Shelly's preferences for consumption and leisure can be expressed as
U(C, L) = (C - 200) ( (L - 80).
This utility function implies that Shelly's marginal utility of leisure is C - 200 and her marginal utility of consumption is L - 80. There are 168 hours in the week available to split between work and leisure. Shelly earns $5 per hour after taxes. She also receives $320 worth of welfare benefits each week regardless of how much she works.
(a) Graph Shelly's budget line.
(b) What is Shelly's marginal rate of substitution when L = 100 and she is on her budget line?
(c) What is Shelly's reservation wage?
(d) Find Shelly's optimal amount of consumption and leisure.