Given indirect utility function of the nature V(P, M)=M²/4P1P2.

Question

a) derive the ordinary demand function
b)Derive associated expenditure function

Answer 1

a) The ordinary demand function is derived by taking the partial derivative of the indirect utility function with respect to the price of the good.

dV/dP1 = -M²/4P1²P2

dV/dP2 = -M²/4P1P2²

The ordinary demand functions for goods 1 and 2 are:

Q1 = M²/4P1²P2

Q2 = M²/4P1P2²

b) The associated expenditure function is derived by taking the partial derivative of the indirect utility function with respect to the income.

dV/dM = M/2P1P2

The associated expenditure function is:

E = M/2P1P2