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4. The CES utility function is given by x°+y° U (x, y) (i). Show that the first-order conditions for a constrained utility maximum with this function reguire individuals to choose goods

4. The CES utility function is given by x°+y° U (x, y) (i). Show that the first-order conditions for a constrained utility maximum with this function reguire individuals to choose goods

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please give detailed explanation of parts c and d

4. The CES utility function is given by x°+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 = Pa 8–1 Py (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 calculated.
Transcribed Image Text:4. The CES utility function is given by x°+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 = Pa 8–1 Py (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 calculated.
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