Question

Interpreting the Edgeworth box : An economy consists of two people, both with perfect compliment preferences: U1(x, y) = U2(xy) = min(x, y). Their initial endowments are:(xi1, yi1) = (7, 9) and (xi2, yi2) = (13, 21). (a) Draw the Edgeworth box for this economy. Label the initial allocation and sketch both person’s indifference curve for the initial allocation. (b) Interpret the Edgeworth box you drew; what would these people do if they tried to trade?

Answer 1

To draw the Edgeworth box for this economy, plot the initial endowments and indifference curves. The individuals will trade to reach a point on the contract curve that maximizes their utility.

Step-by-step explanation:

To draw the Edgeworth box for this economy, we first plot the initial endowments of the two individuals on a grid, with one axis representing person 1's good and the other axis representing person 2's good. Person 1's initial endowment is (7, 9) and person 2's initial endowment is (13, 21). We label these points A and B respectively. Then, we plot indifference curves for each person's initial allocation, which in this case are straight lines where x=y. These curves can be drawn passing through points A and B.

To interpret the Edgeworth box, we need to consider the individuals' preferences. Since both individuals have perfect compliment preferences, they prefer a strict ratio between x and y, specifically xy. They both want to maximize xy. If they were to trade, they would try to reach a point on the contract curve where they can agree on a ratio of xy that maximizes their combined utility. The contract curve represents all possible trades between the individuals that are mutually beneficial.