Irene and Orville live in an isolated valley and trade with no one but each other.They consume only cantaloupes and grapefruits.Irene has an initial endowment of 5 cantaloupes and 12 grapefruits.Orville has an initial endowment of 19 cantaloupes and 25 grapefruits.For Irene, the two goods are perfect substitutes, one for one.For Orville, they are perfect complements, one for one.At all Pareto efficient allocations,
A)Irene must consume at least 17 grapefruits.
B)Irene must consume at least 13 grapefruits.
C)Orville must consume 21.50 cantaloupes.
D)the slopes of the two traders' indifference curves are the same.
E)Orville must consume all of the cantaloupes.

Question

Quizplus · Accepted Answer

At a Pareto efficient allocation, both traders must consume all of their endowments. Since Irene has perfect substitutes, she will consume all of her grapefruits and trade some of her cantaloupes to Orville for more grapefruits. In order to maximize her utility, she will consume all of her grapefruits and trade all of her cantaloupes for more grapefruits. This means she will end up consuming a total of 17 grapefruits (12 initial endowment + 5 traded cantaloupes).

For Orville, since he has perfect complements, he will consume cantaloupes and grapefruits in fixed proportions. At a Pareto efficient allocation, he will consume all of his cantaloupes and grapefruits in the ratio of 19/25 (his initial endowment). This means he will consume 21.5 cantaloupes (19 initial endowment * (12 grapefruits/25 total units of grapefruits and cantaloupes)).

Therefore, the answer is B as Irene must consume at least 13 grapefruits.

Irene and Orville Live in an Isolated Valley and Trade