Problem
Sheryl's preferences for consumption and leisure can be expressed as U(C, L) = (C - 100) × (L - 40). There are 110 (non-sleeping) hours in the week available to split between work and leisure. Sheryl earns $10 per hour after taxes. She also receives $320 worth of welfare benefits each week regardless of how much she works.
i. Graph Sheryl's budget line.
ii. What is Sheryl's marginal rate of substitution when L=$100 and she is on her budget line?
iii. What is Sheryl's reservation wage?
iv. Find Sheryl's optimal amount of consumption and leisure.