Answer to Question #49796 in Economics for Marcus Poon

Question

Given the utility U(x1, x2) = x1^1/2 . x2^1/4
compute:
a. The indirect utility V (p, y) given the income y = 1 and
prices p1 = 1 and p2 = 2.
b. The indirect utility V (p, y) given the income y = 1 and
prices p1 = 2 and p2 = 1.

Answer 1

A consumer's indirect utility function v(p, w) gives the consumer's maximal utility when faced with a price level p and an amount of income w. It represents the consumer's preferences over market conditions.This function is called indirect because consumers usually think about their preferences in terms of what they consume rather than prices. A consumer's indirect utility v(p, w) can be computed from its utility function u(x) by first computing the most preferred bundle x(p, w) by solving the utility maximization problem; and second, computing the utility u(x(p, w)) the consumer derives from that bundle. The indirect utility function for consumers is analogous to the profit function for firms.
a. In this case bundle 1 is more prefferable, so V(p;y) = V(1;1) = U(1;1) = 1^1/2 = 1
b. In this case bundle 1 is more prefferable too, so V(p;y) = V(2;1) = U(2;1) = 2^1/2 = 1.41