Sarah's preferences for leisure and consumption 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 the $6 per hour after taxes. She also receives the $400 each week from rental property she owns regardless of how much she works.
1. Provide the Graph Sarah's budget constraint.
2. Determine her marginal rate of substitution when L=100 and she is on her budget constraint?
3. Determine her reservation wage?
4. How can find her optimal amount of consumption and leisure?