In microeconomics, why does price equal marginal revenue?

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The idea or theory is mainly applicable in competitive markets because the seller or manufacturer will always get the same price for each product regardless of the quantity supplied.

The marginal revenue is the additional revenue obtained from selling an extra unit. Ordinarily, it would be assumed that the extra revenue is or should be the price of the unit. However, depending on the forces of demand and supply and the different market structures, the idea would hold if the market structure is perfectly competitive in line with the number of buyers and sellers and the market price. The seller’s ability to influence the market price is limited (price takers) but the capacity to sell remains highly scalable. In a monopoly, the seller directly influences the price and has some leverage to control how it is set (price makers).

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It is not really correct to say that price equals marginal revenue.  This is only true in limited circumstances.  Specifically, price only equals marginal revenue in perfect competition.

Price equals MR in perfect competition because your demand curve is horizontal.  No matter how much you produce, it always sells at the same price.

In other market structures, you can raise or lower prices.  When you do, MR doesn't equal price.  Example:

Let's say you have a monopoly on something.  You charge $150 for it and no one person buys it.  So now you reduce the price to $138 so more people will buy it.  One person buys it now.  Your price is $138 and so is MR.

Now you reduce the price to $125 to sell more and you sell two.  Price is $125, but what's MR?

MR is actually only $112 while price is $125.

This is because you made $250 selling two for $125 each.  But if price had been $138 you would have sold one.  So you take $250-$138 and you get $112.

So, MR = P but only in perfect competition.

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