Answers to Assignment 1
1a. See Figure 1a:
• The box is 5 by 7, reﬂecting the total endowments of goods 1 and 2. • Given their preferences, the households’ indiﬀerence curves are linear.
In Figure 1a, Household 1’s indiﬀerence curves are blue while those of Household 2 are red.
• The Pareto eﬃcient allocations are along the bottom and right edges of the box.
1b. Consider allocation A in Figure 1a. Allocation A is not Pareto eﬃcient, because allocation A’ is Pareto superior to it. Household 2 is indiﬀerent between the two allocations, but Household 1 strictly prefers allocation A’ as it lies on a higher indiﬀerence curve.
1c. No, the endowment is not an eﬃcient allocation. In the Figure, the endowment is depicted by Ω. It can be seen that it is possible to make both households better oﬀ by moving to another allocation (actually to many other allocations) within the box. In the picture, allocation A’ is Pareto superior to the endowment (Ω), as it lies on a higher indiﬀerence curve for Household 2, while Household 1 is indiﬀerent between it and the endowment.
1d. No, households’ marginal rates of substitution are not equal at the Pareto eﬃcient allocations. In fact, the two households’ marginal rates of substitution diﬀer at every allocation in the box. To see this note that: