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Suppose we have two firms with the following production technologies
f (x1, x2) = min{x1, 2x2}
f (x1, x2) = x1 + 2x2
Suppose the firms face the same prices on inputs. Denote the input prices by w1, w2. Further suppose the firms can sell their output for the same price p.
(1) Find the demand function for the inputs for both firms
(2) Suppose w1 = 1, w2 = 2, and p = 10, what are the profits of the firms
(3) Suppose the price of input 1 goes down to .5, analyze the effect of the decrease in price on the demands and the profits of the firms.
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