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The profits of a competitive firm

September 27, 2011

In the long run when a market is perfectly competitive, all firms will make zero profit, but in the short run firms can make profits (this is what attracts new firms into the market and increases the market supply).

As the firm cannot influence the price by setting its level of output, it just receives a price P on every unit it sells. So its total revenue will be TR=PQ and its marginal revenue will be MR = \frac{d(TR)}{dQ} = P.

So in a competitive market price equals marginal revenue.

To maximise its profit, a firm sells where its marginal revenue equals its marginal cost, so in a competitive market, a firm sells where price equals marginal cost.

Let’s consider a firm in a competitive market which faces an inverse demand function of P=20

The firm has fixed costs of FC=2000 and variable costs of VC=0.4q^{1.5}

So its total cost is TC = FC + VC = 2000 + 0.4q^{1.5}.

Its marginal cost is MC = \frac{d(TC)}{dq} = 0.6q^{0.5}.

It sets its production level where P=MC, so

20 = 0.6q^{0.5} \Rightarrow 33.333 = q^{0.5} \Rightarrow q = 1111.111

What profits does it earn at this point?

Profit is equal to total revenue minus total cost, so

\pi = TR - TC = Pq - FC - VC = 20(1111.111) - 2000 - 0.4(1111.111)^{1.5} = 5407.407

Notice that the marginal cost is not affected by the amount of the fixed cost. If the firm had say, fixed costs of 4000, then it would still produce an output of 1111.111, it would just find that its overall profits were down to 3407.407.

The level of fixed cost affects the overall profits, but it does not affect the overall profit maximising amount.

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