Question

Suppose that Bruce cares only about barbecued chicken (B) and fish (F). His utility function is U = B^0.4 F^0.6. The price of fish is $10 and price of barbecued chicken is $5. Bruce has a budget of $100. What is the solution to Bruce's maximization problem?

6 units of fish and 8 units chicken

7.3 units of fish and 5.5 units chicken

4 units of fish and 3 units chicken

3 units of fish and 4 units of chicken

Answer 1

Answer: A - 6 units of fish and 8 units of chicken.

U = B^0.4 F^0.6

Price of fish Pf = 10

Price of Barbecued chicken Pb = 5

Marginal Utility of fish = dU/df = 0.6B^0.4 F^-0.4

Marginal Utility of Barbecued chicken = dU/db = 0.4B^-0.6 F^0.6

MRS = Marginal Utility of fish / Marginal Utility of Barbecued chicken = 0.6B^0.4 F^-0.4 / 0.4B^-0.6 F^0.6 = 3B/2F

The consumer is at equilibrium where MRS = price ratio

3B/2F = 10/5

3B = 4F

B = 4F/3

Budget line : 10f + 5b = 100

10F + 5*4F/3 = 100

30F + 20F = 300

50F = 300

F = 6

B = 4F/3

B = 8