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