4. The CES utility function is given by a° +y° U (x, y) = (i). Show that the first-order conditions for a constrained utility maximum with this function require individuals to choose goods in the proportion = (* (ii). Show that the result in part (i) implies that individuals will allocate their funds equally between x and y for the case 8 = 0. (iii). How does the ratio depend on the PyY value of 8? Explain your results intuitively. (iv). Derive the indirect utility and expenditure functions for this case and check your results by describing the homogeneity properties of the functions you
4. The CES utility function is given by a° +y° U (x, y) = (i). Show that the first-order conditions for a constrained utility maximum with this function require individuals to choose goods in the proportion = (* (ii). Show that the result in part (i) implies that individuals will allocate their funds equally between x and y for the case 8 = 0. (iii). How does the ratio depend on the PyY value of 8? Explain your results intuitively. (iv). Derive the indirect utility and expenditure functions for this case and check your results by describing the homogeneity properties of the functions you
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Please answer the 3rd and 4th part. If possible for you then solve all parts.
Transcribed Image Text:4. The CES utility function is given by
U (x, y) =
(i). Show that the first-order conditions for a
constrained utility maximum with this
function require individuals to choose goods
8-
in the proportion : =
Px
Py
(ii). Show that the result in part (i) implies
that individuals will allocate their funds
equally between x and y for the case d = 0.
%3D
(iii). How does the ratio
depend on the
PyY
value of 8? Explain your results intuitively.
(iv). 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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