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Assumptions for perfectly competitive market

What assumptions are essential for a market to be perfectly competitive?  Why is each of these assumptions important?

The two basic assumptions of perfect competition are (1) all of the firms in the industry are price takers, and (2) there is free entry & exit of firms from the market. Particularly, we have seen that in a competitive equilibrium, price is equivalent to marginal cost.  Both of the assumptions insure this equilibrium condition in the long run.  In the short run, price could be higher than average cost, implying positive economic profits.  Along with free entry and exit, positive economic profits would encourage other firms to enter.  This entry exerts downward pressure on price till price is equivalent to both marginal cost and minimum average cost.

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