The Supply of Labor Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

4.1: Preferences 4.2: The Constraints 4.3: Optimal Choice I: Determination 4.4: Optimal Choice II: Properties 4.5: The Empirical Evidence Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

Assumptions about workers How they make choices Their goals Inherent restrictions Decline in workweek length, changes in work patterns Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

u=U(c,l) represents the individuals 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 individuals willingness to trade consumption for additional leisure time Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

MRS= -(Δc/Δl)u o >0 Absolute value of the slope of indifference curve MRS can be used to compare individuals work attitudes Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

The marginal utility of leisure (MU l )=Δc/Δl, holding c constant The marginal utility of consumption (MU c )=Δc/Δl, holding l constant Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

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 Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

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 Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

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 workers budget line determines the set of consumption-leisure bundles he can afford by summing labor earnings and initial wealth. Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

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 Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

Assumption 4.4: Utility Maximization The worker examines all feasible consumption- leisure 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. Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

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 workers highest attainable indifference curve so that W = MRS. Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

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 Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

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. Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

Comparative statics: an exercise comparing the decision makers 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 Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

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. Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

An increase in the wage rate will rotate the budget line outward, unleashing two conflicting forces and an ambiguous effect on the workers 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. Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

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 individuals 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. Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

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. Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

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 Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc.

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.1 Average Hours Worked per Person in the United States

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Table 4.1 Change in Hours Worked by Age: 1950–2000

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.1

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.2 The Utility Function u(c,, )

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.3 An Indifference Curve Map

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.2

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.4 The Fundamental Properties of an Indifference Curve

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.3

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Definition 4.1

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.5 Work Attitudes

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Definition 4.2

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.4a

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.4b

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.5

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.6

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.7

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Assumption 4.1

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Assumption 4.2

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Assumption 4.3

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.8

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.9

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.6 The Budget Constraint

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.7 The Effects of an Increase in Wealth, A0, and the Wage, W, on the Workers Budget Set

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Assumption 4.4

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.8 Optimal Behavior

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.10

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.11

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.9 A Nonparticipant

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.12

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.13

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.10 The Behavior of the MRS

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.11 Kinked Budget Lines

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.12 The Effect of an Increase in Wealth

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Assumption 4.5

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.13 The Effect of an Increase in Wage, W

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.14 Income and Substitution Effects

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.15 The Effect of an Increase in the Wage

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.16 Income and Substitution Effects for a Nonparticipant

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.17 The Individual Supply of Labor

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Figure 4.18 The Aggregate Supply of Labor

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.14

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.15

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.16

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.17

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.18

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.19

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.20

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.21

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.22

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.23

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.24

Labor Economics Copyright © 2011 by W.W. Norton & Company, Inc. Equation 4.25