How does the market structure affect output decisions? 

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In a sense, the market structure does not affect output decisions.  All firms should determine the quantity of output in the same way.  

In all market structures, the best quantity of output is the quantity at which the marginal revenue is equal to the marginal cost of the next unit of output.  This rule will lead to different output levels in different markets because the demand curves will be different.  However, the same rule applies in all cases.  In all market structures, the profit-maximizing level of output is that at which marginal revenue is equal to marginal cost.

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