deriving cost functions

deriving cost functions - 1 Deriving cost functions This...

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1 Deriving cost functions This note provides step-by-step details on how to solve for the short-run and and then the solution in the long-run. For the purposes of illustration, suppose Q = 15 K 1 = 4 L 3 = 4 ; the wage rate of labor is w and the rental rate of capital is r: There are no additional costs of production. 1.1 Short-run total and marginal cost functions Remember that a cost function, C ( Q ) ; to produce Q units of output, using the production method that minimizes its hired and the associated variation in the output. We can break the derivation of the cost function into three steps: Step 1: Write down the cost of production in terms of labor and capital The total cost of production is simply the amount of labor and capital that C = rK + wL: In the short run, the level of capital is given, so K = K: the amount of output produced only by altering its level of labor. As a result, we can write the short-run total cost function as STC ( Q ) = r K + wL ( Q ) : Step 2: Find out the relationship between labor and output This relationship is determined by the production function, which tells you,
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This note was uploaded on 04/07/2009 for the course BUAD 351 taught by Professor Eastin during the Spring '07 term at USC.

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deriving cost functions - 1 Deriving cost functions This...

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