Consider an exchange economy with agents 1 and 2 and goods x and y. Agent 1's endowment is (0,1) and agent 2's endowment is (2,0). Suppose agent 1 lexicographically prefers x to y. Suppose agent 2 treats x and y as perfect substitutes.

The set of all competitive equilibrium prices consist of Px>0 and Py>0 such that.

(a) Px/Py = 1

(b) Px/Py >= 1

(c) Px/Py <= 1

(d) Px/Py > 0

Sir, my doubt is that the answer should be (b) Px/Py >= 1 and not (a) as given in the solutions.

Reasoning:

Now if Px< Py then agent 2 will want to consume only good x and his choices will lie on the upper edge of the edgeworth box and will not lie on the pareto efficient allocations.

If Px=Py then he would be indifferent between comsuming the two goods as long as he lies on the same indifference curve, so he would be willing to move his choices onto the red line

If Px>Py then he will want to consume only good y, but as there is only 1 unit of good 2 in the economy he will consume 1 unit of y and then move onto consuming x to move onto a higher indifference curve. All these points also lie on the pareto efficient allocation line (the red line)

Hence the ans should be (B)

An alternative reasoning can be if the economy is moving from (0,1),(2,0) to (1,0),(1,1) then agent 2 would exchange 1 good of y for 1 good of x only if the price of x is equal to y or the price of x is greater than y. So this way to I land up at the same answer.

Could you tell me if there is any flaw in my reasoning?