the supply of labor labor economics copyright © 2011 by w.w. norton & company, inc
TRANSCRIPT
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.