84 34 ?5 40 ?6 45 ?7 49 ?8 52 ?9 54 ?10 55 ?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.
13 MPL and the production function Youtput1MPLAs more labor is added, MPL 1MPLSlope of the production function equals MPLMPL1Llabor
14 Diminishing marginal returns As a factor input is increased, its marginal product falls (other things equal).Intuition: Suppose L while holding K fixed fewer machines per worker lower worker productivityTell class: Many production functions have this property.This slide introduces some short-hand notation that will appear throughout the PowerPoint presentations of the remaining chapters:The up and down arrows mean increase and decrease, respectively.The symbol “” means “causes” or “leads to.”Hence, the text after “Intuition” should be read as follows:“An increase in labor while holding capital fixed causes there to be fewer machines per worker, which causes lower productivity.”Many instructors use this type of short-hand (or something very similar), and it’s much easier and quicker for students to write down in their notes.
15 Exercise (part 2) L Y MPL 0 0 n.a. 1 10 10 Suppose W/P = 6. 2 19 9 2 19 93 27 84 34 75 40 66 45 57 49 48 52 39 54 2Suppose 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?If L=3, then the benefit of hiring the fourth worker (MPL=7) exceeds the cost of doing so (W/P = 6), so it pays the firm to increase L.If L=7, then the firm should hire fewer workers: the 7th worker adds only MPL=4 units of output, yet cost W/P = 6.The point of this slide is to get students to see the idea behind the labor demand = MPL curve.
16 MPL and the demand for labor Units of outputUnits of labor, LEach firm hires labor up to the point where MPL = W/P.MPL, Labor demandReal wageQuantity of labor demanded
17 The equilibrium real wage Units of outputUnits of labor, LLabor supplyThe real wage adjusts to equate labor demand with supply.MPL, Labor demandequilibrium real wage
18 The equilibrium real rental rate Units of outputUnits of capital, KSupply of capitalThe real rental rate adjusts to equate demand for capital with supply.MPK, demand for capitalequilibrium R/P
19 How income is distributed: total labor income =total capital income =If production function has constant returns to scale, thennational incomelabor incomecapital income
20 The ratio of labor income to total income in the U.S. Labor’s share of total incomeLabor’s share of income is approximately constant over time. (Hence, capital’s share is, too.)
21 The Cobb-Douglas Production Function The Cobb-Douglas production function has constant factor shares: = capital’s share of total income:capital income = MPK x K = Ylabor income = MPL x L = (1 – )YThe Cobb-Douglas production function is:where A represents the level of technology.
22 The Cobb-Douglas Production Function Each factor’s marginal product is proportional to its average product:
23 A closed economy, market-clearing model Outline of modelA closed economy, market-clearing modelSupply sidefactor markets (supply, demand, price)determination of output/incomeDemand sidedeterminants of C, I, and GEquilibriumgoods marketloanable funds marketDONE DONE Next
24 Demand for goods & services Components of aggregate demand:C = consumer demand for g & sI = demand for investment goodsG = government demand for g & s(closed economy: no NX )
25 Consumption: Cdef: Disposable income is total income minus total taxes: Y – T.Consumption function: C = C (Y – T )Shows that (Y – T ) Cdef: Marginal propensity to consume (MPC) is the increase in C caused by a one- unit increase in disposable income.
26 The consumption function Y – TC (Y –T )The slope of the consumption function is the MPC.MPC1
27 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 isthe cost of borrowingthe opportunity cost of using one’s own funds to finance investment spending.So, r I
28 The investment function rISpending on investment goods depends negatively on the real interest rate.I (r )
29 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:
30 The market for goods & services Aggregate demand:Aggregate supply:Equilibrium:The real interest rate adjusts to equate demand with supply.
31 The loanable funds market A simple supply-demand model of the financial system.One asset: “loanable funds”demand for funds: investmentsupply of funds: saving“price” of funds: real interest rate
32 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).
33 Loanable funds demand curve IThe investment curve is also the demand curve for loanable funds.I (r )
34 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.
35 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
36 EXERCISE: Calculate the change in saving Suppose MPC = 0.8 and MPL = 20.For each of the following, compute S :a. G = 100b. T = 100c. Y = 100d. L = 10
38 digression: 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.
39 U.S. Federal Government Surplus/Deficit, 1940-2004
40 U.S. Federal Government Debt, 1940-2004 Fact: In the early 1990s, about 18 cents of every tax dollar went to pay interest on the debt (Today it’s about 9 cents.)
41 Loanable funds supply curve S, INational saving does not depend on r, so the supply curve is vertical.
42 Loanable funds market equilibrium S, II (r )Equilibrium real interest rateEquilibrium level of investment
43 The special role of rr adjusts to equilibrate the goods market and the loanable funds market simultaneously:If L.F. market in equilibrium, thenY – C – G = IAdd (C +G ) to both sides to getY = C + I + G (goods market eq’m)Thus,Eq’m in L.F. marketEq’m in goods market
44 Digression: Mastering models 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, knowa. definitionb. intuition for slopec. all the things that can shift the curve3. Use the model to analyze the effects of each item in 2c.
45 Mastering the loanable funds model Things that shift the saving curvepublic savingfiscal policy: changes in G or Tprivate savingpreferencestax laws that affect saving401(k)IRAreplace income tax with consumption tax
46 CASE STUDY: The Reagan deficits Reagan policies during early 1980s:increases in defense spending: G > 0big tax cuts: T < 0Both policies reduce national saving:
47 CASE STUDY: The Reagan deficits 1. The increase in the deficit reduces saving…rS, II (r )r22. …which causes the real interest rate to rise…r13. …which reduces the level of investment.I2I1
48 Are the data consistent with these results? variable 1970s 1980sT – G –2.2 –3.9SrIT–G, S, and I are expressed as a percent of GDPAll figures are averages over the decade shown.
49 Now you try… Draw the diagram for the loanable funds model. Suppose the tax laws are altered to provide more incentives for private saving. (Assume that total tax revenue T does not change)What happens to the interest rate and investment?
50 Mastering the loanable funds model, continued Things that shift the investment curvesome technological innovationsto take advantage of the innovation, firms must buy new investment goodstax laws that affect investmentinvestment tax credit
51 An increase in investment demand S, II2An increase in desired investment…I1…raises the interest rate.r2r1But the equilibrium level of investment cannot increase because the supply of loanable funds is fixed.
52 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?
53 An increase in investment demand when saving depends on r S, IAn increase in investment demand raises r,which induces an increase in the quantity of saving,which allows I to increase.I(r)2I(r)r2I2r1I1
54 Chapter Summary Total output is determined by the economy’s quantities of capital and laborthe level of technologyCompetitive 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).
55 Chapter Summary A closed economy’s output is used for consumptioninvestmentgovernment spendingThe real interest rate adjusts to equate the demand for and supply ofgoods and servicesloanable funds
56 Chapter SummaryA 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.