Question

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 12 cantaloupes and 19 grapefruits. Orville has an initial endowment of 8 cantaloupes and 14 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, Select one: a. Irene must consume at least 13 cantaloupes. b. The slopes of the two individuals’ indifference curves are the same c. Orville must consume all of the cantaloupes. d. Irene must consume at least 17 grapefruits. e. None of the answers is correct. f. Irene must consume at least 13 grapefruits. g. Orville must consume all of the grapefruits.

Answer 1

The correct answer is (f) Irene must consume at least 13 grapefruits

For Orville, both are perfect complements and hence Indifference Curve(IC) will be L shaped and hence kink will occur when Number of cantaloupes = number of grapefruits. Utility will be of the form Uo = min{C,G}

For Irene Both are perfect substitutes and hence Indifference curve(IC) will be a straight line and Hence what exactly matters to her is the sum of cantaloupes and grapefruits. Ui = C + G

For such preferences Pareto optimal points are those points at which IC of Irene intersects kinked point of IC of Orville. Hence Pareto optimal points are those points at which Orville is consuming equal numbers of cantaloupes and grapefruits.

Total number of grapefruits = 19 + 14 = 33

Total number of cantaloupes = 12 + 8 = 20

Hence maximum number of grapefruits Orville can consume is 20 because Orville must consume equal numbers of cantaloupes and grapefruits and total number of cantaloupes available = 20.

Hence, maximum number of grapefruits Orville can consume is 20. So, minimum amount of  grapefruits Irene must consume = 33 - 20 = 13.

Hence, At all Pareto efficient allocations Irene must consume at least 13 grapefruits

Hence, the correct answer is (f) Irene must consume at least 13 grapefruits