Exercise 10. The Good, The Bad, and the MRS (Cobb-Douglas Bads)

You have two employees: The Good and The Bad. The Good loves consumption of x₁ combined with daily hours of leisure, l. The Good's utility is u = x₁l. The Bad also loves consumption of x₁, but hates hours of labor, L. The Bad's utility is v = x₁(24-L). They both have the same 24 hour constraint: 24 = L + l.

Another employee of yours does not like to work either, because it takes away leisure time. Her utility function is v=x₁(24-L).

a)What is The Good's marginal utility for consumption of good, x₁? What is the marginal utility from leisure, l? What is the MRS between x₁ and leisure, l?

b)What is The Bad's marginal utility for consumption of good, x₁? What is the marginal utility from labor, L? What is the MRS between x₁ and labor, L?

Interpret the two MRS you found for The Good and for The Bad. How much leisure is The Good willing to give up for a marginal increase in x₁? How much work is The Bad willing to do for a marginal increase in x₁? Are The Good and The Bad any different?