Question

Harold the Historian and Eddie the Economist are trapped on a different deserted island without any goods to consume. However, on the island there are two items, firewood (F)and pineapple (A), which can be collected. Harold can collect a maximum of 40 units of firewood per day or a maximum of 20 pineapples in a day. Eddie can collect a maximum of 10 units of firewood per day or a maximum of 20 pineapples per day. Both Harold and Eddie like to barbecue the pineapple which requires consuming two units of firewood for each pineapple. Specifically, their utility functions are bothU=min[0.5F,A]. (a) In the morning, Harold sets off to collect 20 units of firewood and 10 pineapples but Eddie stops him and explains the idea of comparative advantage. Being a historian, Harold cannot understand why both individuals could be better off coordinating their collection activities since Harold is at least as good as Eddie both at collecting firewood and pineapples. What collection scheme would Eddie suggest? After only a few days, Eddie starts to become annoyed with Harold (he keeps wanting Eddie to re-enact the civil war with him). To minimize contact with Harold, Eddie wakes up early every morning and carves prices for firewood and pineapples into a tree which will dictate the terms of trade between them. (b) Suppose those prices are pF=2 and pA=2. Draw Harold’s production possibilities frontier and what his budget constraint will be if he specializes in collecting F and what his budget constraint will be if he specializes in collecting A. Do the same for Eddie in a separate diagram. (c) At the prices given in (b), what will the quantity demanded be for F? What about the quantity supplied? Since Eddie is the market designer looking for prices that lead to no excess demand or excess supply, in what direction should Eddie adjust the price of firewood or pineapples? (d) Can you find prices (or a ratio of prices) that result in the same outcome you described in part (a)? (If you find either person is, at the given market prices, indifferent between collecting F or A, you can assume he collects whichever you want)

Answer 1

1. Eddie will suggest that Harold should collect 40 Fire woods a day and he will collect 20 Pineapples a day. A they both like to barbecue the Pineapples & 2 Units of Firewood are required to barbecue one Pine apple , Harold can trade off 20 units of Fire wood with 10 Pine apples from Eddie.

Marginal Rate of Transformation will be constant as Prices of both the commodities are same as for every one Pine Apple two units of Firewood are required

Rate of Change will be 2:1

If Harold specializes in collecting firewood his budget constraint will be 40 * 2 = 80 &

If he specializes in collecting of Pine Apple his budget constraint will be 20 * 2 = 40

If Eddie Specializes in collection of Firewood his budget constraint will be 10 * 2 = 20 &

If Eddie Specializes in collection of Pine Apple his budget constraint will be 20 * 2 = 40

c) Quantity demanded for F will be 40 as 2 per unit is required to barbecue 20 Pine Apples. Quantity supplied will also be same for both the commodities.

d) At price 4/unit for both commodities will result into same outcome