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     Suppose the inverse demand curve for a commodity in a perfectly competitive market takes the functional...

  1.      Suppose the inverse demand curve for a commodity in a perfectly competitive market takes the functional form: P (Q) = -.1Q + 10. Additionally, the firm’s marginal cost (MC) takes the following functional form: MC = 4 + 2Q. Recalling that a perfectly competitive firm is a price-taker in the market and its profit-maximizing output level (Qe) is always found by equating its price with its marginal cost: P = MC. Given all this, how much output (Qe) should the perfectly competitive firm produce-and at what price should it be sold (Pe)-in order to maximize profits? Round your answer for quantity to the nearest whole number and your answer for price to the nearest cent.

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Answer #1

P = - 0.1Q + 10

A perfectly competitive firm maximizes profit by equating Price with MC.

- 0.1Q + 10 = 4 + 2Q

2.1Q = 6

Q = 2.9

Q ~ 3 units

P = - 0.1 x 3 + 10 = - 0.30 + 10 = 9.70

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