Question

Compute the MRS for the following utility functions. Based on your results, explain the curvature of indifference curve associated with each function.

i. (5 marks) U(X,Y) = aln(X) + bln(Y)

ii. (5 marks) U(X,Y) = X^aY^b

iii. (5 marks) U(X,Y) = aX + bY

Answer 1

We known MRS= MUx/MUy

i) MUx= a/X , MUy= b/Y

So, MRS = aY/bX

Indifference curve will have a well behaved convex shape here since this utility function is just a monotonic transformation of X^a Y^b.

ii) MUx = aX^(a-1)Y^b ,MUy=b X^aY^b-1

MRS= a/b(Y/X) = aY/bX

Indifference curve will have a well behave convex shape here

iii) MUx= a , MUy= b

MRS = a/b

Since MRS is constant,so Indifference curve will have a constant slope here i.e. they will be linear