A consumer has utility u(x₁, x2) = x₁x² for two goods. The government subsidizes half of the cost of the purchase of good 1 up to a maximum of 2 units. Thus if the consumer chooses the bundle (1, 2), she pays p₁/2 per unit up to x₁ = 2, and p₁ per unit thereafter. In particular, if she consumes more than two units, she receives a total subsidy of p₁. Assume throughout this question that w > p₁. Recall that the Marshallian demand for this utility function (in the absence of any subsidy) is x(p, w) = W 2w 3p13p2,
A consumer has utility u(x₁, x2) = x₁x² for two goods. The government subsidizes half of the cost of the purchase of good 1 up to a maximum of 2 units. Thus if the consumer chooses the bundle (1, 2), she pays p₁/2 per unit up to x₁ = 2, and p₁ per unit thereafter. In particular, if she consumes more than two units, she receives a total subsidy of p₁. Assume throughout this question that w > p₁. Recall that the Marshallian demand for this utility function (in the absence of any subsidy) is x(p, w) = W 2w 3p13p2,
Chapter6: Consumer Choice Theory
Section: Chapter Questions
Problem 5SQ
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Question
![A consumer has utility u(x₁, x2) = x₁x² for two goods. The government subsidizes half of the
cost of the purchase of good 1 up to a maximum of 2 units. Thus if the consumer chooses the
bundle (1, 2), she pays p₁/2 per unit up to x₁ = 2, and p₁ per unit thereafter. In particular,
if she consumes more than two units, she receives a total subsidy of p₁. Assume throughout
this question that w > p₁. Recall that the Marshallian demand for this utility function (in
the absence of any subsidy) is
x(p, w):
=
2w
3p1' 3p2,
(3P1²
Carefully sketch the budget set. Be sure to identify relevant points of intersection with
the axes.
Find the utility-maximizing bundle as a function of prices (p₁, p2) and wealth w.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1ab2968-d288-4fd8-b87c-74963c459231%2Ff498bfa5-0605-450c-a43d-d57c5e4295d4%2Ff9njr85_processed.png&w=3840&q=75)
Transcribed Image Text:A consumer has utility u(x₁, x2) = x₁x² for two goods. The government subsidizes half of the
cost of the purchase of good 1 up to a maximum of 2 units. Thus if the consumer chooses the
bundle (1, 2), she pays p₁/2 per unit up to x₁ = 2, and p₁ per unit thereafter. In particular,
if she consumes more than two units, she receives a total subsidy of p₁. Assume throughout
this question that w > p₁. Recall that the Marshallian demand for this utility function (in
the absence of any subsidy) is
x(p, w):
=
2w
3p1' 3p2,
(3P1²
Carefully sketch the budget set. Be sure to identify relevant points of intersection with
the axes.
Find the utility-maximizing bundle as a function of prices (p₁, p2) and wealth w.
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