26. Consider an exchange economy with agents 1 and 2 and goods r and y. Agent 1 lexico- graphically prefers y to x, i.e., between two non-identical bundles of x and y, she strictly prefers the bundle with more of y, but if the bundles have the same amount of y, then she strictly prefers the bundle with more of x. Agent 2's utility function is u2(x, y) = x + y Agent l's endowment is (w,w) = (0, 10) and Agent 2's endowment is (w, w;) = (10, 0) The set of competitive equilibrium price ratios P for this economy is || A. {1} В. [0), 1] С. (0, 1] D. e
The question is attached in the image. I mostly encounter problems while calculating competitive equilibrium prices. I sincerely request the expert to resolve all of the following doubts. Please answer the questions individually.
The questions asks us to find competitive price equilibrium. Please answer the following questions:
1. Find the competitive equilibrium prices.
2. Notice that the endowment is a parito efficient point. If endowment is pareto efficient, then why will they even trade? Agent 1 lexicographically prefers y and has all of y; so Agent 1 has not incentive to trade. Could a price equilibrium still exist?
3. The correct answer is C, px/py belongs to (0,1] according to university's records. If px=0 and py>0 (lets say py=1) then agent 2 demands only x and agent 1 demands y irrespective of prices. So, supply will be equal to demand, market clears and px/py=0. Why can px/py not be equal to 0 and correct option be B?
(I understand that we could not have py=0 since both agents would prefer y and market will not clear; but px could still be 0; moreover px has to be less than or equal to 1 (when py=1) in order for the market to clear).
![26. Consider an exchange economy with agents 1 and 2 and goods x and y. Agent 1 lexico-
graphically prefers y to x, i.e., between two non-identical bundles of x and y, she strictly
prefers the bundle with more of y, but if the bundles have the same amount of y, then she
strictly prefers the bundle with more of x. Agent 2's utility function is u2(x, y) = x + y
Agent l's endowment is (w, w) = (0, 10) and Agent 2's endowment is (w, w;) = (10, 0)
The set of competitive equilibrium price ratios P: for this economy is
Ру
A. {1}
В. (0, 1]
С. (0,1]
D. p](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39f4412a-18c0-4f64-8bcf-4dffb42656da%2Ffd07f665-510c-49fd-9b2a-f9ed88995cf7%2Ff2k5adi_processed.png&w=3840&q=75)
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