Questions c) and d) 4.11 CES utilityThe CES utility function we have used in this chapter is given byU(x, y) =a. Show that the first-order conditions for a constrained utility maximum with this function require individuals to choosegoods in the proportion1/(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. c. How does the ratio p,x/p,y depend on the value of ö? 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 homogeneityproperties of the functions you calculated.

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c. How does the ratio p,x/p,y depend on the value of ö? 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.

c. How does the ratio p,x/p,y depend on the value of ö? 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.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Questions c) and d)

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.

c. How does the ratio p,x/p,y depend on the value of ö? 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.

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