# edgeworth_box2.pdf

## Economics 401 with Lauermann at University of Michigan - Ann Arbor *

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Sample Edgeworth Box Problems No. 2 1. Holly and Steven both consume the same goods in a pure exchange econ- omy. Holly is originally endowed with 5 units of good 1 and 3 units of good 2. Steven is originally endowed with 5 units of good 1 and 2 units of good 2. They both have the utility function U = x 1 3 1 · x 2 3 2 . If we let good 1 be the numeraire, so that p 1 =1, then what will be the equilibrium price of good 2? (a) 2 (b) 8 (c) 1 (d) 4 (e) 2 2. DanandMarilynconsumetwogoods,x and y. They have identical Cobb- Douglas utility functions. Initially Dan owns 10 units of x and 10 units of y. Initially Marilyn owns 40 units of x and 20 units of y.Theymake exchanges to reach a Pareto optimal allocation which is better for both than the no-trade allocation. Which of the following is NOT necessarily true about the allocation they trade to? (a) Marilyn consumes 5 units of x for every 3 units of y that she con- sumes. (b) The locus of Pareto optimal allocations is a diagonal straight line in the Edgeworth box. (c) Dan’s consumption of x is greater than his consumption of y. (d) Dan consumes more than 10 units of x. (e) Marilyn consumes at least 40 units of x. 3. If an allocation is Pareto optimal and if the indiﬀerence curves between thetwogoodshavenokinks,thenitmustbethat: (a) two consumers who consume both goods must have the same MRS between them but consumers may consume the goods in diﬀerent ratios. (b) two consumers with the same income who consume both goods must have the same MRS, but if their incomes diﬀer their MRSsmay diﬀer. 1 (c) any two consumers who consume both goods must consume them in thesameratio. (d) for any two consumers who consume both goods, neither will prefer the other consumer’s bundle to his own. (e) all consumers receive the bundle that they prefer to any other bundle the economy could produce for them. 4. A small city state economy has only two consumers, Odysseus and Pene- lope. Odysseus’ utility function is U O = x+84· y 1/2 . Penelope’s utility function is U P = x+7· y. At a Pareto optimal allocation in which both individuals consume some of each good, how much y does Odysseus consume? (a) 6.50 (b) 36 (c) 12 (d) 13 (e) We can’t tell without knowing the initial endowments. 2 Correct Answers 1. (d) 2. (e) 3. (a) 4. (b) 3 Dimitriy V. Masterov edgeworth_box2.dvi

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