For each of the following utility functions calculate the ma

For each of the following utility functions, calculate the marginal utility of good 1, the marginal utility of good 2, and the marginal rate of substitution, respectively at (x, y).

Solution

Ans: a) MUx1= 2, MUx2= 3. MRS= MUx1/ MUx2= 2/3

b) MUx1 =a.(3) (x1)^2 , MU x2= 1 , MRS= a.(3) (x1)^2

c) MUx1= a. (x1)^(a-1), MUx2 = b (x2)^(b-1), MRS= a (x1)^(a-1) / b (x2)^(b-1)

d) MUx1= a (x2), MUx2 = a(x1). Thus, MRS= a (x2) / a (x1)= x2/ x1

e) MUx1= (x2^b) (a) x1^(a-1), MU x2= (x1^a) (b) x2^(b-1)

MRS= (x2^b) (a) x1^(a-1) / (x1^a) (b) x2^(b-1) = (a/b) (x2/x1)

Answers