Maximizing profit with calculus

Chapter 9: Limited Decision-Making in Perfect Competition

Giving up and shutting down

There is a point where you should immediately give up and shut down. But first remember that going out of business in the short run doesn’t mean that your losses go to zero. Because some of the inputs you employ are fixed, going out of business in the short run means you lose your fixed costs. Therefore, if you can make enough revenue to cover all your variable costs (see the previous section), you should stay in business in the short run in order to minimize your losses. However, given your goal is to maximize profits — or, in a bad situation, minimize losses — you should immediately shut down if your revenue doesn’t cover your variable costs. Producing when your revenue is less than your variable costs means that your losses associated with the profit-maximizing quantity of output are greater than your fixed costs. You’re better off shutting down and losing only your fixed costs.

In Figure 9-4, the profit-maximizing quantity of output, based on marginal revenue equals marginal cost, is q0. If you produce this quantity of output, your loss per unit equals price minus average total cost or the distance represented by the double-headed arrow in Figure 9-4. However, your fixed cost is represented by the vertical distance between average total cost, ATC0, and average variable cost, AVC0. Because this distance is less than the loss represented by the double-headed arrow, you’ll lose less money by shutting down — producing zero units of output — and limiting your losses to total fixed cost.

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Figure 9-4:

Shutting down and limiting losses to total fixed cost.