A firm in a perfect competition market will shut down (suspend production) in the short run for a temporary period or forever depending upon the situation , If the firm can't recover even its variable costs of production (P<AVC). Shut down is temporary if it is due to seasonal nature of work , recession etc. It is permanent when its output is outdated. On the other hand a firm in a perfect competition market will exit the market in the long run if it can't recover its entire cost (P<ATC) and earning a loss. In the long run a firm must not earn a loss and should earn a normal profit at least to retain itself in the market.
while shut down is temporary or permanent suspension of production in the short run, exit of a firm is only possible in the long run. Exit of a firm is a permanent closing of production.
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