Answer to Question #51461 in Microeconomics for William Waso Wasonga K Omole

Question

Given the following monotonically transformed utility function faced by the consumer
U(X1X2) = X_1^0.5 X_2^0.5
The price of good X1 is P1 and the price of good X2 is P2.
Derive the optimal demand (Marshallian demand) function for X1 and for X2.

Answer 1

U(X1X2) = X1^0.5 X2^0.5
The price of good X1 is P1 and the price of good X2 is P2.
Marshallian demand (dX1) is a function of the price of X1, the price of
X2 (assuming two goods) and the level of income or wealth (m):
X*=dX1(PX1, PX2, m)
Optimal demand (Marshallian demand) function for X1 and for X2 will be:
X = (0.5I/P1, 0.5I/P2)