Anthony seeks to maximize the following utility function u(x, y) = r'/3y2/3 subject to the budget constraint PrX + PyY = I where pa, Py, x, y, I > 0. a) Find Anthony's utility-maximizing bundle (x*, y*) as a function of pa, Py, and I. b) Show that y* is decreasing in py and increasing in I (hint: use partial derivatives). What share of Anthony's income is spent on x? What share is spent on y? In other words, calculate Pa and P. Are these shares a function of prices? Note: The above utility function is Cobb-Douglas, and all Cobb-Douglas functions have these share formulas for any values for the erponents. d) What is the impact of a change in pz on Anthony's utility?

Anthony seeks to maximize the following utility function u(x, y) = r'/3y2/3 subject to the budget constraint PrX + PyY = I where pa, Py, x, y, I > 0. a) Find Anthony's utility-maximizing bundle (x, y) as a function of pa, Py, and I. b) Show that y* is decreasing in py and increasing in I (hint: use partial derivatives). What share of Anthony's income is spent on x? What share is spent on y? In other words, calculate Pa and P. Are these shares a function of prices? Note: The above utility function is Cobb-Douglas, and all Cobb-Douglas functions have these share formulas for any values for the erponents. d) What is the impact of a change in pz on Anthony's utility?

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Anthony seeks to maximize the following utility function
u(x, y) = x'/3y2/3
subject to the budget constraint
Pæa + PyY = I
1
where pr, Py, x, y, I > 0.
a) Find Anthony's utility-maximizing bundle (x*, y*) as a function of pæ, Py, and I.
b) Show that y* is decreasing in py and increasing in I (hint: use partial derivatives).
c) What share of Anthony's income is spent on x? What share is spent on y? In other words,
calculate Pa and Pu. Are these shares a function of prices?
Pyy*
Note: The above utility function is Cobb-Douglas, and all Cobb-Douglas functions have these share
formulas for any values for the exponents.
d) What is the impact of a change in pr on Anthony's utility?

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