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In a monopolistically competitive firm (not a monopoly), why is marginal revenue (MR) decreasing? Why is P=MR in a perfectly competitive market?
Because in a monopolistically competitive firm, the firm can influence the price of its product to some extent by controlling the quantity of its product produced. Hence their demand curve is downward sloping and hence their MR marginal revenue curve is also downward sloping. In a perfectly competitive market, manufacturers are only price takers, can not change the number of products to affect the price, we can understand that the price elasticity of the product at this time is infinite, so in equilibrium, its P = MR, the manufacturer can not get excess profits.

Not related to the size of the market, but only to see whether there is monopoly power.ATC is the average total cost, its change is affected by MC, its rate of change is slower than MC. And MC goes down before it goes up. So, in general, ATC is above it at equilibrium.

Hope this helps~~