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

Question

a) derive the ordinary demand function
b)Derive associated expenditure function. Show your working clearly

Answer 1

a) Deriving the ordinary demand function:

V(P,M) = M²/4P1P2

Differentiating with respect to P1 and P2, we get:

dV/dP1 = -M²/4P1²P2

dV/dP2 = -M²/4P1P2²

Equating the two derivatives to zero, we get:

-M²/4P1²P2 = 0

-M²/4P1P2² = 0

Solving the above equations, we get:

P1 = 0

P2 = 0

Therefore, the ordinary demand function is:

P1 = 0

P2 = 0

b) Deriving the associated expenditure function:

The expenditure function is given by:

E(P,M) = P1X1 + P2X2

Substituting the values of P1 and P2 from the ordinary demand function, we get:

E(P,M) = 0 + 0

Therefore, the associated expenditure function is:

E(P,M) = 0