Sarah’s preferences for consumption and leisure can be expressed as U(C,L)=4C1/2L1/2.

Sarah’s preferences for consumption and leisure can be expressed as U(C,L)=4C1/2L1/2. This utility function implies that her marginal utility of leisure is 2(C/L)1/2 and her marginal utility of consumption is 2(C/L)−1/2 .

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 owns.