Figure 4.1 Average Hours Worked per Person in the United States

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1 The Supply of Labor Figure 4.1 Average Hours Worked per Person in the United States 1

2 Table 4.1 Change in Hours Worked by Age: : Preferences 4.2: The Constraints 4.3: Optimal Choice I: Determination 4.4: Optimal Choice II: Properties 4.5: The Empirical Evidence 2

3 Assumptions about workers How they make choices Their goals Inherent restrictions Decline in workweek length, changes in work patterns u=u(c,l) represents the individual s tastes over different consumption-leisure pairs u o : indifference curve combinations of c and l over which the individual is indifferent Slope of indifference curve represents the individual s willingness to trade consumption for additional leisure time 3

4 Figure 4.2 The Utility Function u(c,,) Figure 4.3 An Indifference Curve Map 4

5 MRS= -(Δc/Δl)u o >0 Absolute value of the slope of indifference curve MRS can be used to compare individuals work attitudes Figure 4.4 The Fundamental Properties of an Indifference Curve 5

6 Equation 4.2 Definition 4.1 6

7 Figure 4.5 Work Attitudes The marginal utility of leisure (MU l )=Δc/Δl, holding c constant The marginal utility of consumption (MU c )=Δc/Δl, holding l constant 7

8 So, u MU l l + MU c c Along a single indifference curve, set the above equal to 0 Rearrange to find MRS=MU l /MU c > 0 Assumption 4.1: Time allocation Worker enjoys l hours of leisure and works for h hours such that T=h+l=24 Assumption 4.2: Legal and Policy Environment The only function of the government is to enforce property rights and contracts, a task that it does flawlessly 8

9 Assumption 4.3: Market Constraints The worker is free to choose the number of hours (h) that he works. The hourly wage rate $W, and his initial wealth plus earned income is $A o The worker s budget line determines the set of consumption-leisure bundles he can afford by summing labor earnings and initial wealth. The budget line is given by c=a o + W. (T-1) The slope is -$W/h The budget line intercepts the vertical l=t at c=$a o 9

10 Figure 4.6 The Budget Constraint Figure 4.7 The Effects of an Increase in Wealth, A0, and the Wage, W, on the Worker s Budget Set 10

11 Assumption 4.4: Utility Maximization The worker examines all feasible consumptionleisure combinations (c,l) and picks the one that maximizes her utility She chooses the point on the budget line that is tangent to the outermost indifference curve, at which she consumes c 0 * of goods and enjoys l 0 * of leisure. Figure 4.8 Optimal Behavior 11

12 l 0 * is an interior solution in this case because it lies strictly within the binding limits l = 0 and l = T. At the point of tangency the slope of the budget line equals the slope of the worker s highest attainable indifference curve so that W = MRS. At the point of tangency the slope of the budget line equals the slope of the worker s highest attainable indifference curve so that W = MRS. Figure 4.9 A Nonparticipant 12

13 Nonparticipants face the same budget constraint. A nonparticipant chooses the point P = (T, A 0 ) l 0 * is a corner solution in this case since it occurs at the corner of the budget constraint, where l 0 * = T. If W > MRS p, then the worker participates in the labor force. If MRS p W, he does not. If an individual does participate, his optimal choice is located at an interior point of tangency at which MRS = MU l / MU c = W Figure 4.10 The Behavior of the MRS 13

14 A convex budget line may be caused by a tax exemption up to a certain level of earnings, after which each dollar earned is taxed. A concave budget line may be caused by the existence of overtime pay. Figure 4.11 Kinked Budget Lines 14

15 Comparative statics: an exercise comparing the decision maker s behavior in different states. An increase in wealth will shift the budget line outward, allowing greater consumption of both c and l. Wealth is unearned income Figure 4.12 The Effect of an Increase in Wealth 15

16 Assumption 4.5: Leisure is a Normal Good Normal good: the good has a positive wealth effect, since demand for the good will increase with additional wealth. Inferior good: the good has a negative wealth effect, since demand for the good will decrease with additional wealth. An increase in the wage rate will rotate the budget line outward, unleashing two conflicting forces and an ambiguous effect on the worker s demand for leisure. The wealth (income) effect: an increase in the wage unambiguously increases u by allowing the worker to consume more c and l. 16

17 Figure 4.13 The Effect of an Increase in Wage, W Figure 4.14 Income and Substitution Effects 17

18 The substitution effect: an increase in the wage also increases the opportunity cost of leisure. Nonparticipants have a reservation wage (W*) at which they are completely indifferent between participating and not participating in the labor force. An individual s labor supply curve begins at W* and may contain a backward-bending region beginning at W', at which point the substitution effect exceeds the income effect. Figure 4.15 The Effect of an Increase in the Wage 18

19 Figure 4.16 Income and Substitution Effects for a Nonparticipant Figure 4.17 The Individual Supply of Labor 19

20 Aggregate supply of labor, H: the horizontal sum of the labor supply decisions of each individual in the population as a whole Intensive Margin Extensive Margin An increase in wages will increase the aggregate supply of labor hours despite backward-bending individual supply curves. Figure 4.18 The Aggregate Supply of Labor 20

21 There is a large body of empirical research using cross-sectional, time series, panel, and experimental data to estimate elasticity. Carnegie conjecture Deficiencies of neoclassical model 21

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