Application: Long-run profit in perfect competition

Section 5.8 Application: Long-run profit in perfect competition

In this section, our goal is to highlight a unique feature of perfectly competitive outcomes in the long run. At the beginning of this chapter, we discuss how perfectly competitive firms maximize profit: choose a level of output $q^*$ where marginal revenue equals marginal cost (or, equivalently, price equals marginal cost.)

This choice allows the firm to achieve the highest level of profit available to it, whether that profit is positive, negative, or zero dollars. The graphs below show two profit-maximizing scenarios. On the left, the firm’s optimal choice maximizes its profit and the profit earned is positive, since total revenue exceeds total cost. On the right, however, the firm’s optimal cost maximizes its profit but the firm can only achieve a negative profit even at its best! We can see this because at $q^*\text{,}$ the firm’s total cost exceeds its total revenue.

Figure 5.8.1. Left: At the firm’s profit-maximizing choice, the firm makes $\pi > 0\text{.}$ Right: At the firm’s profit-maximizing choice, the firm makes $\pi \lt 0\text{.}$

It is fair to ask why a firm would ever accept making negative profit. In the short run, making negative profit may be the best the firm can do! We know that in the short run, firms have some inputs which are fixed and cannot be changed. This means the firm must still pay its total fixed cost in the short run - $TFC$ is unavoidable! It is possible, though, for the firm to maximize its profit in the short run, make $q^*\text{,}$ and make a less negative profit. It’s better to lose $50 than to lose $200, right? Particularly in the context of unavoidable total fixed cost in the short run, negative profit is possible.

Figure 5.8.2. The negative profit of producing $q_o=0$ is worse than the negative profit of producing $q^* > 0\text{.}$

The story here, however, is a long-run story. What outcomes should we anticipate in the long run in perfect competition? To find out, we need to remember one key assumption embedded in perfectly competitive markets: free entry and free exit. I

Imagine a scenario where perfectly competitive firms are making positive profit. These firms are producing identical goods, have no ability to influence the price in the market, and there is free entry into the market for new sellers. In the long run, over time, we would expect new firms to observe the profit opportunities in the market and enter!

So profit attracts entry. How does entry impact the market? An increase in the number of sellers in a market will lead to an increase in supply, which we know also leads to a decrease in the price in the market. Since perfectly competitive firms have no market power, and price equals marginal revenue, firms’ marginal revenue decreases as well. This should make sense: with more competitors in the market, each individual firm can now sell its output for a lower price, which decreases the amount of revenue earned per sale.

As an individual firm, this has two effects. At a lower market price, the firm will reduce its level of output. This is the Law of Supply at work: as the price goes down, the quantity supplied by the firm will also go down. We can see this in the graph below. As supply in the market increases, and the price comes down, the profit-maximizing choice of $q^*$ - where $P = MC$ - occurs at a lower level of output.

Additionally, at a lower market price, the firm’s profit will decrease as well. Notice how entry affects the total revenue curve of the firm. Since the slope of the firm’s total revenue curve is marginal revenue (which equals price), as price goes down, the slope of total revenue decreases. This flattens total revenue, reduces the profit-maximizing quantity of output, and shrinks profit. Visually, the flatter $TR$ curve squishes the vertical distance between $TR$ and $TC$ - which we know is profit.

Figure 5.8.3. Left: Entry increases supply and reduces price. Right: Since $P = MR$ decreases, the firm’s optimal choice decreases as well.

Figure 5.8.4. Left: Entry increases supply and reduces price. Right: The lower price reduces marginal revenue, flattening total revenue and shrinking profit.

And as long as firms continue to make positive profit, no matter how small, we expect firms to continue to enter until profit is eroded all the way down to zero!

What about the case where individual firms make negative profit in the short run? Here, negative profit will push firms to exit the market. This reduces the market supply, and a decrease in supply leads to an increase in price! This will (1) encourage the remaining individual firms to increase profit-maximizing output (by the Law of Supply) and (2) lead to higher profit for the remaining firms who were making losses. Once again, as long as profit is negative for some firms in the market, we would anticipate firms to exit until the price increases enough to move profit up to zero.

Figure 5.8.5. Left: Exit decreases supply and increases price. Right: Since $P = MR$ increases, the firm’s optimal choice increases as well.

Figure 5.8.6. Left: Exit decreases supply and increases price. Right: The higher price increases marginal revenue, making total revenue steeper and increasing profit. Notice that while profit is still negative after the exit, it is not as negative as it was previously.

In either case, the long-run prediction is clear: in perfectly competitive markets, firm profit in the long run will trend to zero! Free entry attracts new firms to the market if there is profit being made, putting downward pressure on prices and eroding all firms’ profit. Free exit allows firms losing money to exit the market, leaving space for the remaining firms to make slightly higher profit. Both roads lead to the same end: firms making zero profit. Sometimes this is referred to as the zero-profit condition.

The table below gives a quick recap of the two long-run scenarios:

If profit is \ldots	\ldots firms will \ldots	\ldots leading to a \ldots	\ldots forcing price \ldots	\ldots pushing $\pi$

positive	enter	supply increase	downward	down to zero

negative	exit	supply decrease	upward	up to zero

Table: In the long run, individual firm profit in perfectly competitive markets tends toward zero. Positive short-run profit attracts entry, which puts downward pressure on prices and reduces profit. Negative short-run profit leads to exit, reducing supply and raising price until profit reaches zero.

Of course, timing is an important consideration here. What does it mean for profit to trend toward zero in the long run? How long does this actually take?

Much like our discussion on dynamic stability in perfectly competitive equilibrium (section 5.6), convergence toward zero profit can take a long time. And we may never actually observe the final point in that convergence process! At any point in time, we are likely observing a market in the middle of the process: firms making positive or negative profit. Even if we do not observe the zero-profit condition in practice, it can provide useful guidance for where a market is heading. For example, if firms in a perfectly competitive market are making positive profit, one could reasonably anticipate that those profits are unlikely to be tenable in the long run as entry and increased competition put downward pressure on prices and erode those profits. This can help economists forecast in which markets are likely to see increased entry and competition.

Importantly, the zero-profit condition highlights the distinction between perfectly competitive markets and other market structures. If a market has barriers to entry, for example, firms making positive profit will be much less likely to experience an erosion of profits due to an influx of competitors entering the market! Oligopolistic and monopolistic markets are therefore much more likely to experience sustainably high profits in the long run.

Figure 5.8.7. The zero-profit condition, graphed. In the long run, a sequence of entry and exit will lead to zero profit for individual firms.

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