Reference no: EM13887948
There is one primary good, labor, and there are two outputs, goods 1 and 2. Good 1 is used as an input in the production of good 2 and good 2 is used as an input in the production of good 1. The production function for good 1 is y1 = f1(y12, L), where y12 is the amount of good 2 used as an input in the production of good 1. The production function for good 2 is y2 = f2(y21, L), where y21 is the amount of good 1 used in the production of good 2. There is one unit of labor to use in the production of goods 1 or 2.
(a) Compute a formula for the total output possibility set for goods 1 and 2 and draw it when
f1(y12, L) = min(2y12, L) and
f2(y21, L) = min(3y21, L).
(b) Suppose that the price of labor is 1. What are the prices of goods 1 and 2 such that when each production process is operated so as to maximize pro?ts at these prices, the two processes together use up the one unit of labor available and produce a positive total amount of each of goods 1 and 2?
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