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Unformatted text preview: 12-112COST MINIMIZATIONPurposes: To show how a cost minimizing firm chooses inputs in the long-run. To show how toderive 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 ofstudent credit hours, from two inputs, labor, L, and capital, K. The university's provost (chiefacademic officer) can buy any amounts of the two inputs used in production at fixed, knownprices. The problem she faces is to choose the amounts of labor and capital that will minimize thetotal cost of producing a specified output. In other words, this is the standard cost minimizationproblem 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 forwhich (i) the firm can produce the required output, and (ii) the marginal rate of technicalsubstitution 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) wherethe constraint is just tangent to the given isoquant.Once you find the cost minimizing amounts of inputs, you will examine the effects ofchanging input prices on the university's minimum cost of production, and you will derive theschool's long-run total cost curve.The spreadsheet shows a few of the university's isoquants, and a cost constraint for thecurrent level of output and input use. The baseline value for output is 30, and the baseline valuesof labor and capital are $9 and $4, respectively. You can return to these values by clicking on the...
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This note was uploaded on 05/20/2010 for the course MARKETING 107 taught by Professor Vivian during the Spring '10 term at SCA NC.
- Spring '10