(Production processes) Consider a firm that can make use of two different production processes to produce the same good from a single input. The production function for the process 1 is f1(x) = x^1/3, and for process 2 is f2(x) = x^2/3 (a) Find the cost function associated with each process. (b) Suppose that the firm can freely allocate the input x between the two production processes. For example, to produce 2 units of output, the firm could employ 8 units of input in process 1 and none in process 2, or it could employ one unit of input in each process, and so on. Find the production function for the firm. (c) Will the firm generally use both processes to produce output or just one? Explain. (d) Suppose that the firm resulted from a merger between two firms, one that could only use process 1 and another that could only use process 2. Assuming that the firms are price-taking, how does the merger affect the total unconditional input demand? Explain your answer. (Note: you do not need to compute the input demands.)
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