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