Derive the Marginal Rate of Substitution between Consumption and Leisure for the following utility functions. a. K(CL) = 50 × C × L ( 2 points)
b. H(C, L) = 100 × C 2 × L 3 ( 2 points)
c. J(C, L) = 250 × ln(CL) (2 points) (d) U(C, L) = 120 × (ln(C 2 ) + ln(L))
d. There are 52 weeks in a year. Assume that the price of consumption is equal to 1 dollar per unit of consumption and that the wage is 1000 dollars per week. Assume that the individual receives 4000 dollars in non-labor income.

Required:
Determine which of the above utility functions represent the same set of preferences, and for those utility functions that represent the same set of preferences, determine the optimal bundle of consumption and leisure as well as the number of weeks worked.