Sarah's preferences for consumption and leisure can be expressed as U ( C , L ) = ( C - 180 ) × ( L - 80 ) . This utility function implies that her marginal utility of leisure is C - 180 and her marginal utility of consumption is L - 80. There are 168 hours in the week available to split between work and leisure. Sarah earns $6 per hour after taxes. She also receives $400 each week from rental property she owns regardless of how much she works.
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 $1,000 per week from her rental property