4.11 CES utility The CES utility function we have used in this chapter is given by Ux, y xd d yd d :

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.