costmin198 - 12 COST MINIMIZATION Purposes To show how a...

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12-1 12 COST MINIMIZATION Purposes: To show how a cost minimizing firm chooses inputs in the long-run. To show how to derive a firm's long-run total cost curve. Computer file: costmin198.xls . Background information: Consider a firm, say a university, that produces an output, for example, the number of student credit hours, from two inputs, labor, L, and capital, K. The university's provost (chief academic officer) can buy any amounts of the two inputs used in production at fixed, known prices. The problem she faces is to choose the amounts of labor and capital that will minimize the total cost of producing a specified output. In other words, this is the standard cost minimization problem in the theory of the firm. The production function for the university gives the current technology of production. Given the technology of production, the cost minimizing amounts of the inputs are those for which (i) the firm can produce the required output, and (ii) the marginal rate of technical substitution of labor for capital equals the ratio of the price of labor to the price of capital. Another way to say this is that the university should be on a cost constraint (isocost line) where the constraint is just tangent to the given isoquant. Once you find the cost minimizing amounts of inputs, you will examine the effects of changing input prices on the university's minimum cost of production, and you will derive the school's long-run total cost curve. The spreadsheet shows a few of the university's isoquants, and a cost constraint for the current level of output and input use. The baseline value for output is 30, and the baseline values of labor and capital are $9 and $4, respectively.
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