Isabel's preferences for consumption C and leisure L can be expressed as U(C, L) = (C – 120) x (L – 90), implying that her marginal utility of leisure is (C – 120) and her marginal utility of consumption is (L – 90). Assume the most leisure she can consume on any given week is 110 hours. Isabel earns $6 per hour after taxes and receives $200 in weekly welfare assistance regardless of how much she works.
a) Graph Isabel's budget line.
b) What is her marginal rate of substitution when L = 100 and she is on her budget line?
c) What is her reservation wage?
d) Find her optimal amount of consumption and leisure.
e) Now suppose that if Isabel chooses to work the government reduces her welfare benefit. The benefit is now determined according to the formula B = $200 – (.67)x(Earnings). Find her optimal amount of consumption and leisure. Will she sign up for welfare benefits?