ECO-365 Spring 2013
Problem Set 1-Labor Supply
Due by Monday, February 18
1) What does the marginal rate of substitution (MRS)
imply regarding the consumption of goods (C) and leisure (L) under the
assumption of convex indifference curves.
2) Tom earns $15 per hour for the first 40 hours of
work each week. He is paid $30 per hour for every hour worked in excess of 40.
Tom faces a 20 percent tax rate and pays $4 per hour in child care expenses for
each hour he works. Tom receives $80 in child support payments each week. There
are 168 hours in the week. Graph Tom’s weekly budget line.
3) Shelly’s preferences for consumption and leisure
can be expressed as U (C, L) = (C − 20)(L − 80).
This utility function implies that Shelly’s marginal
utility of leisure is C − 20 and her marginal utility of consumption is L − 80.
There are 168 hours in the week available to split between work and leisure.
Shelly earns $5 per hour after taxes. She also receives $320 worth of welfare
benefits each week regardless of how much she works.
a) Graph Shelly’s budget line.
b) What is Shelly’s MRS when L = 100 and she is on
her budget line.
c) Find Shelly’s optimal amount of consumption and
leisure.
d) What is Shelly’s reservation wage?
4) Cindy gains utility from consumption (C) and leisure
(L). The most leisure she can consume in any given week is 168 hours. Her
utility function is U (C, L) = C ∗ L. This functional
form implies that Cindy’s marginal rate of substitution is C/L. Cindy receives
$630 each week from her grandmother (regardless of how much Cindy works). What
is Cindy’s reservation wage?
5) You can either take a bus or drive your car to
work. A bus pass costs $5 per week, whereas driving your car to work costs $60
weekly (parking, tolls, gas, etc.). You spend half-an-hour less on a one-way
trip in your car than on a bus. How would you prefer to travel to work if your
wage rate is $10 per hour? Will
1 you change your preferred mode of transportation
if your wage rate rises to $20 per hour? Assume you work five days a week and
time spent riding on a bus or driving a car does not directly enter your
utility.
6) What happens to the hours of work decision when
there is an increase in the wage rate? Explain your answer in details using a
graph (assume the case where substitution effect dominates the income effect).
7) Among single, college educated men aged 22-25
years old, average annual hours worked is 2,160 and the average wage is $22.50.
If the average wage increases to $25 per hour, average annual hours worked increase
to 2,340. What is the elasticity of labor supply for this group of workers?
8) Derive the labor supply curve of the
representative worker/individual using a graph.
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