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Consider a pure exchange economy with 2 consumers, 1 and 2, who trade financial assets. There are two states of the world, a and b. State a occurs with probability 2/3 and state b occurs with probability 1/3. Two assets are traded: money in state a and money in state . Consumer 1 is risk neutral (i.e. has von Neumann-Morgenstern utility u(x) = x) and consumer 2 is risk averse with von Neumann-Morgenstern utility v(x)=√. Consumer 1's endowment is (6, 6) and consumer 2's endowment is (0, 4); that is, consumer 1 is endowed with 6 dollars in each state while consumer 2 is endowed with 0 dollars in state a and 4 dollars n state b.

Consider a pure exchange economy with 2 consumers, 1 and 2, who trade financial assets. There are two states of the world, a and b. State a occurs with probability 2/3 and state b occurs with probability 1/3. Two assets are traded: money in state a and money in state . Consumer 1 is risk neutral (i.e. has von Neumann-Morgenstern utility u(x) = x) and consumer 2 is risk averse with von Neumann-Morgenstern utility v(x)=√. Consumer 1's endowment is (6, 6) and consumer 2's endowment is (0, 4); that is, consumer 1 is endowed with 6 dollars in each state while consumer 2 is endowed with 0 dollars in state a and 4 dollars n state b.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Consider a pure exchange economy with 2 consumers, 1 and 2, who trade financial assets. There are two states of the world, a and b. State a occurs with probability 2/3 and state b occurs with probability 1/3. Two assets are traded: money in state a and money in state b. Consumer 1 is risk neutral (i.e. has von Neumann-Morgenstern utility u(x) = x) and consumer 2 is risk averse with von Neumann-Morgenstern utility v(x) = √. Consumer 1's endowment is (6,6) and consumer 2's endowment is (0, 4); that is, consumer 1 is endowed with 6 dollars in each state while consumer 2 is endowed with 0 dollars in state a and 4 dollars in state b. (a) Find all Walrasian equilibria of this economy. Solution: Letting money in state b be the numeraire good and p be the price of money in state a, there is a unique Walrasian equilibrium given by x¹ = (14/3,26/3), x² = (4/3,4/3), and p = 2. = (b) How would your answer change if consumer 2 was more risk averse? Solution: The answer would not change. In the Walrasian equilibrium, consumer 2 fully insures against risk. Making her more risk averse would not change her demand at the equilibrium prices.
Transcribed Image Text:Consider a pure exchange economy with 2 consumers, 1 and 2, who trade financial assets. There are two states of the world, a and b. State a occurs with probability 2/3 and state b occurs with probability 1/3. Two assets are traded: money in state a and money in state b. Consumer 1 is risk neutral (i.e. has von Neumann-Morgenstern utility u(x) = x) and consumer 2 is risk averse with von Neumann-Morgenstern utility v(x) = √. Consumer 1's endowment is (6,6) and consumer 2's endowment is (0, 4); that is, consumer 1 is endowed with 6 dollars in each state while consumer 2 is endowed with 0 dollars in state a and 4 dollars in state b. (a) Find all Walrasian equilibria of this economy. Solution: Letting money in state b be the numeraire good and p be the price of money in state a, there is a unique Walrasian equilibrium given by x¹ = (14/3,26/3), x² = (4/3,4/3), and p = 2. = (b) How would your answer change if consumer 2 was more risk averse? Solution: The answer would not change. In the Walrasian equilibrium, consumer 2 fully insures against risk. Making her more risk averse would not change her demand at the equilibrium prices.
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