Long Run Costs

In the long run, the firm has time to adapt fully its plan implying that all inputs are variable. The long run average cost (LAC) curve is the cost curve showing the average cost of production at different levels of output, turned out by different size plants. This is shown in the following diagram under the assumption that the number of possible short run is infinitely large, i.e., plant of virtually any size can be built.

The long run marginal cost (LMC) curve is obtained by taking the first derivative of the long run total cost function with respect to output.
        


The LMS is not the envelope of the short run marginal cost (SMC) curves. The SMC is the rate of change of total costs with respond to out with some cost variable and other fixed. The LMC is the rate of change of total costs with all cost variables.

The relation between the long run average cost and long run marginal costs, when stated in term of a ratio, works out to be the inverse of ‘output elasticity of costs’.

Note that output elasticity of costs

The shapes of the run average and marginal cost curve are contrastable to those of short run curves. Both LAC and SAC are U shaped, thought the LAC is the LMC also passers through the minimum point of the LAC.
 
The long run average cost first falls, remains constant and then rises. The movement along the LAC and shifts in the LAC can be explained in the terms of the economic concepts of economies and diseconomies of scale.

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