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First, your question needs to be rephrased. In a perfectly competitive market where firms with the same product sell at the same price, Marginal Revenue (increase in revenue by producing another product) equals the price the product is sold. This marginal revenue (MR) needs to be greater than or equal to the variable cost (VC) in the short run, because if their MR < VC that means they are losing money for every unit they are producing. So in the short run it is better to not produce anything so you don't lose money (they would still lose money due to fixed costs, FC). In the long run MR needs to be greater than or equal to total cost (TC = VC + FC). If not, you lose money and it is best to stop producing and leave the market altogether so you do have VC or FC.

To maximize profits MR must equal MC, marginal cost, or how much it costs to produce another unit. If MR > MC, the firm can produce more because they would gain more revenue than it would cost. If MR < MC, the firm should produce less because it is costing them more to produce then they are receiving revenue.

Hope that answers both sides of your question.

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Q: Why must revenue equal variable cost in the short run and total cost in the long run to reach maximum profits?
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