Linus Straight€™s utility function is U(a, b) = a + 2b, where a is his consumption of apples and b is his consumption of bananas. Lucy Kink€™s utility function is U(a, b) = min{a, 2b}. Lucy initially has 12 apples and no bananas. Linus initially has 12 bananas and no apples. In the Edgeworth box below, goods for Lucy are measured from the upper right corner of the box and goods for Linus are measured from the lower left corner. Label the initial endowment point on the graph with the letter E. Draw two of Lucy€™s indifference curves in red ink and two of Linus€™s indifference curves in blue ink. Use black ink to draw a line through all of the Pareto optimal allocations.

(a) In this economy, in competitive equilibrium, the ratio of the price of apples to the price of bananas must be ____________
(b) Let aS be Linus€™s consumption of apples and let bS be his consumption of bananas. At competititive equilibrium, Linus€™s consumption will have to satisfy the budget constraint, as + ________ bS = ________ This gives us one equation in two unknowns. To find a second equation, consider Lucy€™s consumption. In competitive equilibrium, total consumption of apples equals the total supply of apples and total consumption of bananas equals the total supply of bananas. Therefore Lucy will consume 12 ˆ’ as apples and _________ ˆ’bs bananas. At a competitive equilibrium, Lucy will be consuming at one of her kink points. The kinks occur at bundles where Lucy consumes __________ apples for every banana that she consumes. Therefore we know that 12ˆ’as/12ˆ’bs = _________
(c) You can solve the two equations that you found above to find the quantities of apples and bananas consumed in competitive equilibrium by Linus and Lucy. Linus will consume _______ units of apples and ________ units of bananas. Lucy will consume _________ units of apples and 3 units of bananas.

Transcribed Image Text:

Bananas Lucy Red curves Bladk line 6 〈Blue curves 12 Apples Linus