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An enterprising entrepreneur purchases two firms to produce widgets. Each firm produces identical products, and each has a production function given byThe firms differ, however, in the amount of capital equipment each has. In particular, firm 1 has k1= 25 whereas firm 2 has k2= 100. Rental rates for k and l are given by w = v = \$1.a. If the entrepreneur wishes to minimize short-run total costs of widget production, how should output be allocated between the two firms?b. Given that output is optimally allocated between the two firms, calculate the short-run total, average, and marginal cost curves. What is the marginal cost of the 100th widget? The 125thwidget?The 200th widget?c. How should the entrepreneur allocate widget production between the two firms in the long run? Calculate the long-run total, average, and marginal cost curves for widget production.d. How would your answer to part (c) change if both firms exhibited diminishing returns to scale?
a) The SRMC must be the same in each firm. Set MC1= MC2 50q1 = 200q 2q1= 4q2 b) c) In the long run, since the two firms have identical CRS cost functions, it doesnt matter how widget production is allocated. The long run production function is:q= (K L)K = L at equilibrium. q = K = L TC = L + K = q + q = 2q MC = 2 AC = 2 d) If both firms exhibited…

ng returns to scale, the entrepreneur would split the production equally between the two firms in the long run; if both firms exhibited increasing returns to scale, the entrepreneur would close one firm down and transfer all production to the other.

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