Chapter 3: National Income: Where it Comes From and Where it Goes (Classical Model)

Chapter 3: National Income: Where it Comes From and Where it Goes (Classical Model) Prof. Chris Foote Harvard University Department of Economics February 4, 2008 Foote (Ec 1010b) Classical Model February 4, 2008 1 / 67

Outline 1 A Snapshot of the Economy at a Point in Time 2 What Determines Total Production by Firms? 3 How is Income Distributed to the Factors of Production? 4 What Determines the Demand for Goods and Services? 5 What Brings the Supply and Demand for Output Into Equilibrium? 6 Case Study: Consumption in the Late 1990s and Today Foote (Ec 1010b) Classical Model February 4, 2008 2 / 67

A Snapshot of the Economy at a Point in Time The Simple Circular Flow Diagram Foote (Ec 1010b) Classical Model February 4, 2008 4 / 67

A Snapshot of the Economy at a Point in Time The More Complex Circular Flow Diagram Foote (Ec 1010b) Classical Model February 4, 2008 5 / 67

What Determines Total Production by Firms? Factors of Production at a Point in Time Firms use two main factors of production 1 Capital: machines, factories, etc. Denote as K. How much capital do we have? Assume K = K, which is some fixed number We ll worry about how capital is determined in another chapter 2 Labor: Time spent working. Denote as L How much labor do we have? Assume L = L. In this chapter, assume that labor is fixed exogenously, like capital. Key assumption for both: No unemployed K or L. Foote (Ec 1010b) Classical Model February 4, 2008 7 / 67

What Determines Total Production by Firms? The Production Function Y = F(K, L) Mathematical way of saying that output depends on capital and labor Reflects the economy s level of technology for turning inputs into output Becomes more interesting when we make assumptions about the form of this function Important assumption: F is constant returns to scale Definition The production function F(K, L) is constant returns to scale (CRS) if zy = F(zK, zl). Foote (Ec 1010b) Classical Model February 4, 2008 8 / 67

What Determines Total Production by Firms? Constant Returns to Scale: Example 1 Assume a form for the production function Y = F(K, L) = KL Is this equation CRS? F(zK, ZL) = (zk)(zl) = z 2 KL = z 2 KL = z KL = zf(k, L) It works! Candidate function is CRS. Foote (Ec 1010b) Classical Model February 4, 2008 9 / 67

What Determines Total Production by Firms? Constant Returns to Scale: Example 2 Assume a form for the production function Is this equation CRS? Y = F(K, L) = K + L F(zK, ZL) = (zk) + (zl) = z K + z L = z[ K + L] = zf(k, L) It doesn t work. Candidate function is decreasing returns to scale for any z > 1. Foote (Ec 1010b) Classical Model February 4, 2008 10 / 67

What Determines Total Production by Firms? Supply of Goods and Services We are now ready to pin down the economy s long-run supply of goods and services Technology, capital, and labor are all fixed, so Y = F(K, L) = F(K, L) = Y Simple concept, but you will hear me say the phrase Y = Y often In the long run, no unemployment or idle capital, so output gravitates to its potential level, Y Foote (Ec 1010b) Classical Model February 4, 2008 11 / 67

How is Income Distributed to the Factors of Production? Factor Prices: Some Definitions Price of output = P Wage = price of L W = nominal wage (specified in dollars per time-period worked) W P = real wage Rental Rate = price of K R = nominal rental rate (specified in dollars per time-period that K is employed) R P = real rental rate Foote (Ec 1010b) Classical Model February 4, 2008 13 / 67

How is Income Distributed to the Factors of Production? Determination of Factor Prices What determines factor prices? Supply and Demand Supply curve for both factors are assumed to be inelastic Supply of factor does not vary with its reward Recall: Supplies of factors are fixed at K and L Demand curves for factors (K and L) slope down Firms want to employ less of a factor if it gets more expensive Foote (Ec 1010b) Classical Model February 4, 2008 14 / 67

How is Income Distributed to the Factors of Production? How a Factor of Production is Compensated Foote (Ec 1010b) Classical Model February 4, 2008 15 / 67

How is Income Distributed to the Factors of Production? Firm-Level Factor Demand in Detail Why do factor demand curves slope down? Assume a competitive firm Small in relation to both its input and output markets Its decisions have no impact on prices (P) or factor returns (W and R) Price taker in both input and output markets Basic idea: Firm continues hiring a factor until the extra benefit of an additional factor is equal to the extra cost of that factor Cost of factor: Real wage or real rental rate Benefit of factor: Marginal product of labor or capital Foote (Ec 1010b) Classical Model February 4, 2008 16 / 67

How is Income Distributed to the Factors of Production? Marginal Products of Capital and Labor Definition The marginal product of a factor is the increment to output that occurs when more of that factor is employed. The marginal product of a factor typically declines as more of the factor is added to the production process. MPL = F(K, L + 1) F(K, L) MPK = F(K + 1, L) F(K, L) Foote (Ec 1010b) Classical Model February 4, 2008 17 / 67

How is Income Distributed to the Factors of Production? The Production Function and MPL Foote (Ec 1010b) Classical Model February 4, 2008 18 / 67

How is Income Distributed to the Factors of Production? MPL and MPK using Calculus Notation Book defines MPL as resulting from a discrete change of 1 unit of L This is essentially a derivative how F(.) changes when we change L Calculus makes the point at which we are taking the derivative more precise MPL = F(K, L + 1) F(K, L) df dl MPK = F(K + 1, L) F(K, L) df dk Foote (Ec 1010b) Classical Model February 4, 2008 19 / 67

How is Income Distributed to the Factors of Production? The Firm s Problem Profit function is: Profit = Revenue - Labor costs - Capital Costs Mathematically, we have: Profit = PY WL RK = PF(K, L) WL RK Firm wants to maximize profits It will add more K and L to F(.) until doing so no longer increases profits So, set the change in profits that comes with one more unit of K or L = 0 Foote (Ec 1010b) Classical Model February 4, 2008 20 / 67

How is Income Distributed to the Factors of Production? Maximizing profits with respect to L Profit = PF(K, L) WL RK Profit = 0 P MPL W = 0 MPL = W P Foote (Ec 1010b) Classical Model February 4, 2008 21 / 67

How is Income Distributed to the Factors of Production? Maximizing profits with respect to K Profit = PF(K, L) WL RK Profit = 0 P MPK R = 0 MPK = R P Foote (Ec 1010b) Classical Model February 4, 2008 22 / 67

How is Income Distributed to the Factors of Production? Firm-Level Demand for Labor Foote (Ec 1010b) Classical Model February 4, 2008 23 / 67

How is Income Distributed to the Factors of Production? Division of National Income Think of economy as one big pie How big are the total slices going to labor and capital? Is there any real economic profit left over? Real economic profit = Y (MPK K) (MPL L) Rearranging, we have Y = (MPK K) + (MPL L) + (Real economic profit) Turns out that in competitive economic, real economic profit is zero! Foote (Ec 1010b) Classical Model February 4, 2008 24 / 67

How is Income Distributed to the Factors of Production? Euler s Theorem If F(K, L) has constant returns to scale, then F(K, L) = (MPK K) + (MPL L) Implication: If the two factors (K and L) are paid their marginal products... then there is no pie left over after labor and capital have received their total slices Foote (Ec 1010b) Classical Model February 4, 2008 25 / 67

How is Income Distributed to the Factors of Production? Absence of economic profit If F(K, L) = Y = (MPK K) + (MPL L) and Y = (MPK K) + (MPL L) + (Real economic profit) then (Real economic profit) = 0. Note that accounting profit can still be positive Accounting profit = (MPK K) + (Real economic profit) = (MPK K) Foote (Ec 1010b) Classical Model February 4, 2008 26 / 67

How is Income Distributed to the Factors of Production? Cobb-Douglas Production Function Figure 1. Paul H. Douglas (1892-1976) In 1927, economist (later Senator) Paul Douglas notices that labor s share of income has been stable over time. It still is. Foote (Ec 1010b) Classical Model February 4, 2008 27 / 67

How is Income Distributed to the Factors of Production? Ratio of Labor Income to Total Income Foote (Ec 1010b) Classical Model February 4, 2008 28 / 67

How is Income Distributed to the Factors of Production? Cobb-Douglas Production Function (con t) Douglas asked a colleague, Charles Cobb: What type of function would generate this regularity? To generate constant capital share (α), we need Capital income = (MPK K) = αy Labor income = (1 - Capital income) = (MPL L) = (1 α)y Cobb says that the required function looks like this: F(K, L) = AK α L 1 α Here, A is a technology parameter (more on this later) Foote (Ec 1010b) Classical Model February 4, 2008 29 / 67

How is Income Distributed to the Factors of Production? Cobb-Douglas Production Function in Action What is the (MPL L) for a Cobb-Douglas function: F(K, L) = AK α L 1 α MPL L = df dl L = (1 α)ak α L α L = (1 α)ak α L α+1 = (1 α)ak α L 1 α = (1 α)y Foote (Ec 1010b) Classical Model February 4, 2008 30 / 67

How is Income Distributed to the Factors of Production? Implications of Cobb-Douglas Total Payment to L = MPL L = (1 α)y Total Payment to K = MPK K = αy Capital share α is a parameter of the production function F(.) It does not depend on... Amount of K Amount of L Level of A Foote (Ec 1010b) Classical Model February 4, 2008 31 / 67

How is Income Distributed to the Factors of Production? Implications of Cobb-Douglas (con t) Total Payment to L = MPL L = (1 α)y Total Payment to K = MPK K = αy W P = MPL = (1 α)y L R P = MPK = αy K MPL = W P is proportional to average labor productivity ( Y L ) Implication: Periods of high average productivity growth are times of high real wage growth Foote (Ec 1010b) Classical Model February 4, 2008 32 / 67

How is Income Distributed to the Factors of Production? Growth in Labor Productivity and Wages Foote (Ec 1010b) Classical Model February 4, 2008 33 / 67

What Determines the Demand for Goods and Services? A Model of Aggregate Demand We have looked at the supply-side of the economy: Y = Y = F(K, L). Now we need a model for the individual components of demand: Y = C + I + G + NX Consumption (C): Consumer demand for goods and services Investment (I): Firm demand for investment goods Government Purchases (G): Government demand for goods and services Net Exports (NX): Exports minus imports This one is easy Assume a closed economy (for now), so NX = 0 Foote (Ec 1010b) Classical Model February 4, 2008 35 / 67

What Determines the Demand for Goods and Services? Consumption Demand For most of the course, we will have a very simple model of consumption demand Consumption will depend mostly on disposable income or (Y T ) T is total taxes paid (not the tax rate!) Foote (Ec 1010b) Classical Model February 4, 2008 36 / 67

What Determines the Demand for Goods and Services? The Consumption Function Foote (Ec 1010b) Classical Model February 4, 2008 37 / 67

What Determines the Demand for Goods and Services? The Consumption Function In Detail The general form for our consumption function is C = C(Y T). The specific functional form for this equation will be C = C(Y T) = a + MPC (Y T) MPC is the marginal propensity to consume out of disposable income MPC is also the slope of the consumption function a is autonomous consumption or all other determinants of consumption We will take a as exogenous Foote (Ec 1010b) Classical Model February 4, 2008 38 / 67

What Determines the Demand for Goods and Services? What might be included in a? 1 Wealth (including housing prices) 2 Optimism about the future (including future earnings) 3 Reward to delaying consumption until later (such as interest rate earned on your savings) 4 Ability to delay gratification (self-control) The determinants of consumption remains an active area of macroeconomic research Foote (Ec 1010b) Classical Model February 4, 2008 39 / 67

What Determines the Demand for Goods and Services? Definition of Real Interest Rate (r) Definition The real interest rate (r) is the nominal interest rate (i) corrected for the effects of inflation: r = i π e, where π e is the expected rate of inflation. To be more precise, this is the ex ante real interest rate. For now, assume that actual inflation π equals π e are equal, so r = i π. This formulation is the ex post real interest rate. Foote (Ec 1010b) Classical Model February 4, 2008 40 / 67

What Determines the Demand for Goods and Services? Our Investment Function Our investment function is where a higher r reduces I. More formally, write I = I(r) I = φ d r where d > 0 is the sensitivity of I to r φ is animal spirits, or all factors that change investment apart from r Like a in the consumption function, we take φ as exogenous Foote (Ec 1010b) Classical Model February 4, 2008 41 / 67

What Determines the Demand for Goods and Services? Why Does Higher r Reduce I? If firms have to borrow, this is easy to see Higher r raises the interest bill firms have to pay for financing a given investment project Fewer projects are therefore profitable if real interest rates are high Also true if firms finance investment out of retained earnings Firms could loan out their savings to others (through a bank) at r This is more attractive (relative to paying for an investment project) when r rises Foote (Ec 1010b) Classical Model February 4, 2008 42 / 67

What Determines the Demand for Goods and Services? The Investment Function Foote (Ec 1010b) Classical Model February 4, 2008 43 / 67

What Determines the Demand for Goods and Services? Government Purchases and Taxes Throughout this course, we will take G and T to be exogenous G = G T = T G and T are important policy variables Congress and the President are now considering ways of increasing G or lowering T to stave off recession Higher G would include more public works projects (like fixing roads and bridges) Increased transfers (like extended unemployment benefits) do not count in G Foote (Ec 1010b) Classical Model February 4, 2008 44 / 67

What Brings the Supply and Demand for Output Into Equilibrium? Equilibrium in the Markets for Goods and Services Aggregate supply: Y = F(K, L) Aggregate demand: Y = C(Y T) + I(r) + G Equilibrium: Y = C(Y T) + I(r) + G What ensures that equilibrium occurs, given the values of the exogenous variable? Has to be the real interest rate, r: Y = C(Y T) + I(r) + G Foote (Ec 1010b) Classical Model February 4, 2008 46 / 67

What Brings the Supply and Demand for Output Into Equilibrium? The Loanable Funds Market The intuition for how the real interest rate equilibrates the goods market is most easily seen by examining the market for loanable funds Rewrite national accounts identity as Y C G = I Define total saving (S) as Y C G so that I = S = Y C G Separate saving into public saving and private saving by adding and subtracting T from right-hand-side S = (Y C T) + }{{} (T G) }{{} Private saving Public saving Foote (Ec 1010b) Classical Model February 4, 2008 47 / 67

What Brings the Supply and Demand for Output Into Equilibrium? 3 Federal Government Budget Surplus: 1962-2006 2 1 0 Percent of GDP -1-2 -3-4 -5-6 -7 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 Source: Congressional Budget Office Foote (Ec 1010b) Classical Model February 4, 2008 48 / 67

What Brings the Supply and Demand for Output Into Equilibrium? 24 Federal Government Revenues and Outlays: 1962-2006 23 Outlays 22 21 Percent of GDP 20 19 18 Revenues 17 16 15 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 Source: Congressional Budget Office Foote (Ec 1010b) Classical Model February 4, 2008 49 / 67

What Brings the Supply and Demand for Output Into Equilibrium? Equilibrium in the Loanable Funds Market Rearranging the national accounts identity and substituting our consumption function for C gives Y C(Y T) G = I(r) G and T are fixed by government policy, and Y is fixed by supplies of K and L, so we have Y C(Y T) G = I(r) Left-hand-side: If Y, G and T are fixed, then saving (S) is also fixed at S Right-hand-side: I depends negatively on r S = I(r) Foote (Ec 1010b) Classical Model February 4, 2008 50 / 67

What Brings the Supply and Demand for Output Into Equilibrium? Saving, Investment, and the Interest Rate Foote (Ec 1010b) Classical Model February 4, 2008 51 / 67

What Brings the Supply and Demand for Output Into Equilibrium? Interpretation of Loanable Funds Equilibrium Think of the loanable funds market as a true market The good is the amount of loanable funds available for investment Saving is the supply of this good Investment generates the demand for this good r is the price of this good If r is too high, then supply of funds > demand for funds, so r falls If r is too low, then demand for funds > supply of funds, so r rises Foote (Ec 1010b) Classical Model February 4, 2008 52 / 67

What Brings the Supply and Demand for Output Into Equilibrium? Policy Experiment # 1: Change in Fiscal Policy Consider an increase in government purchases G What effect does this have on national saving? S = (Y C T) + }{{} (T G) }{{} Private saving Public saving National saving declines as G rises, so saving schedule shifts to the left r has to rise in order to equilibrate goods market, so investment gets crowded out by higher G Foote (Ec 1010b) Classical Model February 4, 2008 53 / 67

What Brings the Supply and Demand for Output Into Equilibrium? A Reduction in Saving Foote (Ec 1010b) Classical Model February 4, 2008 54 / 67

What Brings the Supply and Demand for Output Into Equilibrium? Experiment # 2: An Increase in Investment Demand Consider an increase in our animal spirits variable in the investment function: I = φ dr Other things equal, investment would rise Problem is, other things will not be equal r will rise to completely offset the increase in animal spirits Why? We know that S = I, but no piece of S rises I = S = (Y C T) + }{{} (T G) }{{} Private saving Public saving Foote (Ec 1010b) Classical Model February 4, 2008 55 / 67

What Brings the Supply and Demand for Output Into Equilibrium? An Increase in Investment Demand Foote (Ec 1010b) Classical Model February 4, 2008 56 / 67

What Brings the Supply and Demand for Output Into Equilibrium? Experiment # 2 (con t): An Increase in Investment Demand One way in which I can rise is if saving depends on the interest rate Higher r means that return to delaying consumption is greater, so S may rise Foote (Ec 1010b) Classical Model February 4, 2008 57 / 67

What Brings the Supply and Demand for Output Into Equilibrium? An Increase in Investment Demand when S depends on r Foote (Ec 1010b) Classical Model February 4, 2008 58 / 67

What Brings the Supply and Demand for Output Into Equilibrium? Simplifying assumptions Ignored the role of money (relaxed in Chapter 4) Assumed a closed economy (Chapter 5) Assumed full employment (Chapter 6) Assumed that K and L are fixed (Chapters 7 & 8) Ignored the role of short-run sticky prices (Chapters 9 through 13) Foote (Ec 1010b) Classical Model February 4, 2008 59 / 67

Case Study: Consumption in the Late 1990s and Today Consumption Growth in the 1990s We saw in the current events class that output grew strongly in the late 1990s, before the 2001 recession Consumption growth grew especially quickly during this time One reason for strong consumption growth: Strong growth in wages This last relationship is consistent with C = C(Y T) Foote (Ec 1010b) Classical Model February 4, 2008 61 / 67

Case Study: Consumption in the Late 1990s and Today 6 Real Consumption Growth: 1987-2007 5 Percent Change from Four Quarters Ago 4 3 2 1 0-1 Q1:1987 Q1:1990 Q1:1993 Q1:1996 Q1:1999 Q1:2002 Q1:2005 Foote (Ec 1010b) Classical Model February 4, 2008 62 / 67

Case Study: Consumption in the Late 1990s and Today 12 Consumption Growth: 1948-2007 10 Percent Change from Four Quarters Ago 8 6 4 2 0-2 -4 Q1:1948 Q1:1953 Q1:1958 Q1:1963 Q1:1968 Q1:1973 Q1:1978 Q1:1983 Q1:1988 Q1:1993 Q1:1998 Q1:2003 Foote (Ec 1010b) Classical Model February 4, 2008 63 / 67

Case Study: Consumption in the Late 1990s and Today 5.0 Growth in Nominal Wages: 1987-2007 4.5 Percent Change from Four Quarters Ago 4.0 3.5 3.0 2.5 2.0 1.5 1.0 Employment Cost Index: Wages and Salaries for Private Industries Average Hourly Earnings (from Establishment Survey) 0.5 0.0 Q1:1987 Q1:1990 Q1:1993 Q1:1996 Q1:1999 Q1:2002 Q1:2005 Foote (Ec 1010b) Classical Model February 4, 2008 64 / 67

Case Study: Consumption in the Late 1990s and Today Role of Stock Market Wealth in 1990s and Today Another reason for the strong growth in consumption was higher stock-market wealth Lower stock prices in the past several months could dampen consumption growth in 2008 Foote (Ec 1010b) Classical Model February 4, 2008 65 / 67

Case Study: Consumption in the Late 1990s and Today 1800 U.S. Stock Market Indexes: Jan 1982 to Dec 2007 1600 1400 Dow Jones Industrial Average Index Value (Jan:1982 = 100) 1200 1000 800 600 S&P 500 400 200 0 Jan:1982 Jan:1985 Jan:1988 Jan:1991 Jan:1994 Jan:1997 Jan:2000 Jan:2003 Jan:2006 Foote (Ec 1010b) Classical Model February 4, 2008 66 / 67

Case Study: Consumption in the Late 1990s and Today U.S. Stock Market Indicies in 2007 and 2008 14500 1600 14000 13500 S&P 500 (right scale) 1550 1500 13000 12500 12000 Dow Jones Industrial Average (left scale) 1450 1400 1350 1300 11500 1250 11000 1200 10500 1150 01:Jan:2007 19:Feb:2007 09:Apr:2007 28:May:2007 16:Jul:2007 03:Sep:2007 22:Oct:2007 10:Dec:2007 28:Jan:2008 Foote (Ec 1010b) Classical Model February 4, 2008 67 / 67