A consumer can consume three goods, x₁, x2, and x3. In the marketswhere she buys them, she is a price-taker and faces prices for the three goods equal toP₁, P₂, and p3, respectively. The consumer has m dollars to spend. Her preferences canbe represented by the following utility function: U(x₁, x₂, x3) = x₁x²x².Xa) Derive the consumption bundle that maximizes the consumer's utility, subject to herbudget constraint.b) Show that the optimal consumption bundle found in part a) is a global maximum.IMG_4479-2.png

Utility, in economics, implies the usefulness or happiness a consumer can get from a service or…

Answered: A consumer can consume three goods, x₁,…

Economics: Private and Public Choice (MindTap Course List)

16th Edition

ISBN:9781305506725

Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Chapter20: Consumer Choice And Elasticity

Section: Chapter Questions

Problem 4CQ

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A consumer can consume three goods, x₁, x2, and x3. In the markets
where she buys them, she is a price-taker and faces prices for the three goods equal to
P₁, P₂, and p3, respectively. The consumer has m dollars to spend. Her preferences can
be represented by the following utility function: U(x₁, x₂, x3) = x₁x²x².
X
a) Derive the consumption bundle that maximizes the consumer's utility, subject to her
budget constraint.
b) Show that the optimal consumption bundle found in part a) is a global maximum.
IMG_4479-2.png

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