Davidson College Mark C. Foley
Department of Economics Jan – May 2008
Intermediate Microeconomic Theory
Homework #3
Due Tuesday, in class1
1. Economic Modeling Problem
What is the effect of winning the lottery on hours worked?
Recall that our discussion about modeling the effect of winning the lottery
on hours worked produced the following utility maximization problem:
€
maxU(C,leisure) = C
α
l
1−α
s.t.C=w(T−leisure) + V
where
€
C
is composite consumption good,
l
is hours of leisure,
w
is the
wage rate (the opportunity cost or “price” of leisure),
€
T
is the total time a
person has available to divide between leisure and hours of work, and
V
is
nonlabor income (which can be a lump-sum lottery payment as it will be for
us, or inheritance, investment income – dividends/capital gains, welfare
payment, unemployment insurance payment).
Solve for the demand function for leisure (remembering that only
exogenous variables are allowed in it), and then, to answer the original
question, use the equation
€
T=l+h
, where 1 is the amount of time a person
is endowed with and
l
is hours of leisure and
h
is hours of labor (i.e., hours
worked). We built this equation into the constraint above.
1* Don't forget to write a note indicating whom you worked with, if anyone, giving credit
where credit is due.
