How can an individual firm sell ANY quantity for the market price under perfect competition?

Question

I keep hearing that under perfect competition, an individual firm can sell ANY quantity as long as they sell at the equilibrium price. But this doesn’t make sense to me. For the market supply and demand graph, the equilibrium price has an equilibrium quantity to go along with it. Wouldn’t the maximum quantity that a supplier would be able to sell at the equilibrium price also be the equilibrium quantity?

For instance, shouldn’t the quantity that the single firm is able to sell at the equilibrium price (price P) be the same as the quantity represented by Q in the industry graph?

Answer 1

The textbook model assumes that an individual firm could sell any quantity at the market price, but of course it will only sell the quantity which maximizes its profit. (Graphically speaking, while the firm could choose any point on the red line in the right figure, it will choose point $A$.)

You seem to argue that an individual firm even could not sell more at the market price than total quantity demanded in the industry (i.e., the equilibrium quantity in the left figure). That's true: In "reality" the red horizontal line should start to decline at some extremely large output quantity, where it already serves a significant fraction of industry demand. But this is irrelevant for the firm's actual quantity decision, since out there, marginal costs would already be astronomical anyway. The horizontal individual demand curve is just a simplification that ignores this irrelevant difficulty. The individual firm is simply assumed to act as if it could sell any quantity it wished to sell at the prevailing market price, just as it is assumed to act as if the market price didn't react to its own quantity decision (which is also, strictly speaking, wrong).

Answer 2

In my opinion, you are right. This is a question that upsets many students, and I think they are right.

'The individual firm can sell ANY quantity as long as they sell at the equilibrium price' is a way of saying, but it isn't very rigorous.

The point of the question is about the horizontal line in correspondence of the market equilibrium price, about what is called 'the individual demand function’, in opposition to the 'market demand function'.

This line says simply that the price the firm faces is the same regardless of the quantity it supplies. That is, in formal terms, the price is a constant function of $Q$. This does not mean that the firm actually can sell whatever quantity it wants: instead, maybe, it could be better to say that the firm chooses the optimal quantity 'as if' it could sell whatever quantity of product.

The core of the definition of a perfect competitive market is that a firm is price taker: in the sense that the firm believes that it can't affect the market price with its actions, in particular with the quantity it supplies, and takes the price as given. So, the price line is horizontal.

The fact that, at the market equilibrium price, the firm actually sells all the quantity it wants is an ex post consideration, that depends on the equilibrium assumption, not on the 'individual demand' being horizontal: if the price is at its equilibrium level, by definition, demand equals supply, so the plans of the agents are consistent, and the firm can sell the optimal quantity chosen in correspondence of that price.

If the firms made their optimal choices at a price different from equilibrium price, for example at a higher price, and the exchanges occurs out of equilibrium, they couldn't sell what they would. But this depends on the fact of being outside equilibrium. The individual optimization problem would be, in the same way, on the basis of a horizontal 'individual demand', a horizontal line in correspondence of the non-equilibrium price: but evidently in this case firms cannot sell what they want, after optimization, even if the ‘individual demand curve’ is still horizontal.

We are in a context of equilibrium and of maximizing behaviour of the firms: these hypotheses are crucial to say that the firms can sell what they want. But suppose that the firm's owners go crazy, they stop optimizing and decide to produce at loss, supplying a big amount of product at the market equilibrium price: they can't sell what they want at the 'theoretical' equilibrium price of the market.

Nevertheless, their 'individual demand curve' is still horizontal.

These are just imaginative examples to remark the importance of both assumptions, optimizing behaviour and the fact that exchanges occur in equilibrium.

Answer 3

The firm can’t really sell any quantity they wanted at the equilibrium price (even if it had not increasing but constant marginal costs). Since Revenue is $R = P q$, we have that the marginal revenue is $MR = P + q \frac{dP}{dq}$.

That second term is usually negative because consumers only demand a limited quantity for a given price level. So the firms would have to reduce the price in order to sell a lot more units.

It’s just that when there are a lot of firms, i.e. in an oligopoly with $N$ firms for big enough $N$ (which is what actually happens in real life), the price effect they generate with their supply is very small (not actually $0$), and for simplicity, it can be approximated to $0$ for big enough $N$ (the perfect competion model):

• $\frac{dP}{dq} \approx 0$

Derivatives are actually a linear approximation of how one variable changes with respect to small changes in another related variable.

But if a firm went crazy and suddenly produced a trillion units, those “very small changes” would really add up and the price would suffer a severe crash.