Question: Exercise 8. Inverse Demand Function Consider the following utility functions: u = (x 1 + x 2 ) 2 and v = (x 3 -1

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 MRS1,2?

b)Using the utility maximizing condition MRS1,2=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 MRS3,4?

f)Using the utility maximizing condition MRS3,4=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?

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