Question

There is an economy with three goods: Audis (a), BMWs (b), and Cadillacs (c). There are 10 total units of each good. Klaus has utility function Uᴷ(a,b,c)=a+b, while Larry has utility function Uᴸ(a,b,c)=c. Describe the set of Pareto efficient allocations in this economy (i.e., the contract curve). Note: You should not try to do this mathematically. Use the definition of Pareto efficiency and do your best to describe verbally what the set of Pareto efficient allocations is.

Answer 1

The set of Pareto efficient allocations in an economy with Klaus and Larry's utility functions would include any distribution where Klaus has more Audis and BMWs and Larry has more Cadillacs, to the point where neither can be better off without the other being worse off.

Step-by-step explanation:

To describe the set of Pareto efficient allocations in an economy with three goods where Klaus's utility function is UK(a,b,c)=a+b and Larry's utility function is UL(a,b,c)=c, one must consider that an allocation is Pareto efficient if no individual can be made better off without making someone else worse off. In this case, since Klaus derives utility from Audis and BMWs and Larry from Cadillacs, any allocation where Klaus has more Audis and BMWs and fewer Cadillacs, while Larry has more Cadillacs and fewer Audis and BMWs, could be Pareto efficient. For instance, if Klaus had 9 Audis and 9 BMWs and Larry had 2 Cadillacs, further improving Klaus's utility would mean taking away Cadillacs from Larry, thus making Larry worse off. Similarly, giving Larry more Cadillacs would necessitate taking Audis or BMWs from Klaus. Hence, the contract curve in this economy would include all allocations where Klaus and Larry have maximized their utility based on their preferences, and no further gains can be made without harming the other.