Shelly’s preferences for consumption and leisure can be expressed as U(C, L) = (C – 200) x (L – 80). There are 168 hours in the week available to split between work and leisure. Shelly earns $5 per hour after taxes. Shelly currently has no non-labor income. For the pre-class assignment today, you found that at a wage of $5 per hour, Shelly will work 64 hours, take 104 hours of leisure, and have $320 of consumption. A. Graph Shelly's budget constraint.
B. How many hours will Shelly choose to work when she is maximizing her utility? How much leisure time will she have at that point? How much will she be able to consume?
C. Now suppose that Shelly receives $320 worth of welfare benefits each week regardless of how much she works. How many hours will Shelly choose to work with welfare? How much leisure time will she have at that point? How much will she be able to consume?
D. Take a close look at the utility function. Is there a minimum level of consumption and leisure that Shelly would need in order to achieve positive utility? Explain why you might expect the utility function to have these properties.
E. Suppose that Shelly qualifies for a welfare benefit of $500 per month. She does not lose the benefit if she goes to work. What wage would she need to earn to work a positive number of hours with the welfare benefit?