Suppose two people want to see if they could benefit from trading with one another in a 2-good world.

A: In each of the following cases, determine whether trade might benefit the two individuals:

(a) As soon as they start talking with one another, they find that they own exactly the same amount of each good as the other does.

(b) They discover that they are long-lost twins who have identical tastes.

(c) The two goods are perfect substitutes for each of them €” with the same MRS within and across their indifference maps.

(d) They have the same tastes, own different bundles of goods but are currently located on the same indifference curve.

B: Suppose that the two individuals have CES utility functions, with individual 1's utility given by

And individual 2€™s by

(a) For what values of α, β and ρ is it the case that owning the same bundle will always imply that there are no gains from trade for the two individuals.

(b) Suppose α = β and the two individuals therefore share the same preferences. For what values of α = β and ρ is it the case that the two individuals are not able to gain from trade regardless of what current bundles they own?

(c) Suppose that person 1 owns twice as much of all goods as person 2. What has to be true about α, β and ρ for them not to be able to trade?

-p u(x1,x2) = (ax," + (1 a)x," -P)-1/p