Question: 4.9 The general CES utility function is given by U(X,Y)= -- + --. o o a. Show that the first-order conditions for a constrained utility

4.9 The general CES utility function is given by U(X,Y)= -£- + -£-.

o o

a. Show that the first-order conditions for a constrained utility maximum with this function require individuals to choose goods in the proportion X = /Px Y \Py

b. Show that the result in part

(a) implies that individuals will allocate their funds equally between Xand Ffor the Cobb-Douglas case (5 = 0), as we have shown before in several problems.

c. How does the ratio PXX/PYY depend on the value of 5? Explain your results intuitively.

(For further details on this function, see Extension E4.3.)

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