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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.
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