6. Suppose that a fast-food junkie derives utility from three goods - softdrinks (x), 0.5 0.5 hamburgers (y), and ice cream sundaes (2) - according to the Cobb-Douglas utility function U(x, y, z)=xºsyas (1+z)05. Suppose also that the prices for these goods are given by p=0.25, p, = 1, and p. = 2 and that this consumer's income is equal to 2. a) How much will this consumer buy of each good to maximize utility? b) Show that the utility function is maximized (Use |H₂| to identify whether it is a maximum or a minimum). c) What is the maximum utility of the fast-food junkie?
6. Suppose that a fast-food junkie derives utility from three goods - softdrinks (x), 0.5 0.5 hamburgers (y), and ice cream sundaes (2) - according to the Cobb-Douglas utility function U(x, y, z)=xºsyas (1+z)05. Suppose also that the prices for these goods are given by p=0.25, p, = 1, and p. = 2 and that this consumer's income is equal to 2. a) How much will this consumer buy of each good to maximize utility? b) Show that the utility function is maximized (Use |H₂| to identify whether it is a maximum or a minimum). c) What is the maximum utility of the fast-food junkie?
Micro Economics For Today
10th Edition
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter6: Consumer Choice Theory
Section: Chapter Questions
Problem 24SQ
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Transcribed Image Text:6.
Suppose that a fast-food junkie derives utility from three goods - softdrinks (x),
0.5
hamburgers (y), and ice cream sundaes (z) – according to the Cobb-Douglas utility
function U(x, y, z)=x5y5 (1+z)05. Suppose also that the prices for these goods are
given by p=0.25, p, = 1, and p. = 2 and that this consumer's income is equal to 2.
a) How much will this consumer buy of each good to maximize utility?
b) Show that the utility function is maximized (Use |H₂| to identify whether it is a
maximum or a minimum).
c) What is the maximum utility of the fast-food junkie?
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