Imagine a Primitive Society in Which There Are Two Goods

Essay

Imagine a primitive society in which there are two goods: food and shelter. The utility functions for two representative members of the society, Jane and Paul, are given below.
Jane's utility function:
U^J = 25F^0.5S^0.5
Paul's utility function:
U^P = 50F^0.75S^0.25
where F = units of food, and S = units of shelter.
a. Determine the marginal rate of substitution for each individual.
b. The current prices of food and shelter are $12 and $6, respectively. Determine the proportions in which Jane and Paul should consume food and clothing to achieve an exchange equilibrium.