Exercise 8. Inverse Demand Function

Consider the following utility functions: u = (x₁ + x₂)² and v = (x₃^-1 + x₄^-1)^-1.

a)What is MU₁? What is MU₂? What is MRS_1,2?

b)Using the utility maximizing condition MRS_1,2=p₁/p₂ derive the inverse demand curve p₁(p₂,x₁,x₂).

c)Suppose p₂=1 and you are at the bundle x₁=4, x₂=100. How much are you willing to pay for a marginal increase in x₁?

d)Suppose p₂=1 and you are at the bundle x₁=25, x₂=100. How much are you willing to pay for a marginal increase in x₁?

e)What is MU₃? What is MU₄? What is MRS_3,4?

f)Using the utility maximizing condition MRS_3,4=p₃/p₄ derive the inverse demand curve p₃(p₄,x₃,x₄).

g)Suppose p₄=1 and you are at the bundle x₃=4, x₄=100. How much are you willing to pay for a marginal increase in x₃?

h)Suppose p₄=1 and you are at the bundle x₃=25, x₄=100. How much are you willing to pay for a marginal increase in x₃?