4.11 CES utility The CES utility function we have used in this chapter is given by U(x, y) =+. a. Show that the first-order conditions for a constrained utility maximum with this function require individuals to choose goods in the proportion 1/(8–1) Px Py y b. Show that the result in part (a) implies that individuals will allocate their funds equally between x and y for the Cobb- Douglas case (d = 0), as we have shown before in several problems. ||

Microeconomic Theory
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Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.11P
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4.11 CES utility
The CES utility function we have used in this chapter is given by
U(x, y) =
a. Show that the first-order conditions for a constrained utility maximum with this function require individuals to choose
goods in the proportion
1/(8–1)
b. Show that the result in part (a) implies that individuals will allocate their funds equally between x and y for the Cobb-
Douglas case (ô = 0), as we have shown before in several problems.
Transcribed Image Text:4.11 CES utility The CES utility function we have used in this chapter is given by U(x, y) = a. Show that the first-order conditions for a constrained utility maximum with this function require individuals to choose goods in the proportion 1/(8–1) b. Show that the result in part (a) implies that individuals will allocate their funds equally between x and y for the Cobb- Douglas case (ô = 0), as we have shown before in several problems.
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