Remember T-bone Pickens, the corporate raider? Now he’s concerned about his chicken farms, Pickens’s Chickens. He feeds his chickens on a mixture of soybeans and corn, depending on the prices of each. According to the data submitted by his managers, when the price of soybeans was $10 a bushel and the price of corn was $10 a bushel, they used 50 bushels of corn and 150 bushels of soybeans for each coop of chickens. When the price of soybeans was $20 a bushel and the price of corn was $10 a bushel, they used 300 bushels of corn and no soybeans per coop of chickens. When the price of corn was $20 a bushel and the price of soybeans was $10 a bushel, they used 250 bushels of soybeans and no corn for each coop of chickens.
(a) Graph these three input combinations and isocost lines in the following diagram.
(b) How much money did Pickens’ managers spend per coop of chickens when the prices were (10, 10)? ______. When the prices were (10, 20)? ______. When the prices were (20, 10)? ______.
(c) Is there any evidence that Pickens’s managers were not minimizing costs? Why or why not? (d) Pickens wonders whether there are any prices of corn and soybeans at which his managers will use 150 bushels of corn and 50 bushels of soybeans to produce a coop of chickens. How much would this production method cost per coop of chickens if the prices were ps = 10 and pc = 10? ______. if the prices were ps = 10, pc = 20? ______. if the prices were ps = 20, pc = 10? ________.
(e) If Pickens’s managers were always minimizing costs, can it be possible to produce a coop of chickens using 150 bushels and 50 bushels of soybeans?