Microeconomics
Problem Set 8 Solutions
Due March 10th, 2010
Winter 2010 ECON 100A
1.
Cheryl consumes leisure and consumption goods each day. Her indifference curves are
smooth and
convex. For each of the following scenarios,
taken separately
, draw Cheryl’s budget line, a
representative indifference curve, and her equilibrium leisure and consumption. Note that each part is
a
separate
question independent of the others. Except where noted, Cheryl is free to choose her
hours.
a.
If Cheryl decides to work for any positive length of time, she must commute to her place of work
which takes a total of two hours and costs a total of t dollars each day. In equilibrium, Cheryl works
H
0
hours, where H
0
> 0.
C
N*
22
24
N
t
Although it does not show well on the graph, the budget line has a slope of w, is equal to –t below N=22,
and then is a straight horizontal line from 22 to 24. That is, Cheryl cannot increase her consumption by
selling her first or second hour of leisure, because this must be spent on the commute. If she commutes,
she has 22 hours left in the day and has an income of –t plus what she earns equal to wH
0
= w(22 – N*).
b.
Cheryl works at two jobs. She has a full time job (the higher paying of the two), and assuming she
goes to work on a given day, she is required to put in 8 hours per day. She also has a lower paying
part time job but she can go in for any number of hours she chooses. In equilibrium, Cheryl works 8
hours at her full time job and H
3
hours at her part time job, where H
3
> 0.
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C
N*
16
24
N
We are assuming here that she does not prefer one job to the other (except that one pays better). If Cheryl
wants to work less than eight hours a day, she must work at the low paying job. The slope of the budget
line is w
LOW
. If she works eight hours (16 hours leisure), she will work those 8 hours at the high paying
job. Because it pays more, there will be a discrete jump in income relative to working
7.9999 hours at the
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 Spring '08
 staff
 Economics, Microeconomics, Cheryl

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