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
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
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text: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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