Suppose the production function for a newly discovered product through research is given by Y = 100 (L- F), where Y = output of the new product, L = labor input, and F =fixed amount of labor input required to invent the idea (cost incurred before the first unit of output can be produced). Assume that there is no production if L < F; and each unit of labor L costs a wage rate w.
(a) Find the cost function C(y) that represents the minimum cost required to produce Y units of output.
(b) Given a price P which the firm faces for each unit of output produced, show that the firm cannot make profit and operate in perfectly competitive market settings.
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