Productivity, Output, and Employment - Understanding the Labor Market

1. Ch3: Productivity, Output, and Employment Abel & Bernake: Macro Ch3 Varian: Ch10, Ch19 1

2. Chapter Outline The Production Function The Demand for Labor The Supply of Labor Labor Market Equilibrium Unemployment Relating Output and Unemployment: Okun’s Law 2

3. The production function • describe relationship between inputs and output. • Real Output (Y) • Inputs: factors of production 生產要素 Y = AF(K, N) (3.1) K = capital: tools, machines, and structures N = labor: physical and mental efforts of workers F(．) reflects the economy’s level of technology A= “total factor productivity” (the effectiveness with which capital and labor are used) 3

4. Table 3.1 The Production Function of the United States, 1979-2007 Assumes constant returns to scale Cobb-Douglas production function works well for U.S. economy: Y = AK0.3N0.7 (3.2) Productivity grew slowly in 1980s and the first half of the 1990s, but increased since the mid-1990s. 4

5. Returns to scale: Initially Y1 = AF (K1 , N1 ) Scale all inputs by the same factor z: K2 = zK1 and N2 = zN1 (e.g., if z = 1.25, then all inputs are increased by 25%) What happens to output, Y2 = F (K2, N2 )? • If constant returns to scale, Y2 = zY1 • If increasing returns to scale, Y2 > zY1 • If decreasing returns to scale, Y2 < zY1 5

6. Examples 6

7. Diminishing marginal returns: diminishing MPN • Marginal Product of Labor: • Diminishing marginal returns: diminishing MPN • Suppose N while holding Kfixed fewer machines per worker  lower worker productivity • Marginal Product of Capital:

8. Fig 3.1 The Production Function Relating Output and Capital Fig 3.2 The marginal product of capital 8

9. MPN 1 As more labor is added, MPN  MPN 1 Slope of the production function equals MPN 1 Fig 3.3: MPN ( K fixed )Diminishing marginal returns Y output N MPN N labor 9

10. Eg, diminishing MPN Which of these production functions have diminishing marginal returns to labor? 10

11. Supply shocks Supply shock = productivity shock = a shift in an economy’s production function (Fig. 3.4) Supply shocks affect the amount of output that can be produced for a given amount of inputs Negative (adverse) shock: Usually slope of production function decreases at each level of input (eg, if shock causes parameter A to decline) Positive shock: Usually slope of production function increases at each level of output (eg, if parameter A increases) eg, weather, inventions and innovations, government regulations, oil prices 11

12. Fig3.4 An adverse supply shock that lowers the MPN 12

13. Firm: Profit Optimization • Assume: Supply of each factor is fixed. • Assume markets are competitive: each firm takes W, Re, and P as given. P = price of output, W = nominal wage, Re= nominal rental rate W /P = real wage (measured in units of output), Re /P= real rental rate 13

14. Demand for labor • benefit = MPN, cost = real wage A firm hires each unit of labor if the cost does not exceed the benefit. 14

15. Units of output Real wage MPN, Labor demand Units of labor, N Quantity of labor demanded Fig 3.5: MPN = Demand for labor Each firm hires labor up to the point where MPN = W/P. 15

16. Summary 2 16

17. Labor supply Units of output equilibrium real wage MPN, Labor demand Units of labor, N Labor Market: the equilibrium real wage N 17

18. A↑ or K↑→ ? → ?Fig 3.6 The effect of a beneficial supply shock on labor demand (here A↑) 18

19. Summary 3 19

20. The Supply of Labor Aggregate supply of labor is the horizontal sum of individuals’ labor supply Labor supply of individuals depends on consumption-leisure choice 20

21. Individual: Utility Optimization The consumption-leisure trade-off Max U(C, L) St. time constraint: L + h = T budget constraint: C ≦ wh + V U: utility, C: consumption, L: leisure, h: working hours, T: time endowment, w: real wage rate, V: nonlabor income, w: price of leisure, opportunity cost of leisure Constraint combined: C ≦ w(T-L) + V Trade-off: more h, less L, but more income and more C 21

22. Consumption ($) $1200 Y A $1100 P $500 U1 U* E $100 U0 Hours of Leisure 110 0 70 Hours of Work 0 110 40 Optimal consumption and leisure (參考)h > 0: working, h=0: not in the LFat point E: corner solution -- indifferent

23. A pure income effect (IE): V↑ Winning a lottery : V↑ A pure income effect: Demand for normal goods increase: C↑, L↑ Winning the lottery: no SE because it doesn’t affect the reward for working L↑=> h↓ 23

24. An increase in real wages: w↑ An increase in the real wage : w↑ Substitution effect (SE): w↑: price of leisure ↑ Use cheaper C to substitute more costly L => C↑,L↓ => h↑ Income effect (IE): w↑for same h => income ↑ => C↑,L ↑ => h ↓ w↑total effect: has offsetting IE and SE h ↑ if SE > IE h ↓ if SE < IE 24

25. Fig 3.7 labor supply curve of an individualworker 25

26. Temporary vs. Permanent increase in wOptimization over time (Ch4) • ISE: intertemporal substitution effect • ISE between current C and future C’ ISE between current L and future L’ • If temporary w↑: strong ISE + weak IE ISE > IE => L↓, h ↑ • If permanent w↑ : weak ISE + strong IE ISE < IE => L ↑, h ↓ • Empirical evidence support the implication.

27. Aggregate labor supply When current real wage rises Some people work more hours Other people enter labor force Result: Aggregate labor supply curve slopes upward 27

28. Fig 3.8 The effect on labor supply of an increase in wealth 28

29. Factors that shifts aggregate labor supply Factors increasing labor supply Decrease in wealth Decrease in expected future real wage Increase in working-age population (higher birth rate, immigration) Increase in labor force participation (increased female labor participation, elimination of mandatory retirement) 29

30. Summary 4 30

31. Application:comparing U.S. and European labor markets Unemployment rates were similar in the U.S. and Europe in 1970s and 1980s, but are higher in Europe since then (Fig. 3.9) 3 reasons for higher unemployment rates in Europe: generous unemployment insurance systems, high tax rates, government policies that interfere with labor markets 31

32. Fig 3.9 Unemployment rates in the U.S. and Europe, 1982-2008 Source: OECD Factbook 2009, Harmonised Unemployment Rates. 32

33. Labor Market Equilibrium Equilibrium: Labor supply equals labor demand Classical model of the labor market: real wage adjusts quickly Determines full-employment level of employment and market-clearing real wage Problem with classical model: can’t study unemployment 33

34. Fig 3.10Labor market equilibrium 34

35. Full-employment output Full-employment output = potential output = level of output when labor market in equilibrium Yf= AF(K, Nf) (3.4) An adverse supply shock: A↓ MPN =AFN ↓→ DN↓→ Nf↓ (Fig. 3.11) Yf ↓ because both A↓and Nf ↓ 35

36. Fig 3.11 Effects of a temporary adverse supply shock on the labor market Sources: Producer price index for fuels and related products and power from research.stlouisfed.org/fred2/series/PPIENG; GDP deflator from research.stlouisfed.org/fred2/GDPDEF. Data were scaled so that the relative price of energy equals 100 in year 2000. 36

37. Application: output, employment, and the real wage during oil price shocks Sharp oil price increases in 1973–1974, 1979–1980, 2003–2008 (Fig. 3.12) Adverse supply shock—lowers labor demand, employment, the real wage, and the full-employment level of output First two cases: U.S. economy entered recessions Research result: 10% increase in price of oil reduces GDP by 0.4 percentage points 37

38. Fig 3.12 Relative price of energy,1960-2008 38

39. Determination of factor prices （補充）Varian: 19.7-19.9 and Appendix Factor prices are determined by supply and demand in factor markets. Assume: Supply of each factor is fixed. Assume markets are competitive: each firm takes W, Re, and P as given. 39

40. Why assuming CRS?Eg, Cobb-Douglas Production Function A is exogenous, CRS: α+β=1  β=1-α Each factor’s MP is proportional to its AP.

41. Neoclassical Theory of Distribution: C-D production function in competitive markets • In the competitive market: • C-D production function (CRS)  constant factor shares: capital income≡ labor income ≡  = capital’s share of total income 1- = labor’s share of total income • Assumes CRS Cobb-Douglas production function works well for U.S. economy: Y = AK0.3N0.7 (3.2)

42. The ratio of labor income to total income in the U.S. Labor’s share of total income Labor’s share of income is approximately constant over time.(Hence, capital’s share is, too.)

43. Taiwan data: labor share

44. Neoclassical Theory of Distribution Proof that • Exhaustion of the product • imply zero profits for competitive firms in the LR. • Since π=0 for all periods, can ignore intertemporal analysis: profit maximization over-time

45. Ch3: 勞動力之分類

46. Fig 3.13 Worker flow: Changes in employment status in a typical month (June 2007) 46

47. Duration of Unemployment失業期間 Duration of unemployment （length of unemployment spell） Most unemployment spells are of short duration Most unemployed people on a given date are experiencing unemployment spells of long duration 47

48. 3 types of unemployment Frictional unemployment摩擦性失業 Search activity of firms and workers due to heterogeneity. Matching process takes time. Structural unemployment結構性失業 Reallocation of workers (lack of new skill) out of shrinking industries or depressed regions: matching takes a long time Cyclical unemployment景氣性失業 48

49. The natural rate of unemployment The natural rate of unemployment ( ) when output and employment are at full-employment levels = frictional + structural unemployment Cyclical unemployment: difference between actual unemployment rate and natural rate of unemployment, 49

50. Okun’s Law:Relating Output and Unemployment Relationship between output (relative to full-employment output) and cyclical unemployment (3.5) Alternative formulation: if average growth rate of full-employment output is 3%: Y/Y = 3 – 2 u (3.6) 50