The Supply of Labor

Labor EconomicsCopyright © 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 EconomicsCopyright © 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 EconomicsCopyright © 2011 by W.W. Norton & Company, Inc.

u=U(c,l) represents the individual’s tastes over different consumption-leisure pairs

uo: 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

Labor EconomicsCopyright © 2011 by W.W. Norton & Company, Inc.

MRS= -(Δc/Δl)uo>0

Absolute value of the slope of indifference curve

MRS can be used to compare individuals’ work attitudes

Labor EconomicsCopyright © 2011 by W.W. Norton & Company, Inc.

The marginal utility of leisure (MUl)=Δc/Δl, holding c constant

The marginal utility of consumption (MUc)=Δc/Δl, holding l constant

Labor EconomicsCopyright © 2011 by W.W. Norton & Company, Inc.

So, ∆u ≈ MUl∙ ∆l + MUc ∙ ∆c

Along a single indifference curve, set the above equal to 0

Rearrange to find MRS=MUl/MUc > 0

Labor EconomicsCopyright © 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 EconomicsCopyright © 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 $Ao

◦ The worker’s budget line determines the set of consumption-leisure bundles he can afford by summing labor earnings and initial wealth.

Labor EconomicsCopyright © 2011 by W.W. Norton & Company, Inc.

The budget line is given by c=Ao + W . (T-1)

The slope is -$W/h

The budget line intercepts the vertical l=T at c=$Ao

Labor EconomicsCopyright © 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 c0* of goods and enjoys l0* of leisure.

Labor EconomicsCopyright © 2011 by W.W. Norton & Company, Inc.

l0* 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.

Labor EconomicsCopyright © 2011 by W.W. Norton & Company, Inc.

Nonparticipants face the same budget constraint. A nonparticipant chooses the point P = (T, A0)

l0* is a corner solution in this case since it occurs at the corner of the budget constraint, where l0* = T.

If W > MRSp, then the worker participates in the labor force. If MRSp ≤ W, he does not. If an individual does participate, his optimal choice is located

at an interior point of tangency at which MRS = MUl / MUc = W

Labor EconomicsCopyright © 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 EconomicsCopyright © 2011 by W.W. Norton & Company, Inc.

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

Labor EconomicsCopyright © 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 EconomicsCopyright © 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 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.

Labor EconomicsCopyright © 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 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.

Labor EconomicsCopyright © 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 EconomicsCopyright © 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 EconomicsCopyright © 2011 by W.W. Norton & Company, Inc.