# Why is the Market-Clearing Price also an Equilibrium Price?

When the price is such that supply equals demand for e.g. bicycles, everybody who wants to buy a bike at that price gets one, and every bike gets sold. Everybody goes home happy and the marketplace clears. Hence the price at which the supply and demand curves cross is the Market-Clearing Price.

This isn't enough to make it an equilibrium price. "Equilibrium" means that if the price is there, it'll stay there. If it's a stable equilibrium, then even if it starts above or below that price, it'll get pushed towards it.

I feel like I understand why prices starting below the market clearing price, will get pushed up. Of course a firm will raise prices: they can charge more per unit, and sell more units (assuming a rising supply curve).

If you start above market-clearing price, there is a trade-off, because sales are demand-limited (assuming the demand curve is decreasing). Raised prices would mean more revenue per sale, but fewer sales. Lowering the price would mean more sales, but less revenue per sale. Intro textbooks (e.g. Mankiw) seem to claim that the mere fact of there being a trade-off at all, is sufficient to push prices down, but it doesn't seem like that to me. Whether lowering prices would increase profits depends on the slope of the demand curve; if it's shallow enough, then the large increase in revenue-per-sale could make up for the small decrease in number of sales.

If I'm not wrong then a firm with a monopoly on bicycles would set prices to maximize revenue, i.e. the area of a rectangle whose length is quantity and whose height is price. The corner of this rectangle would lie somewhere on the demand curve, at or above the market-clearing price. The profit-maximizing price might be one where there's excess potential supply (bikes you would have been willing to make and sell - presumably you didn't actually bother making them).

I assume that competition is what makes the difference, and somehow forces prices down to (but not below) the market-clearing price, making that the equilibrium for competitive markets. But I don't get how this works, e.g. why underselling won't stop being worth it until there's excess demand.

• (I do understand why competition can't push prices below market clearing - below that there are more than enough customers for all the sellers, so they don't have to compete for them. But I don't see why, all the way down to that price, it's always profitable to undersell (as opposed to even just "often" being profitable).) – David Bahry May 28 '17 at 21:31

(This is referring both to the initial question and to the comment. I would respond to each individually, but I don't think I have the reputation to address the comment directly.)

Paraphrasing a bit from your question, you're right- an equilibrium price is one where no firm has an incentive to deviate in their pricing or production decisions, and demand is perfectly satisfied (again, given the price). While the exact "mechanism" that would push price down might differ depending on what market type you're considering, the common feature will be that there is always a marginal incentive to deviate down to the lower price.

In terms of perfect competition- as you mentioned, it can be seen as a race for different firms to undercut their competitors, until they hit the no profit condition. That pushes the market clearing price down to marginal cost, which is the equilibrium price.

For monopolists, they're looking to maximize profit, not necessarily revenue. But, as every firm does, they choose a price p to satisfy:

$$max\{q(p-c)\} = \pi$$

They will choose a price higher than the one found under a perfectly competitive framework; hence why the market clearing price, and equilibrium price, is higher under monopoly than perfect competition.

But if the monopolist were to set a price different from the one that satisfies that maximization problem, they are pricing, as you described, too high. That tells them when to produce more units at a lower price; until their profit maximization price is hit. That becomes the clearing price, and the equilibrium price for a monopolist.

I'm sorry if that was too repetitive or elementary. You're question is an excellent one, and a somewhat subtle point has to be made. If it wasn't clear, or you'd like it re-framed, let me know!

• "[for monopolists] the market clearing price, and equilibrium price, is higher under monopoly than under perfect competition." If so then I misunderstood something I guess? I was imagining the supply and demand curves as fixed/the same, for like, one competitive market and for one monopolist market, i.e. with the same market clearing price; but thinking that the monopolist could conceivably maximize profit by pricing higher than market clearing. Was I wrong? Are market clearing price and profit maximizing price always the same, even for a monopolist? – David Bahry May 29 '17 at 16:38
• Like, I was thinking that there might be conditions where the profit maximizing price doesn't clear the market. Was I wrong about that – David Bahry May 29 '17 at 16:40

The difference between the competitive and monopolist markets is that the monopolist is not a price taker, he is large enough that when he sets prices and determines his output there is no circumventing his choices (this is the nature of monopoly). This is in contrast to the competitive firm, which is forced to either take market prices or be completely avoided by the market of buyers (or sell for cheaper than others, we would be at a loss).

The demand curve for each individual buyer is fixed, but the curve for the monopolist curve is downward sloping, as compared with a competitive firm's demand curve which is horizontal (this is equivalent to the firm being a price taker).

With regard to your point about profit maximizing prices not clearing the market, it seems that that shouldn't be the case. When the monopolist is making his choices about maximizing profit he is using the demand curve to 1) find his marginal revenue, which must be set equal to marginal cost, and 2) set a price for his good at the output level he chooses. Why would he choose a non-clearing price?

If he chooses too high a price he would be better off producing fewer goods, until he has none left over after his sales in the market (this would be market-clearing). If he chooses too low a price...well it is obvious he shouldn't and wouldn't do that.

I found an answer that satisfies me, in Alfred Marshall's original argument from Principles of Economics.

The answer seems to have to do with who has bargaining power. At any higher price, when supply exceeds demand, every buyer can truthfully say to prospective sellers: "If you aren't willing to accept a lower price, I'll find somebody else who is". At any lower price, when demand exceeds supply, every seller can truthfully say to prospective buyers: "If you aren't willing to accept a higher price, I'll find somebody else who is".

Here's the passage:

… Let us take an illustration from a corn-market in a country town. The amount which each former or other seller offers for sale at any price is governed by his own need for money in hand, and by his calculation of the present and future conditions of the market with which he is connected. There are some prices which no seller would accept, some which no one would refuse. There are other intermediate prices which would be accepted for larger or smaller amounts by many or all of the sellers. Let us assume for the sake of simplicity that all the corn in the market is of the same quality. An acute dealer having corn for sale may perhaps, after looking around him, come to the conclusion that if 37$s$ could be got throughout the day, the farmers between them would be willing to sell to the extent of about 1,000 quarters; and that if no more than 36$s$ could be got, several would refuse to sell, or wold sell only small quantities, so that only 700 quarters would be brought forward for sale; and that a price of 35$s$ would only induce some 500 quarters to be brought forward. Suppose him further to calculate that millers and others would be willing to buy 900 quarters if they could be got at 35$s$ each, but only 700 if they could not be got for less that 36$s$, and only 600 if they could not be got for less than 37$s$. He will conclude that a price of 36$s$, if established at once, would equate supply and demand, because the amount offered for sale at that price would equal the amount which could just find purchasers at that price. He will therefore take at once any offer considerably over 36$s$; and other sellers will do the same.

Buyers on their part will make similar calculations and if at any time the price should rise considerably above 36$s$ they will argue that the supply will be much greater than the demand at that price; therefore even those of them who would rather pay that price than go unserved, wait, and by waiting they help to bring the price down. On the other hand, when the price is much below 36$s$ even those sellers who would rather take the price than leave the market with their corn unsold, may argue that at that price the demand will be in excess of the supply: so they wait, and by waiting help to bring the price up.

The price of 36$s$ has thus a claim to be called the true equilibrium price: because if it were fixed on at the beginning, and adhered to throughout, it would exactly equate demand and supply; and because every dealer who has a perfect knowledge of the circumstances of the market expects that price to be established. If he sees the price differing much from 36$s$ he expects that a change will come before long, and by anticipating it he helps it to come quickly…

This argument sounds different from what other answers have said, and didn't mention sellers being "price taking", which others have said is important. So I suspect there's more to it than Marshall's argument.