Can we say that the profit maximization condition (Marginal Revenue=Marginal Cost) holds in non-competitive market structures (monopoly or oligopoly) as well as in competitive markets?
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Yes, we can say this. In fact, we can say that any firm will maximize its profits when it produces its product at the quantity where its marginal costs are equal to its marginal revenues. This applies to firms (or individuals) in any market structure from perfect competition up through monopoly.
The different market structures will yield different amounts of profit at the profit-maximizing quantity. Perfect competition allows no economic profit while other market structures allow varying amounts of economic profit. But in all cases, the profit is maximized by producing the quantity where MC=MR.
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