Given indirect utility function of the nature V(P, M)=M²/4P1P2.
a) derive the ordinary demand function
b)Derive associated expenditure function
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