Consider Noelle, who runs a Christmas tree farm. Suppose that the market price of Christmas trees is $18 per tree and that Noelle is a price-taker—she can sell as many as she likes at that price. Then we can use the data in Table 12-1 to find her profit-maximizing level of output by direct calculation.

The first column shows the quantity of output in number of trees, and the second column shows Noelle’s total revenue from her output: the market value of trees she produced. Total revenue, TR, is equal to the market price multiplied by the quantity of output:

In this example, total revenue is equal to $18 per tree times the quantity of output in trees.

The third column of Table 12-1 shows Noelle’s total cost. The fourth column shows her profit, equal to total revenue minus total cost:

As indicated by the numbers in the table, profit is maximized at an output of 50 trees, where profit is equal to $180. But we can gain more insight into the profit-maximizing choice of output by viewing it as a problem of marginal analysis, a task we’ll do next.

Recall from Chapter 9 the profit-maximizing principle of marginal analysis: the optimal amount of an activity is the level at which marginal benefit is equal to marginal cost. To apply this principle, consider the effect on a producer’s profit of increasing output by one unit. The marginal benefit of that unit is the additional revenue generated by selling it; this measure has a name—it is called the marginal revenue of that unit of output. The general formula for marginal revenue is:

or

MR = ΔTR/ΔQ

So Noelle maximizes her profit by producing trees up to the point at which the marginal revenue is equal to marginal cost. We can summarize this as the producer’s optimal output rule: profit is maximized by producing the quantity at which the marginal revenue of the last unit produced is equal to its marginal cost. That is, MR = MC at the optimal quantity of output.

We can learn how to apply the optimal output rule with the help of Table 12-2, which provides various short-run cost measures for Noelle’s farm. The second column contains the farm’s variable cost, and the third column shows its total cost of output based on the assumption that the farm incurs a fixed cost of $140. The fourth column shows marginal cost. Notice that, in this example, the marginal cost initially falls as output rises but then begins to increase. This gives the marginal cost curve the “swoosh” shape described in the Selena’s Gourmet Salsas example in Chapter 11. Shortly it will become clear that this shape has important implications for short-run production decisions.

The fifth column contains the farm’s marginal revenue, which has an important feature: Noelle’s marginal revenue equal to price is constant at $18 for every output level. The sixth and final column shows the calculation of the net gain per tree, which is equal to marginal revenue minus marginal cost—or, equivalently in this case, market price minus marginal cost. As you can see, it is positive for the 10th through 50th trees; producing each of these trees raises Noelle’s profit. For the 60th through 70th trees, however, net gain is negative: producing them would decrease, not increase, profit. (You can verify this by examining Table 12-1.) So a quantity of 50 trees is Noelle’s profit-maximizing output; it is the level of output at which marginal cost is equal to the market price, $18.

This example, in fact, illustrates another general rule derived from marginal analysis—the price-taking firm’s optimal output rule, which says that a price-taking firm’s profit is maximized by producing the quantity of output at which the market price is equal to the marginal cost of the last unit produced. That is, P = MC at the price-taking firm’s optimal quantity of output. In fact, the price-taking firm’s optimal output rule is just an application of the optimal output rule to the particular case of a price-taking firm. Why? Because in the case of a price-taking firm, marginal revenue is equal to the market price.

A price-taking firm cannot influence the market price by its actions. It always takes the market price as given because it cannot lower the market price by selling more or raise the market price by selling less. So, for a price-taking firm, the additional revenue generated by producing one more unit is always the market price. We will need to keep this fact in mind in future chapters, where we will learn that marginal revenue is not equal to the market price if the industry is not perfectly competitive. As a result, firms are not price-takers when an industry is not perfectly competitive.

For the remainder of this chapter, we will assume that the industry in question is like Christmas tree farming, perfectly competitive. Figure 12-1 shows that Noelle’s profit-maximizing quantity of output is, indeed, the number of trees at which the marginal cost of production is equal to price. The figure shows the marginal cost curve, MC, drawn from the data in the fourth column of Table 12-2. As in Chapter 9, we plot the marginal cost of increasing output from 10 to 20 trees halfway between 10 and 20, and so on. The horizontal line at $18 is Noelle’s marginal revenue curve.

Note that whenever a firm is a price-taker, its marginal revenue curve is a horizontal line at the market price: it can sell as much as it likes at the market price. Regardless of whether it sells more or less, the market price is unaffected. In effect, the individual firm faces a horizontal, perfectly elastic demand curve for its output—an individual demand curve for its output that is equivalent to its marginal revenue curve. The marginal cost curve crosses the marginal revenue curve at point E where MC = MR. Sure enough, the quantity of output at E is 50 trees.

Does this mean that the price-taking firm’s production decision can be entirely summed up as “produce up to the point where the marginal cost of production is equal to the price”? No, not quite. Before applying the profit-maximizing principle of marginal analysis to determine how much to produce, a potential producer must as a first step answer an “either-or” question: should it produce at all? If the answer to that question is yes, it then proceeds to the second step—a “how much” decision: maximizing profit by choosing the quantity of output at which marginal cost is equal to price.

To understand why the first step in the production decision involves an “either–or” question, we need to ask how we determine whether it is profitable or unprofitable to produce at all.

Recall from Chapter 9 that a firm’s decision whether or not to stay in a given business depends on its economic profit—the measure of profit based on the opportunity cost of resources used in the business. To put it a slightly different way: in the calculation of economic profit, a firm’s total cost incorporates the implicit cost—the benefits forgone in the next best use of the firm’s resources—as well as the explicit cost in the form of actual cash outlays.

In contrast, accounting profit is profit calculated using only the explicit costs incurred by the firm. This means that economic profit incorporates the opportunity cost of resources owned by the firm and used in the production of output, while accounting profit does not.

A firm may make positive accounting profit while making zero or even negative economic profit. It’s important to understand clearly that a firm’s decision to produce or not, to stay in business or to close down permanently, should be based on economic profit, not accounting profit.

So we will assume, as we always do, that the cost numbers given in Tables 12-1 and 12-2 include all costs, implicit as well as explicit, and that the profit numbers in Table 12-1 are therefore economic profit. So what determines whether Noelle’s farm earns a profit or generates a loss? The answer is that, given the farm’s cost curves, whether or not it is profitable depends on the market price of trees—specifically, whether the market price is more or less than the farm’s minimum average total cost.

In Table 12-3 we calculate short-run average variable cost and short-run average total cost for Noelle’s farm. These are short-run values because we take fixed cost as given. (We’ll turn to the effects of changing fixed cost shortly.) The short-run average total cost curve, ATC, is shown in Figure 12-2, along with the marginal cost curve, MC, from Figure 12-1. As you can see, average total cost is minimized at point C, corresponding to an output of 40 trees—the minimum-cost output—and an average total cost of $14 per tree.

To see how these curves can be used to decide whether production is profitable or unprofitable, recall that profit is equal to total revenue minus total cost, TR − TC. This means:

We can also express this idea in terms of revenue and cost per unit of output. If we divide profit by the number of units of output, Q, we obtain the following expression for profit per unit of output:

TR/Q is average revenue, which is the market price. TC/Q is average total cost. So a firm is profitable if the market price for its product is more than the average total cost of the quantity the firm produces; a firm loses money if the market price is less than average total cost of the quantity the firm produces. This means:

Figure 12-3 illustrates this result, showing how the market price determines whether a firm is profitable. It also shows how profits are depicted graphically. Each panel shows the marginal cost curve, MC, and the short-run average total cost curve, ATC. Average total cost is minimized at point C. Panel (a) shows the case we have already analyzed, in which the market price of trees is $18 per tree. Panel (b) shows the case in which the market price of trees is lower, $10 per tree.

In panel (a), we see that at a price of $18 per tree the profit-maximizing quantity of output is 50 trees, indicated by point E, where the marginal cost curve, MC, intersects the marginal revenue curve—which for a price-taking firm is a horizontal line at the market price. At that quantity of output, average total cost is $14.40 per tree, indicated by point Z. Since the price per tree exceeds average total cost per tree, Noelle’s farm is profitable.

Noelle’s total profit when the market price is $18 is represented by the area of the shaded rectangle in panel (a). To see why, notice that total profit can be expressed in terms of profit per unit:

or, equivalently,

Profit = (P − ATC) × Q

since P is equal to TR/Q and ATC is equal to TC/Q. The height of the shaded rectangle in panel (a) corresponds to the vertical distance between points E and Z. It is equal to P − ATC = $18.00 − $14.40 = $3.60 per tree. The shaded rectangle has a width equal to the output: Q = 50 trees. So the area of that rectangle is equal to Noelle’s profit: 50 trees × $3.60 profit per tree = $180—the same number we calculated in Table 12-1.

What about the situation illustrated in panel (b)? Here the market price of trees is $10 per tree. Setting price equal to marginal cost leads to a profit-maximizing output of 30 trees, indicated by point A. At this output, Noelle has an average total cost of $14.67 per tree, indicated by point Y. At the profit-maximizing output quantity—30 trees—average total cost exceeds the market price. This means that Noelle’s farm generates a loss, not a profit.

How much does she lose by producing when the market price is $10? On each tree she loses ATC − P = $14.67 − $10.00 = $4.67, an amount corresponding to the vertical distance between points A and Y. And she would produce 30 trees, which corresponds to the width of the shaded rectangle. So the total value of the losses is $4.67 × 30 = $140.00 (adjusted for rounding error), an amount that corresponds to the area of the shaded rectangle in panel (b).

But how does a producer know, in general, whether or not its business will be profitable? It turns out that the crucial test lies in a comparison of the market price to the producer’s minimum average total cost. On Noelle’s farm, minimum average total cost, which is equal to $14, occurs at an output quantity of 40 trees, indicated by point C.

Whenever the market price exceeds minimum average total cost, the producer can find some output level for which the average total cost is less than the market price. In other words, the producer can find a level of output at which the firm makes a profit. So Noelle’s farm will be profitable whenever the market price exceeds $14. And she will achieve the highest possible profit by producing the quantity at which marginal cost equals the market price.

Conversely, if the market price is less than minimum average total cost, there is no output level at which price exceeds average total cost. As a result, the firm will be unprofitable at any quantity of output. As we saw, at a price of $10—an amount less than minimum average total cost—Noelle did indeed lose money. By producing the quantity at which marginal cost equals the market price, Noelle did the best she could, but the best that she could do was a loss of $140. Any other quantity would have increased the size of her loss.

The minimum average total cost of a price-taking firm is called its break-even price, the price at which it earns zero profit. (Recall that’s economic profit.) A firm will earn positive profit when the market price is above the break-even price, and it will suffer losses when the market price is below the break-even price. Noelle’s break-even price of $14 is the price at point C in Figures 12-2 and 12-3.

So the rule for determining whether a producer of a good is profitable depends on a comparison of the market price of the good to the producer’s breakeven price—its minimum average total cost:

You might be tempted to say that if a firm is unprofitable because the market price is below its minimum average total cost, it shouldn’t produce any output. In the short run, however, this conclusion isn’t right.

In the short run, sometimes the firm should produce even if price falls below minimum average total cost. The reason is that total cost includes fixed cost—cost that does not depend on the amount of output produced and can only be altered in the long run.

In the short run, fixed cost must still be paid, regardless of whether or not a firm produces. For example, if Noelle rents a refrigerated truck for the year, she has to pay the rent on the truck regardless of whether she produces any trees. Since it cannot be changed in the short run, her fixed cost is irrelevant to her decision about whether to produce or shut down in the short run.

Although fixed cost should play no role in the decision about whether to produce in the short run, other costs—variable costs—do matter. An example of variable costs is the wages of workers who must be hired to help with planting and harvesting. Variable costs can be saved by not producing; so they should play a role in determining whether or not to produce in the short run.

Let’s turn to Figure 12-4: it shows both the short-run average total cost curve, ATC, and the short-run average variable cost curve, AVC, drawn from the information in Table 12-3. Recall that the difference between the two curves—the vertical distance between them—represents average fixed cost, the fixed cost per unit of output, FC/Q.

Because the marginal cost curve has a “swoosh” shape—falling at first before rising—the short-run average variable cost curve is U-shaped: the initial fall in marginal cost causes average variable cost to fall as well, before rising marginal cost eventually pulls it up again. The short-run average variable cost curve reaches its minimum value of $10 at point A, at an output of 30 trees.

We are now prepared to fully analyze the optimal production decision in the short run. We need to consider two cases:

When the market price is below minimum average variable cost, the price the firm receives per unit is not covering its variable cost per unit. A firm in this situation should cease production immediately. Why? Because there is no level of output at which the firm’s total revenue covers its variable costs—the costs it can avoid by not operating.

In this case the firm maximizes its profits by not producing at all—by, in effect, minimizing its losses. It will still incur a fixed cost in the short run, but it will no longer incur any variable cost. This means that the minimum average variable cost is equal to the shut-down price, the price at which the firm ceases production in the short run. In the example of Noelle’s tree farm, she will cease production in the short run by laying off workers and halting all planting and harvesting of trees.

When price is greater than minimum average variable cost, however, the firm should produce in the short run. In this case, the firm maximizes profit—or minimizes loss—by choosing the output quantity at which its marginal cost is equal to the market price. For example, if the market price of each tree is $18, Noelle should produce at point E in Figure 12-4, corresponding to an output of 50 trees. Note that point C in Figure 12-4 corresponds to the farm’s break-even price of $14 per tree. Since E lies above C, Noelle’s farm will be profitable; she will generate a per-tree profit of $18.00 − $14.40 = $3.60 when the market price is $18.

But what if the market price lies between the shut-down price and the break-even price—that is, between minimum average variable cost and minimum average total cost? In the case of Noelle’s farm, this corresponds to prices anywhere between $10 and $14—say, a market price of $12. At $12, Noelle’s farm is not profitable; since the market price is below minimum average total cost, the farm is losing the difference between price and average total cost per unit produced.

Yet even if it isn’t covering its total cost per unit, it is covering its variable cost per unit and some—but not all—of the fixed cost per unit. If a firm in this situation shuts down, it would incur no variable cost but would incur the full fixed cost. As a result, shutting down generates an even greater loss than continuing to operate.

This means that whenever price lies between minimum average total cost and minimum average variable cost, the firm is better off producing some output in the short run. The reason is that by producing, it can cover its variable cost per unit and at least some of its fixed cost, even though it is incurring a loss. In this case, the firm maximizes profit—that is, minimizes loss—by choosing the quantity of output at which its marginal cost is equal to the market price. So if Noelle faces a market price of $12 per tree, her profit-maximizing output is given by point B in Figure 12-4, corresponding to an output of 35 trees.

It’s worth noting that the decision to produce when the firm is covering its variable costs but not all of its fixed cost is similar to the decision to ignore sunk costs. You may recall from Chapter 9 that a sunk cost is a cost that has already been incurred and cannot be recouped; and because it cannot be changed, it should have no effect on any current decision.

In the short-run production decision, fixed cost is, in effect, like a sunk cost—it has been spent, and it can’t be recovered in the short run. This comparison also illustrates why variable cost does indeed matter in the short run: it can be avoided by not producing.

And what happens if market price is exactly equal to the shut-down price, minimum average variable cost? In this instance, the firm is indifferent between producing 30 units or 0 units. As we’ll see shortly, this is an important point when looking at the behavior of an industry as a whole. For the sake of clarity, we’ll assume that the firm, although indifferent, does indeed produce output when price is equal to the shut-down price.

Putting everything together, we can now draw the short-run individual supply curve of Noelle’s farm, the red line in Figure 12-4; it shows how the profit-maximizing quantity of output in the short run depends on the price. As you can see, the curve is in two segments. The upward-sloping red segment starting at point A shows the short-run profit-maximizing output when market price is equal to or above the shut-down price of $10 per tree.

As long as the market price is equal to or above the shut-down price, Noelle produces the quantity of output at which marginal cost is equal to the market price. That is, at market prices equal to or above the shut-down price, the firm’s short-run supply curve corresponds to its marginal cost curve. But at any market price below minimum average variable cost—in this case, $10 per tree—the firm shuts down and output drops to zero in the short run. This corresponds to the vertical segment of the curve that lies on top of the vertical axis.

Do firms really shut down temporarily without going out of business? Yes. In fact, in some businesses temporary shut-downs are routine. The most common examples are industries in which demand is highly seasonal, like outdoor amusement parks in climates with cold winters. Such parks would have to offer very low prices to entice customers during the colder months—prices so low that the owners would not cover their variable costs (principally wages and electricity). The wiser choice economically is to shut down until warm weather brings enough customers who are willing to pay a higher price.

Although fixed cost cannot be altered in the short run, in the long run firms can acquire or get rid of machines, buildings, and so on. As we learned in Chapter 11, in the long run the level of fixed cost is a matter of choice. There we saw that a firm will choose the level of fixed cost that minimizes the average total cost for its desired output quantity. Now we will focus on an even bigger question facing a firm when choosing its fixed cost: whether to incur any fixed cost at all by remaining in its current business.

In the long run, a producer can always eliminate fixed cost by selling off its plant and equipment. If it does so, of course, it can’t ever produce—it has exited the industry. In contrast, a potential producer can take on some fixed cost by acquiring machines and other resources, which puts it in a position to produce—it can enter the industry. In most perfectly competitive industries the set of producers, although fixed in the short run, changes in the long run as firms enter or exit the industry.

Consider Noelle’s farm once again. In order to simplify our analysis, we will sidestep the problem of choosing among several possible levels of fixed cost. Instead, we will assume from now on that Noelle has only one possible choice of fixed cost if she operates, the amount of $140, Noelle’s minimum average total cost, that was the basis for the calculations in Tables 12-1, 12-2, and 12-3. (With this assumption, Noelle’s short-run average total cost curve and long-run average total cost curve are one and the same.) Alternatively, she can choose a fixed cost of zero if she exits the industry.

Suppose that the market price of trees is consistently less than $14 over an extended period of time. In that case, Noelle never fully covers her fixed cost: her business runs at a persistent loss. In the long run, then, she can do better by closing her business and leaving the industry. In other words, in the long run firms will exit an industry if the market price is consistently less than their break-even price—their minimum average total cost.

Conversely, suppose that the price of Christmas trees is consistently above the break-even price, $14, for an extended period of time. Because her farm is profitable, Noelle will remain in the industry and continue producing.

But things won’t stop there. The Christmas tree industry meets the criterion of free entry: there are many potential tree producers because the necessary inputs are easy to obtain. And the cost curves of those potential producers are likely to be similar to those of Noelle, since the technology used by other producers is likely to be very similar to that used by Noelle. If the price is high enough to generate profits for existing producers, it will also attract some of these potential producers into the industry. So in the long run a price in excess of $14 should lead to entry: new producers will come into the Christmas tree industry.

As we will see next, exit and entry lead to an important distinction between the short-run industry supply curve and the long-run industry supply curve.

In this chapter, we’ve studied where the supply curve for a perfectly competitive, price-taking firm comes from. Every perfectly competitive firm makes its production decisions by maximizing profit, and these decisions determine the supply curve. Table 12-4 summarizes the perfectly competitive firm’s profitability and production conditions. It also relates them to entry into and exit from the industry.