There are two primary goods, goods 1 and 2, and there are two produced goods, goods 3 and 4. There is an endowment of one unit of each of the primary goods. The production functions for goods 3 and 4 are, respectively, f3(y1, y2) = min(2y1, y2) and f4(y1, y2) = min(y1, 2y2).
(a) In a box diagram, indicate the set of ef?cient allocations of goods 1 and 2 to the production of goods 3 and 4.
(b) Draw the output possibility set for goods 3 and 4.
(c) Suppose that equal positive quantities of goods 3 and 4 are produced at a point, z, on the output possibility frontier for goods 3 and 4. If the price of good 4 is 1, what are the possible prices of goods 1, 2, and 3, such that the point z would be produced if both production processes were operated so as to maximize pro?ts at these prices and if no more than the endowments of goods 1 and 2 were used in production?