Firm Supply

In this chapter we will see how to derive the supply curve of a competitive firm from its cost function using the model of profit maximization. The first thing we have to do is to describe the market environment in which the firm operates.

22.1 Market Environments

Every firm faces two important decisions: choosing how much it should produce and choosing what price it should set. If there were no constraints on a profit-maximizing firm, it would set an arbitrarily high price and produce an arbitrarily large amount of output. But no firm exists in such an unconstrained environment. In general, the firm faces two sorts of constraints on its actions.

First, it faces the technological constraints summarized by the production function. There are only certain feasible combinations of inputs and outputs, and even the most profit-hungry firm has to respect the realities of the physical world. We have already discussed how we can summarize the technological constraints, and we've seen how the technological constraints lead to the economic constraints summarized by the cost function.

But now we bring in a new constraint—or at least an old constraint from a different perspective. This is the market constraint. A firm can produce whatever is physically feasible, and it can set whatever price it wants ... but it can only sell as much as people are willing to buy.

If it sets a certain price p it will sell a certain amount of output x. We call the relationship between the price a firm sets and the amount that it sells the demand curve facing the firm.

If there were only one firm in the market, the demand curve facing the firm would be very simple to describe: it is just the market demand curve described in earlier chapters on consumer behavior. For the market demand curve measures how much of the good people want to buy at each price. Thus the demand curve summarizes the market constraints facing a firm that has a market all to itself.

But if there are other firms in the market, the constraints facing an individual firm will be different. In this case, the firm has to guess how the other firms in the market will behave when it chooses its price and output.

This is not an easy problem to solve, either for firms or for economists. There are a lot of different possibilities, and we will try to examine them in a systematic way. We'll use the term market environment to describe the ways that firms respond to each other when they make their pricing and output decisions.

In this chapter we'll examine the simplest market environment, that of pure competition. This is a good comparison point for many other environments, and it is of considerable interest in its own right. First let's give the economist's definition of pure competition, and then we'll try to justify it.

22.2 Pure Competition

To a lay person, "competition" has the connotation of intense rivalry. That's why students are often surprised that the economist's definition of competition seems so passive: we say that a market is purely competitive if each firm assumes that the market price is independent of its own level of output. Thus, in a competitive market, each firm only has to worry about how much output it wants to produce. Whatever it produces can only be sold at one price: the going market price.

In what sort of environment might this be a reasonable assumption for a firm to make? Well, suppose that we have an industry composed of many firms that produce an identical product, and that each firm is a small part of the market. A good example would be the market for wheat. There are thousands of wheat farmers in the United States, and even the largest of them produces only an infinitesimal fraction of the total supply. It is

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reasonable in this case for any one firm in the industry to take the market price as being predetermined. A wheat farmer doesn't have to worry about what price to set for his wheat—if he wants to sell any at all, he has to sell it at the market price. He is a price taker: the price is given as far as he is concerned; all he has to worry about is how much to produce.

This kind of situation-—an identical product and many small firms—is a classic example of a situation where price-taking behavior is sensible. But it is not the only case where price-taking behavior is possible. Even if there are only a few firms in the market, they may still treat the market price as being outside their control.

Think of a case where there is a fixed supply of a perishable good: say fresh fish or cut flowers in a marketplace. Even if there are only 3 or 4 firms in the market, each firm may have to take the other firms' prices as given. If the customers in the market only buy at the lowest price, then the lowest price being offered is the market price. If one of the other firms wants to sell anything at all, it will have to sell at the market price. So in this sort of situation competitive behavior—taking the market price as outside of your control—seems plausible as well.

We can describe the relationship between price and quantity perceived by a competitive firm in terms of a diagram as in Figure 22.1. As you can see, this demand curve is very simple. A competitive firm believes that it will sell nothing if it charges a price higher than the market price. If it sells at the market price, it can sell whatever amount it wants, and if it sells below the market price, it will get the entire market demand at that price.

As usual we can think of this kind of demand curve in two ways. If we think of quantity as a function of price, this curve says that you can sell any amount you want at or below the market price. If we think of price as a function of quantity, it says that no matter how much you sell, the market price will be independent of your sales.

(Of course, this doesn't have to be true for literally any amount. Price has to be independent of your output for any amount you might consider selling. In the case of the cut-flower seller, the price has to be independent of how much she sells for any amount up to her stock on hand—the maximum that she could consider selling.)

It is important to understand the difference between the "demand curve facing a firm" and the "market demand curve." The market demand curve measures the relationship between the market price and the total amount of output sold. The demand curve facing a firm measures the relationship between the market price and the output of that particular firm.

The market demand curve depends on consumers' behavior. The demand curve facing a firm not only depends on consumers' behavior but it also depends on the behavior of the other firms. The usual justification for the competitive model is that when there are many small firms in the market, each one faces a demand curve that is essentially flat. But even if there are only two firms in the market, and one insists on charging a fixed price no matter what, then the other firm in the market will face a competitive demand curve like the one depicted in Figure 22.1. Thus the competitive model may hold in a wider variety of circumstances than is apparent at first glance.

Market price

Market demand

Demand curve facing firm

Market demand

Demand curve facing firm

The demand curve facing a competitive firm. The firm's demand is horizontal at the market price. At higher prices, the firm sells nothing, and below the market price it faces the entire market demand curve.

22,3 The Supply Decision of a Competitive Firm

Let us use the facts we have discovered about cost curves to figure out the supply curve of a competitive firm. By definition a competitive firm ignores its influence on the market price. Thus the maximization problem facing a competitive firm is maxpy — c(y). y

This just says that the competitive firm wants to maximize its profits: the difference between its revenue, py, and its costs, c(y).

What level of output will a competitive firm choose to produce? Answer: it will operate where marginal revenue equals marginal cost-^where the extra revenue gained by one more unit of output just equals the extra cost

THE SUPPLY DECISION OF A COMPETITIVE FIRM 387

of producing another unit. If this condition did not hold, the firm could always increase its profits by changing its level of output.

In the case of a competitive firm, marginal revenue is simply the price. To see this, ask how much extra revenue a competitive firm gets when it increases its output by Ay. We have

AR = pAy since by hypothesis p doesn't change. Thus the extra revenue per unit of output is given by

which is the expression for marginal revenue.

Thus a competitive firm will choose a level of output y where the marginal cost that it faces at y is just equal to the market price. In symbols:

For a given market price, p, we want to find the level of output where profits are maximal. If price is greater than marginal cost at some level of output ?/, then the firm can increase its profits by producing a little more output. For price greater than marginal costs means

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