# How is it possible for demand to be perfectly elastic under perfect competition? So according to perfect competition, a single firm is a price taker, having to sell at the equilibrium price as determined by supply and demand. As you can see from the single firm graph, demand is perfectly elastic. However, from what I’ve read about perfectly elastic demand, that means the quantity demanded is infinite at the given price (P). But according to the industry graph, the quantity demanded at price P is Q, a finite quantity. How is it possible that the quantity demanded for a single firm at Price P is infinite, when the quantity demanded for the entire industry (which includes the single firm) at Price P is a finite quantity (Q)?

How is it possible that the quantity demanded for a single firm at Price P is infinite, when the quantity demanded for the entire industry (which includes the single firm) at Price P is a finite quantity (Q)?

It is not completely correct to say quantity demanded for perfectly elastic demand is infinite. That is quite common misconception. Rather, demand can be any quantity between $$[0,\infty)$$ but that is not the same as being only $$\infty$$. Horizontal demand curve says that consumers would be willing to buy any $$Q$$. This is why the line goes to infinity but $$Q$$ itself will not be infinite.

In fact as your own graph show the firm will produce $$Q$$ such that $$MR=MC$$ and clearly as the graph shows the $$Q$$ is well below infinity.

• Thank you for your answer. Only thing I have a hard time understanding is that if the single firm sells at the equilibrium price, it can’t just sell ANY non-zero quantity. At most, it could only sell the equilibrium quantity as determined by the industry graph. For instance, let’s say the industry equilibrium price is 5 dollars and the industry equilibrium quantity is 100 units. If an individual supplier sells units at 5 dollars, it would only be able to sell 100 units at most Nov 10, 2022 at 15:24

The demand for the firm being perfectly elastic in perfect competition means if the firm increased the price a bit, its demand would go down to 0 as their consumers would all flee to their competition as competitors are selling the same product cheaper.

On the other hand, if they decreased the price a bit, they would steal all their competitors’ demand as they are the firm producing that product the cheapest of all.

The horizontal red line in the right figure is not the graph of the demand function $$Q(p)$$ but the graph of the indirect demand function $$p(Q)\equiv P$$, which is constant at the market price $$P$$ and indicates that a firm can sell any quantity it wants but will always achieve just the market price. Thus, "perfectly elastic demand" really means perfectly inelastic indirect demand.

The "demand function" $$Q(p)$$ indicating the demand facing the firm as a function of the firm's price is not well defined as a function into the real numbers. Instead, one can work with the (set-valued) demand correspondence $$Q(p)\in\left\{ \begin{array} \{\{0\} \ldots p>P \\ [0,\infty) \ldots p\le P \end{array} \right.$$