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micro economics


In such a case, for this level of output the short run total cost when the firm is constrained to use k units of input 2 is equal to the long run total cost: STCx(y)(short run total cost) = TC(y)(total cost). We generally assume that for any level at which input 2 is fixed, there is some level of output for which that amount of input 2 is appropriate, so that for any value of x, TC(y)(total cost) = STCk(y)(short run total cost) for some y. For a total cost function with the typical shape, the following figure shows the relations between STC and TC. .
             .
             Long run and short run average cost functions.
             Given the relation between the short and long run total costs, the short and long run average and marginal cost functions have the forms shown in the following figure. .
             .
             Note: .
            
             • The SMC (short run marginal cost) goes through the minimum of the SAC (short run average cost) and the LMC (long run marginal cost) goes through the minimum of the LAC (long run average cost). .
            
             • When SAC (short run average c cost) = LAC (long run average cost) we must have SMC (short run marginal cost) = LMC (long run marginal cost) (since slopes of total cost functions are the same there). .
             In the case that the production function has, the LAC is horizontal, as in the following figure.
             .
             The differences between the short run and long run concepts.
             Two distinctions between long and short run costs and supply:.
             (1) Fixed costs do not matter in the short run. So, short-run shut-down point is different from the long-run shut-down point.
             (2) The quantity of some inputs can be fixed in the short-run, but variable in the Long-run. Capital is often fixed in the short run.
             Consider a firm with production function q = f (K; L). Suppose that capital is fixed in the short-run at the level k. Then, the firm's short-run production function is q = f (k; L). So, only labor is variable. Fixing q to Solve the equation q = f (k; L) for L.


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