Shelly’s preferences for consumption and leisure can be expressed asU(C, L) = (C-100) × (L-40)This utility function implies that Shelly’s marginal utility of leisure is C-100 and her marginal utility of consumption is L-40. There are 110 (non-sleeping) hours in the week available to split between work and leisure. Shelly earns $10 per hour after taxes. She also receives $320 worth of welfare benefits each week regardless of how much she works.(b) What is Shelly’s marginal rate of substitution when L=100 and she is on her budget line?(c) The reservation wage is defined as the MRS when working 0 hour. It is the wage at which she is indifferent between not working at all and working for just one hour. What is Shelly’s reservation wage?(d) Find Shelly’s optimal amount of consumption and leisure.
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