Reference no: EM132200818
Question: A firm has two factories to produce widgets. Each factory has production function f(ki, li) = (ki*li)1/2 , i= 1, 2. The factories differ, however, in the amount of capital equipment each has. In particular, factory 1 has k1 = 25, whereas factory 2 has k2 = 100. Price for capital and labor are r = $1 and w = $1.
(a) If the firm wants to minimize short-run total cost of widget production, how should output be allocated between the two factories?
(b) Given that output is allocated optimally between the two factories, calculate SC(q), SAC(q) and SMC(q).
(c) Now suppose that firm can adjust k1 and k2 in the long-run. How should the firm allocate widget production between the two factories in the long-run? Calculate LC(q), LAC(q) and LMC(q).
[HINT: Assume a division of total output q between the firms, say q1 and q2, and show that the cost does not depend on the division.]
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