Consider an exchange economy with two consumers, A and B, whose utilities are given as above. How- ever, the parameter d is lower for consumer A than for consumer B, i.e., we have ª ≤ 6³. Consumer A is endowed with 2 units of good 1, but has no endowment of good 2. Consumer B has no endowment of good 1, but has 2 units of good 2. In the remainder of this question, let p denote the price of good 1 and the price of good 2 be normalised to 1. (ii) Find the competitive equilibrium price p and the equilibrium allocation expressed as a function of the parameters 84 and 6B. Who is consuming more of good 1 and who consumes more of good 2? Interpret your results by referring to your answer in part (i).
Consider an exchange economy with two consumers, A and B, whose utilities are given as above. How- ever, the parameter d is lower for consumer A than for consumer B, i.e., we have ª ≤ 6³. Consumer A is endowed with 2 units of good 1, but has no endowment of good 2. Consumer B has no endowment of good 1, but has 2 units of good 2. In the remainder of this question, let p denote the price of good 1 and the price of good 2 be normalised to 1. (ii) Find the competitive equilibrium price p and the equilibrium allocation expressed as a function of the parameters 84 and 6B. Who is consuming more of good 1 and who consumes more of good 2? Interpret your results by referring to your answer in part (i).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Please answer part ii only.
![Consider an economy with two goods t = 1, 2. Whenever an individual consumes ri units of good 1 and
T2 units of good 2, their utility is given by
u(x1, 12) = Inx1+ 5 In x2,
where d is a parameter taking values 0 < 8 < 1.
(i) How does the parameter ð affect the marginal rate of substitution between goods 1 and 2? Explain
intuitively how does the relative preference for goods 1 and 2 change as the parameter ổ increases.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a398711-6bb1-446b-9b69-373cfacdd600%2F24ca0601-3b79-4edc-b46f-e5fbe148dfe2%2F09oyy9n_processed.png&w=3840&q=75)
Transcribed Image Text:Consider an economy with two goods t = 1, 2. Whenever an individual consumes ri units of good 1 and
T2 units of good 2, their utility is given by
u(x1, 12) = Inx1+ 5 In x2,
where d is a parameter taking values 0 < 8 < 1.
(i) How does the parameter ð affect the marginal rate of substitution between goods 1 and 2? Explain
intuitively how does the relative preference for goods 1 and 2 change as the parameter ổ increases.
![Consider an exchange economy with two consumers, A and B, whose utilities are given as above. How-
ever, the parameter ð is lower for consumer A than for consumer B, i.e., we have 8ª < 8B. Consumer A
is endowed with 2 units of good 1, but has no endowment of good 2. Consumer B has no endowment of
good 1, but has 2 units of good 2. In the remainder of this question, let p denote the price of good 1 and
the price of good 2 be normalised to 1.
(ii) Find the competitive equilibrium price p and the equilibrium allocation expressed as a function of
the parameters &A and 85. Who is consuming more of good 1 and who consumes more of good 2?
Interpret your results by referring to your answer in part (i).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a398711-6bb1-446b-9b69-373cfacdd600%2F24ca0601-3b79-4edc-b46f-e5fbe148dfe2%2Fo6islnn_processed.png&w=3840&q=75)
Transcribed Image Text:Consider an exchange economy with two consumers, A and B, whose utilities are given as above. How-
ever, the parameter ð is lower for consumer A than for consumer B, i.e., we have 8ª < 8B. Consumer A
is endowed with 2 units of good 1, but has no endowment of good 2. Consumer B has no endowment of
good 1, but has 2 units of good 2. In the remainder of this question, let p denote the price of good 1 and
the price of good 2 be normalised to 1.
(ii) Find the competitive equilibrium price p and the equilibrium allocation expressed as a function of
the parameters &A and 85. Who is consuming more of good 1 and who consumes more of good 2?
Interpret your results by referring to your answer in part (i).
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