Frank's utility function for WWE wrestling event tickets (r,) and NASCAR race tickets (2) is of the following 0.25 0.75 Cobb-Douglas form: U(x,,x₂) = x^^" 2 1 xhis income is Y, the price of WWE tickets is p., and the price of NASCAR tickets is p2.a. Mathematically derive his demand functions for x, and 2. No graphs! You are not required to use Lagrangian Function, you can just use the demand formulas for the Cobb - Douglas utility function (Chapter 5, fourth slide). b. Using your answers from part (a), find the demand functions for x and x,, and mathematically prove that they have the proper negative slope.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.13P
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Frank's utility function for WWE wrestling event tickets
(x,) and NASCAR race tickets (2) is of the following
Cobb - Douglas form: U(x,, ) = x
1
2
0.25 0.75
x
2
his income
is Y, the price of WWE tickets is p₁, and the price of
NASCAR tickets is p₂. a. Mathematically derive his
1
demand functions for x, and x2. No graphs! You are
not required to use Lagrangian Function, you can just
use the demand formulas for the Cobb - Douglas utility
function (Chapter 5, fourth slide). b. Using your
answers from part (a), find the demand functions for x
and x2, and mathematically prove that they have the
proper negative slope.
Transcribed Image Text:Frank's utility function for WWE wrestling event tickets (x,) and NASCAR race tickets (2) is of the following Cobb - Douglas form: U(x,, ) = x 1 2 0.25 0.75 x 2 his income is Y, the price of WWE tickets is p₁, and the price of NASCAR tickets is p₂. a. Mathematically derive his 1 demand functions for x, and x2. No graphs! You are not required to use Lagrangian Function, you can just use the demand formulas for the Cobb - Douglas utility function (Chapter 5, fourth slide). b. Using your answers from part (a), find the demand functions for x and x2, and mathematically prove that they have the proper negative slope.
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