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 cquilibrium priono
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 cquilibrium priono
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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
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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