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Unformatted text preview: 319 Answers to Problems on Measuring the Gains-From-Trade Answer to Problem 11.1. What is a Pareto efficient economic state? Answer. A Pareto efficient, or economically efficient, or simply efficient economic state is one in which if any one person is made happier then at least one other person must be made less happy. Answer to Problem 11.2. Suppose a cake is to be allocated between Juan, Jose and Juanita. Each of them always prefers more cake to less. (i) What are the Pareto efficient allocations of the cake? Answer. Any allocation of the whole cake is Pareto efficient. (ii) Give an example of a Pareto inefficient allocation of the cake? Answer. Any allocation of less than the entire cake is Pareto inefficient. (iii) Is any of the Pareto efficient allocations fair? Answer. What is fair? If, for example, you believe that equal shares is fair, then the only fair and efficient allocation is allocating one-third of the cake to each of Juan, Jose and Juanita. If instead you think that fair means that each of the three people should get at least one-quarter of the cake, then any allocation of the whole cake that gives at least one-quarter to each person will be both fair and Pareto efficient. (iv) Is any of the Pareto efficient allocations unfair? Answer. Again, what is fair or unfair? For example, if you still think that fair means that each of the three people should get at least one-quarter of the cake, then any allocation of the whole cake that gives less than one-quarter to at least one person will be Pareto efficient but unfair. Some efficient allocations would be regarded as unfair by most people. For example, if the whole cake was given to Juan then, while he might consider this to be fair, probably Jose and Juanita would consider it to be unfair. (v) Is any inefficient allocation of the cake fair? Answer. Yet again, what is fair? Since an inefficient allocation must mean that not all of the cake is allocated to the three people, for such an allocation to be fair you must believe that wasting some cake is fair. Particularly, you would have to believe that it would be fair not to allocate the waste cake to any one of the three people, even while not taking from any one of them the cake already allocated. Answer to Problem 11.3. This is an extension of Problem 11.2. We observe that Juan values the last piece of cake he has at $4, that Jose values his last piece of cake at $4, and that Juanita values her last piece of cake at $6. (i) Is the total value of the consumption of the cake maximized? Answer. No. (ii) Is the allocation of the cake economically efficient? 320 CHAPTER 11. MEASURING THE GAINS-FROM-TRADE Answer. No. While it is true that all of the cake is allocated, the allocation does not maximize the consumption value of the cake. An allocation is efficient if and only if any reallocation of the cake that improves someones happiness necessarily reduces at least one other persons happiness. In part (iii) we will see that it is possibleat least one other persons happiness....
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This note was uploaded on 03/01/2011 for the course ECO 182 taught by Professor Morgan during the Spring '08 term at SUNY Buffalo.
- Spring '08