4.11 CES utility The CES utility function we have used in this chapter is given by Ux,...

4.11 CES utility The CES utility function we have used in this chapter is given by Uðx, yÞ ¼ xd d þ yd d :

a. Show that the first-order conditions for a constrained utility maximum with this function require individuals to choose goods in the proportion x

y ¼ px py

!1=ðd#1Þ

:

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 ¼ 0), as we have shown before in several problems.