The Shut-Down Rule

point of minimum average cost. Figure 6.6 shows the problem with this contention: The profit-maximizing output Q* falls well short of Qmin. In fact, if the firm were to produce at Qmin, it would suffer an economic loss. (The demand line falls below the average-cost curve at Qmin.)

The general point is that the firm’s optimal output depends on demand as well as cost. In Figure 6.6, the level of demand for the firm’s product is insufficient to justify exploiting all economies of scale. However, we easily could depict a much higher level of demand—one that pushes the firm to an output well above Qmin, that is, into the range of increasing average cost. The figure shows part of a (hypothetical) demand curve and the associated marginal revenue curve that intersects marginal cost at output Q . For this level of demand, Q (a quantity much greater than Qmin) is the profit-maximizing output.

The second fallacy works in the opposite direction of the first. It states that if the current output and price are unsatisfactory, the firm should raise its price to increase profits. The intuitive appeal of this “rule” is obvious. If price is too low relative to average cost, the remedy is to increase price. However, this contention is not necessarily so. In Figure 6.6, raising price is appropriate only if the current price is lower than P* (with output greater than Q*). If price is already greater than P*, further price increases only reduce profits. In fact, the figure can readily demonstrate the classic fallacy of managing the product out of business. Suppose management makes the mistake of setting its output at Q . Here the firm’s price P is slightly below average cost, so the firm is incurring a loss. As a remedy, the firm raises price. Does this improve profits? No. The increase in price causes a decrease in quantity (which is expected) but also an increase in average cost (perhaps unexpected). At a higher price and lower output, the firm still is generating a loss. If it raises price again, its volume will shrink further and its price still will fail to catch up with its increasing average cost. By using this strategy, the firm quickly would price itself out of the market.

Under adverse economic conditions, managers face the decision of whether to cease production of a product altogether, that is, whether to shut down. Although the choice may appear obvious (shut down if the product is generating monetary losses), a correct decision requires a careful weighing of relevant options. These alternatives differ depending on the firm’s time horizon.

In the short run, many of the firm’s inputs are fixed. Suppose the firm is producing a single item that is incurring economic losses—total cost exceeds revenues or, equivalently, average total cost exceeds price. Figure 6.7 displays the situation. At the firm’s current output, average cost exceeds price: AC P*; the firm is earning negative economic profit. Should the firm cease production and shut down? The answer is no. To see this, write the firm’s profit as

FIGURE 6.7

Shutting Down

In the short run, the firm should continue to produce at Q* (even if it is suffering a loss) so long as price exceeds average variable cost. In the long run, the firm should shut down if price falls short of average cost. Dollars per Unit of Output

P MC

AC

AVC

Q Marginal revenue Demand

Output

(R VC) FC (P AVC)Q FC. [6.5]

The first term, R VC, is referred to as the product’s contribution. As long as revenue exceeds variable costs (or, equivalently, P AVC), the product is making a positive contribution to the firm’s fixed costs. Observe that price exceeds average variable cost in Figure 6.7. (The average variable cost curve is Ushaped, and it lies below the AC curve because it excludes all fixed costs.) Therefore, continuing to produce the good makes a contribution to fixed costs. (In fact, output Q* delivers maximum contribution because MR MC.) If instead the firm were to discontinue production (Q 0), this contribution would be lost. In the short run, the firm is stuck with its fixed costs. It will incur these costs whether or not it produces output. If the firm shuts down, its profit will be FC. (The firm will earn no revenues but will pay its fixed costs.)