Sarah’s preferences for consumption and leisure can be expressed
as U(C,L)= 4Cˆ1/2
Lˆ1/2. This utility function implies that her
marginal utility of leisure is 2(C/L)ˆ1/2 and her
marginal utility of consumption is
There are 110 hours in the week available to split between work
and leisure. Sarah earns $20 per hour after taxes. She also
receives $400 each week in royalty payments from an oil well she
a) Graph Sarah’s budget constraint.
b) What is her marginal rate of substitution when L=100 and she is
on her budget constraint?
c) What is her reservation wage?
d) Find her optimal amount of consumption and leisure.
e) Answer (a) through (d) if Sarah instead receives Sarah instead receives $1,000 per week
in royalty payments but she can only work for the
minimum wage earning .25 per hour.