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