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Labor Supply
Labor Supply
Labor supply is an application of the model of individual choice
•
Individual chooses between consumption (C) and hours of
leisure (H), where H is hours spent not working
•
C and H are composite goods

C reflects utility gain by consuming a variety of goods
and services

H reflects all nonmarket uses of time
•
A composite commodity is a bundle of goods for which
prices vary proportionately

the goods can be lumped together and treated as a
single commodity

Individual allocates funds to consumption and leisure
activities and then makes choices within these
categories
2
Utility Is Maximized Subject to Two
Utility Is Maximized Subject to Two
Constraints
Constraints
Time constraint
H + L = T, where T is total amount of
available time and L is hours of labor (work)
Budget constraint
C = wL + N, where wL is earnings and N is
nonwage income (transfers, gifts, interest
income)
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Budget and Time Constraints Are
Budget and Time Constraints Are
Combined into Full Income
Combined into Full Income
Constraint
Constraint
Substituting the time constraint into the budget constraint,
we have
C = w(TH) + N
Full income constraint:
C + wH = Tw + N
•
LHS shows prices times quantities (the price of C is
normalized to 1)
•
RHS shows the total resources available (endowment),
if individual worked fulltime
Opportunity cost of H is w:
for each hour of leisure, the
individual foregoes w in wages
4
Labor Supply Decision Is Standard
Labor Supply Decision Is Standard
Utility Maximization Problem
Utility Maximization Problem
Lagrangian multiplier:
= U(C,H) +
λ
(C+wHTwN)
∂
/
∂
C =
∂
U/
∂
C +
λ
= 0
∂
/
∂
H =
∂
U/
∂
H +
λ
w
= 0
Therefore, MRS(H for C) = MU
H
/MU
C
= w
Utility maximization requires the individual to equate
the ratio of marginal utilities to the ratio of prices
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5
Graph of Labor Supply Problem
Graph of Labor Supply Problem
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This note was uploaded on 05/26/2008 for the course ECON 101 taught by Professor Buddin during the Winter '08 term at UCLA.
 Winter '08
 Buddin
 Microeconomics, Utility

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