CES utility The CES utility function we have used in this chapter is given by U 1x, y2 5 xδ

δ 1 yδ

δ

.

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 5 a px py b

1/1δ212

.

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 1δ 5 02, as we have shown before in several problems.

c. How does the ratio pxx/pyy depend on the value of δ?

Explain your results intuitively. (For further details on this function, see Extension E4.3.)

d. Derive the indirect utility and expenditure functions for this case and check your results by describing the homogeneity properties of the functions you calculated.