Answer to Question #109024 in Economics of Enterprise for Mahlet Tekeste

Question

show the matimatical proof for P=AR=MR

Answer 1

The condition that price equals both average revenue and marginal revenue (P = AR = MR) is the standard condition for a perfectly competitive firm. This condition means that a firm is a price taker with no market control and faces a perfectly elastic demand curve equal to the market price.

Pol, for example, can sell all of his tomato production for $3 per pound of tomatoes. There is no way he can receive more and no reason to accept less. If Pol sells one pound of tomatoes, then he receives $3. If he sells 15 pounds, he receives $3 for per pound.

The going market price is also Pol's average revenue. In fact, average revenue and price are really just two terms for the same thing. Average revenue is the revenue Pol receives per pound of tomatoes. Price is the revenue Pol receives per pound of tomatoes. So price is almost always equal to average revenue, whether or not a firm is perfectly competitive.

Perfect competition, however, is indicated because price and average revenue are also equal to marginal revenue. Because Pol is a perfectly competitive tomato grower who can sell all of his output at the going $3 market price, each EXTRA pound of tomatoes he sells generates the same EXTRA revenue as ever other pound. The first pound of tomatoes Pol sells adds $3 to his total revenue. The second pound of tomatoes Pol sells adds $3 to his total revenue. The tenth pound of tomatoes Pol sells adds $3 to his total revenue. The twentieth pound of tomatoes Pol sells adds $3 to his total revenue. Because the price is constant, marginal revenue is constant and equal to the price.