4.13 CES indirect utility and expenditure functions In this problem, we will use a more standard form of the CES utility function to derive indirect utility and expenditu functions. Suppose utility is given by U(x, y) = (x³ +y®)/& [in this function the elasticity of substitution o = 1/(1 – ò)]. a. Show that the indirect utility function for the utility function just given is V = I(p, + P,)/", where r = d/(d – 1) = 1 – 6. b. Show that the function derived in part (a) is homogeneous of degree zero in prices and income. c. Show that this function is strictly increasing in income.
4.13 CES indirect utility and expenditure functions In this problem, we will use a more standard form of the CES utility function to derive indirect utility and expenditu functions. Suppose utility is given by U(x, y) = (x³ +y®)/& [in this function the elasticity of substitution o = 1/(1 – ò)]. a. Show that the indirect utility function for the utility function just given is V = I(p, + P,)/", where r = d/(d – 1) = 1 – 6. b. Show that the function derived in part (a) is homogeneous of degree zero in prices and income. c. Show that this function is strictly increasing in income.
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.13P
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