IN THIS LECTURE, YOU WILL LEARN: Am simple perfect competition production medium-run model view of what determines the economy s total output/income how the prices of the factors of production are determined according to this model how total income is distributed what determines the demand for goods and services how equilibrium in the goods market is achieved 2 theories of consumption 0
Outline of 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 goods market loanable funds market 1
Production Model Vast oversimplifications of the real world in a model can still allow it to provide important insights. Consider the following model Single, closed economy One consumption good 2
Factors of production K = capital: tools, machines, and structures used in production L = labor: the physical and mental efforts of workers 3
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 We assume that the production function for the economy as a whole exhibits constant returns to scale 4
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 5
Returns to scale: Example 1 F( K, L) KL F( zk, zl) ( zk)( zl) 2 z KL z 2 KL z KL z F( K, L) constant returns to scale for any z > 0 6
Returns to scale: Example 2 F( K, L) K L F( zk, zl) zk zl z K z L z K L z F( K, L) decreasing returns to scale for any z > 1 7
Returns to scale: Example 3 F( K, L) K L 2 2 F( zk, zl) ( zk) ( zl) 2 2 z K L 2 2 2 z F( K, L) 2 increasing returns to scale for any z > 1 8
NOW YOU TRY Returns to scale Determine whether each of these production functions has constant, decreasing, or increasing returns to scale: (a) F( K, L) K L 2 (b) F( K, L) K L 9
ANSWERS Returns to scale, part (a) F( K, L) K L 2 F( zk, zl) ( zk) zl 2 zk zl 2 2 K z L 2 z F( K, L) constant returns to scale for any z > 0 CHAPTER 1 The Science of Macroeconomics 10
ANSWERS Returns to scale, part (b) F( K, L) K L F( zk, zl) zk zl z( K L) z F( K, L) constant returns to scale for any z > 0 CHAPTER 1 The Science of Macroeconomics 11
Assumptions 1. Technology is fixed. 2. The economy s supplies of capital and labor are fixed at K K and L L 12
Determining GDP Output is determined by the fixed factor supplies and the fixed state of technology: Y F( K, L) 13
The distribution of national income determined by factor prices, the prices per unit firms pay for the factors of production wage = price of L rental rate = price of K 14
Notation W R P W /P = nominal wage = nominal rental rate = price of output = real wage (measured in units of output) R /P = real rental rate 15
How factor prices are determined Factor prices determined by supply and demand in factor markets. Recall: Supply of each factor is fixed. What about demand? 16
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 17
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) 18
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 10? 2 19? 3 27 8 4 34? 5 40? 6 45? 7 49? 8 52? 9 54? 10 55? 19
ANSWERS Compute & graph MPL Marginal Product of Labor MPL (units of output) 12 10 8 6 4 2 0 0 1 2 3 4 5 6 7 8 9 10 Labor (L) 20
MPL and the production function Y output As more labor is added, MPL 1 MPL 1 MPL F ( K, L) 1 MPL Slope of the production function equals MPL L labor 21
Diminishing marginal returns As an input is increased, its marginal product falls (other things equal). Intuition: Suppose L while holding K fixed fewer machines per worker lower worker productivity 22
NOW YOU TRY Identifying Diminishing 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 23
ANSWERS Identifying Diminishing Returns a) F( K, L) 2K 15L No, MPL = 15 for all L b) F( K, L) KL Yes, MPL falls as L rises c) F( K, L) 2 K 15 L Yes, MPL falls as L rises CHAPTER 1 The Science of Macroeconomics 24
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? L Y MPL 0 0 n.a. 1 10 10 2 19 9 3 27 8 4 34 7 5 40 6 6 45 5 7 49 4 8 52 3 9 54 2 10 55 1 CHAPTER 1 The Science of Macroeconomics 25
ANSWERS MPL and labor demand If L = 3, should firm hire more or less labor? Answer: YES, because the benefit of the 4th worker (MPL = 7) exceeds its cost (W/P = 6) If L = 7, should firm hire more or less labor? Answer: NO, the firm should reduce 9 54 2 labor. The 7th worker adds 10 55 1 MPL = 4 units of output but costs the firm W/P = 6. 26 CHAPTER 1 The Science of Macroeconomics L Y MPL 0 0 n.a. 1 10 10 2 19 9 3 27 8 4 34 7 5 40 6 6 45 5 7 49 4 8 52 3
MPL and the demand for labor Units of output Real wage Each firm hires labor up to the point where MPL = W/P. Quantity of labor demanded MPL, Labor demand Units of labor, L 27
The equilibrium real wage Units of output Labor supply The real wage adjusts to equate labor demand with supply. equilibrium real wage L MPL, Labor demand Units of labor, L 28
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. 29
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 30
The Neoclassical Theory of Distribution states that each factor input is paid its marginal product a good starting point for thinking about income distribution 31
How income is distributed to L and K total labor income = W L P total capital income = R 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 32
The ratio of labor income to total income in the U.S., 1960-2010 Labor s share of total income 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Labor s share of income has historically been fairly constant over time. (Thus, capital s share is, too.) However, over the last 40 years or so it has been falling somewhat. 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Share of Labor Income by Sector 34
The Cobb-Douglas Production Function The Cobb-Douglas production function has constant factor shares: = capital s share of total income: capital income = MPK K = Y labor income = MPL L = (1 )Y The Cobb-Douglas production function is: Y 1 AK L where A represents the level of technology. 35
The Cobb-Douglas Production Function Each factor s marginal product is proportional to its average product: MPK AK L MPL 1 1 Y (1 ) AK L K (1 ) Y L 36
Labor productivity and wages Theory: wages depend on labor productivity U.S. data: period productivity growth real wage growth 1960 2010 2.2% 1.9% 1960 1973 2.9% 2.8% 1973 1995 1.4% 1.2% 1995 2010 2.7% 2.2% 37
Analyzing the Production Model Per capita = per person Per worker = per member of the labor force. In this model, the two are equal. We can perform a change of variables to define output per capita (y) and capital per person (k). 38
Output per person equals the productivity parameter times capital per person raised to the one-third power. Output per person Productivity parameter Capital per person 39
What makes a country rich or poor? Output per person is higher if the productivity parameter is higher or if the amount of capital per person is higher. What can you infer about the value of the productivity parameter or the amount of capital in poor countries? 40
Diminishing returns to capital implies that: Countries with low K will have a high MPK Countries with a lot of K will have a low MPK, and cannot raise GDP per capita by much through more capital accumulation If the productivity parameter is 1, the model overpredicts GDP per capita. 41
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Case Study: Why Doesn t Capital Flow from Rich to Poor Countries? If MPK is higher in poor countries with low K, why doesn t capital flow to those countries? Short Answer: Simple production model with no difference in productivity across countries is misguided. We must also consider the productivity parameter. 45
Productivity Differences: Improving the Fit of the Model The productivity parameter measures how efficiently countries are using their factor inputs. Often called total factor productivity (TFP) If TFP is no longer equal to 1, we can obtain a better fit of the model. 46
However, data on TFP is not collected. It can be calculated because we have data on output and capital per person. TFP is referred to as the residual. A lower level of TFP Implies that workers produce less output for any given level of capital per person 47
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Output differences between the richest and poorest countries? Differences in capital per person explain about one-quarter of the difference. TFP explains the remaining three-quarters. Thus, rich countries are rich because: They have more capital per person. More importantly, they use labor and capital more efficiently. 51
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 52
Demand for goods and 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) 53
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. 54
The consumption function C C (Y T ) 1 MPC The slope of the consumption function is the MPC. Y T 55
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 56
The investment function r Spending on investment goods depends negatively on the real interest rate. I (r ) I 57
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 58
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 The real interest rate adjusts to equate demand with supply. 59
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 60
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). 61
Loanable funds demand curve r The investment curve is also the demand curve for loanable funds. I (r ) I 62
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. 63
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 64
Notation: = change in a variable For any variable X, X = 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 65
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 66
NOW YOU TRY 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 c. S 0.2 100 20 d. Y MPL L 20 10 200, CHAPTER 1 S 0.2 Y 0.2 200 40. The Science of Macroeconomics 67
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. 68
percent of GDP U.S. Federal Government Surplus/Deficit, 1940 2016 10 5 0-5 -10-15 -20-25 -30-35 1940 1950 1960 1970 1980 1990 2000 2010
percent of GDP U.S. Federal Government Debt, 1940 2016 140 120 100 80 60 40 20 0 1940 1950 1960 1970 1980 1990 2000 2010
Loanable funds supply curve r S Y C ( Y T ) G For now, we assume that national saving does not depend on r, so the supply curve is vertical. S, I 71
Loanable funds market equilibrium r S Y C ( Y T ) G Equilibrium real interest rate I (r ) Equilibrium level of investment S, I 72
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 Eq m in L.F. market (goods market eq m) Eq m in goods market 73
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, know: a. definition b. intuition for slope c. all the things that can shift the curve 74
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 replace income tax with consumption tax 75
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 76
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 77
Are the data consistent with these results? 1970s 1980s 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. 78
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 79
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 1 I 2 S, I 80
Another look at Consumption, 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? 81
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 S( r) I(r) 2 I(r) I 1 I 2 S, I 82
Increase in Global Savings 83
Effect on Global Balances 84
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Consumption How do you decide how much to spend on consumption? 88
Consumption 2 competing views of consumption 1. Consumption depends primarily on current income (Keynesian consumption function). 2. People prefer a smooth path for consumption compared to a path that involves large movements (Permanent Income/Life Cycle Hypothesis). 89
The Keynesian consumption function C As income rises, consumers save a bigger fraction of their income, so APC falls. C C cy C C APC c Y Y slope = APC Y 90
Early empirical successes: Results from early studies Households with higher incomes: consume more, MPC > 0 save more, MPC < 1 save a larger fraction of their income, APC as Y Very strong correlation between income and consumption: income seemed to be the main determinant of consumption 91
Problems for the Keynesian consumption function Based on the Keynesian consumption function, economists predicted that C would grow more slowly than Y over time. This prediction did not come true: As incomes grew, APC did not fall, and C grew at the same rate as income. Simon Kuznets showed that C/Y was very stable from decade to decade. 92
The Consumption Puzzle C Consumption function from long time-series data (constant APC ) Consumption function from cross-sectional household data (falling APC ) Y 93
Irving Fisher and Intertemporal Choice The basis for much subsequent work on consumption. Assumes consumer is forward-looking and chooses consumption for the present and future to maximize lifetime satisfaction. Consumer s choices are subject to an intertemporal budget constraint, a measure of the total resources available for present and future consumption. 94
The basic two-period model Period 1: the present Period 2: the future Notation Y 1, Y 2 = income in period 1, 2 C 1, C 2 = consumption in period 1, 2 S = Y 1 C 1 = saving in period 1 (S < 0 if the consumer borrows in period 1) 95
Deriving the intertemporal budget constraint Period 2 budget constraint: Rearrange terms: C 2 Y2 (1 r ) S Y (1 r )( Y C ) 2 1 1 (1 r ) C C Y (1 r ) Y 1 2 2 1 Divide through by (1+r ) to get 96
The intertemporal budget constraint C C Y Y 1 r 1 r 2 2 1 1 present value of lifetime consumption present value of lifetime income 97
The intertemporal budget constraint C 2 C C Y Y 1 r 1 r 2 2 1 1 (1 r ) Y Y The budget constraint shows all combinations of C 1 and C 2 that just exhaust the consumer s resources. 1 2 Y 2 Saving Y 1 Consump = income in both periods Borrowing Y Y (1 r ) 1 2 C 1 98
The intertemporal budget constraint The slope of the budget line equals (1+r ) C 2 1 C C Y Y 1 r 1 r 2 2 1 1 (1+r ) Y 2 Y 1 C 1 99
Consumer preferences An indifference curve shows all combinations of C 1 and C 2 that make the consumer equally happy. C 2 Higher indifference curves represent higher levels of happiness. IC 2 IC 1 C 1 100
Consumer preferences Marginal rate of substitution (MRS ): the amount of C 2 the consumer would be willing to substitute for one unit of C 1. C 2 1 MRS The slope of an indifference curve at any point equals the MRS at that point. IC 1 C 1 101
Optimization The optimal (C 1,C 2 ) is where the budget line just touches the highest indifference curve. C 2 O At the optimal point, MRS = 1+r C 1 102
How C responds to changes in Y Results: Provided they are both normal goods, C 1 and C 2 both increase, whether the income increase occurs in period 1 or period 2. C 2 An increase in Y 1 or Y 2 shifts the budget line outward. C 1 103
Keynes vs. Fisher Keynes: Current consumption depends only on current income. Fisher: Current consumption depends only on the present value of lifetime income. The timing of income is irrelevant because the consumer can borrow or lend between periods. 104
How C responds to changes in r As depicted here, C 1 falls and C 2 rises. However, it could turn out differently C 2 B An increase in r pivots the budget line around the point (Y 1,Y 2 ). A Y 2 Y 1 C 1 105
How C responds to changes in r income effect: If consumer is a saver, the rise in r makes him better off, which tends to increase consumption in both periods. substitution effect: The rise in r increases the opportunity cost of current consumption, which tends to reduce C 1 and increase C 2. Both effects C 2. Whether C 1 rises or falls depends on the relative size of the income & substitution effects. 106
Constraints on borrowing In Fisher s theory, the timing of income is irrelevant: Consumer can borrow and lend across periods. Example: If consumer learns that her future income will increase, she can spread the extra consumption over both periods by borrowing in the current period. However, if consumer faces borrowing constraints (a.k.a. liquidity constraints), then she may not be able to increase current consumption and her consumption may behave as in the Keynesian theory even though she is rational & forward-looking. 107
Constraints on borrowing C 2 The budget line with no borrowing constraints Y 2 Y 1 C 1 108
Constraints on borrowing The borrowing constraint takes the form: C 1 Y 1 Y 2 C 2 The budget line with a borrowing constraint Y 1 C 1 109
Consumer optimization when the borrowing constraint is not binding The borrowing constraint is not binding if the consumer s optimal C 1 is less than Y 1. C 2 Y 1 C 1 110
Consumer optimization when the borrowing constraint is binding The optimal choice is at point D. C 2 But since the consumer cannot borrow, the best he can do is point E. E D Y 1 C 1 111
L E C T U R E S U M M A R Y Total output 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). 112
L E C T U R E S U M M A R Y A closed economy s output is used for consumption, investment, and government spending. The real interest rate adjusts to equate the demand for and supply of: goods and services. loanable funds. 113
L E C T U R E S U M M A R Y 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. 114
L E C T U R E S U M M A R Y CHAPTER 1 Alternative Views of Consumption 1. Keynesian consumption theory Keynes s conjectures MPC is between 0 and 1 APC falls as income rises current income is the main determinant of current consumption Empirical studies in household data & short time series: confirmation of Keynes s conjectures in long-time series data: APC does not fall as income rises The Science of Macroeconomics 115
L E C T U R E S U M M A R Y 2. Fisher s theory of intertemporal choice Consumer chooses current & future consumption to maximize lifetime satisfaction of subject to an intertemporal budget constraint. Current consumption depends on lifetime income, not current income, provided consumer can borrow & save. CHAPTER 1 The Science of Macroeconomics 116