What is the meaning of long-run and short-run with regard to perfect competition?

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The meaning of "long run" and "short run" are the same in all aspects of economics.  The short run is a time period in which at least one factor of production is fixed.  For example, in the short run, it might be impossible for the size of a factory to...

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The meaning of "long run" and "short run" are the same in all aspects of economics.  The short run is a time period in which at least one factor of production is fixed.  For example, in the short run, it might be impossible for the size of a factory to be increased.  In the long run, by contrast, all factors can change.  

With respect to perfect competition, this is relevant because in the short run an economic profit is possible.  But in the long run, many firms can enter the market.  This drives prices down to the point where a long run equilibrium is reached and no economic profit can be made.

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