# Why does supply equal demand?

My question is simple: in theory, why should we expect the total quantity that firms want to sell to be (at least approximately) equal to the total quantity that consumers want to buy?

As I understand it, the standard explanation is something like this. If supply were greater than demand (for instance), then there must be some 'frustrated' sellers who cannot sell all of the units that they want to sell. Instead of paying the market price, buyers could therefore pay a lower price to these sellers while still buying all the units that they want to purchase. This pushes the price downwards, a process that continues until supply equals demand.

I find this kind of explanation unsatisfying for two reasons:

• In the standard framework of competitive equilibrium, agents choose quantities (and view prices as fixed). And yet, the disequilibrium adjustment story here relies on price setting.
• The explanation is highly informal. As a result, it is unclear what assumptions are necessary for it to hold and when we should expect supply to equal demand.

I would be very grateful if anyone could improve on this explanation.

Edit: what I am looking for is a rigorous story explaining why:

• If the number of units that producers want to sell exceeds the number that consumers want to buy, the price will fall.

• If the number of units that consumers want to buy exceeds the number that producers want to sell, the price will increase.

This is a very fundamental assumption in economics so I think deserves a good answer on economics SE (apparently, not everyone agrees, judging by the recent downvotes!)

The puzzle (for me) is how this can happen in an environment when everyone views the price as given (i.e. the standard model of perfect competition).

• Somewhat knitpicking, but it is important that supply equals demand in equilibrium. You can easily show with very general assumptions that if the two quantities are not equal, some firms or consumers could have done better in most frameworks (quantity setting, price setting, Kreps-Scheinkman etc.). So basically you seem to be asking why we are expecting a market to converge to an equilibrium state. This is a question with some literature. – Giskard Aug 9 '18 at 15:40
• Because the context is only mean for the mystically "free market". Any monopoly will break the context. E.g. salt trade in history; Debeer diamond monopoly, etc. – mootmoot Aug 9 '18 at 16:19
• @mootmoot Please post incorrect answers as answers so I can downvote them. – Giskard Aug 10 '18 at 0:20
• 1) Like much (all?) of the general equilibrium literature, the Arrow/Hurwitz paper simply $assumes$ that, if there is excess demand (supply) of a good, then the price of that good will increase (decrease) - see the differential equation on p. 525. No justification is given for this assumption. But my question was precisely what justifies this assumption! – user17900 Aug 15 '18 at 16:48
• 2) The second paper (Kalai and Lehrer) concerns convergence to Nash equilibrium over time. That would be relevant if you could show that supply/demand equilibrium is a Nash equilibrium of a suitably defined game (and satisfies the other Kalai/Lehrer assumptions, e.g. the 'grain of truth' assumption). However, in the absence of this demonstration, I am unclear about the relevance of this paper. – user17900 Aug 15 '18 at 16:52

I am not entirely sure if I can agree to the OP's comment that the disequilibrium analysis depends on price setting. I would rather argue that the analysis depends on quantity selection. With 1000 buyers and sellers in a market, where each seller is a firm and the market equilibrium price is $P^e$ and quantity $Q^e$, a single seller will produce $q_i^e$ such that $P^e = MC_i(q_i^e)$.

If the seller increases production to say $$q_i^1>q_i^e$$, then the seller can do the following:

(1) If the seller charges $P^e$, the seller is making a loss for each of the extra units and the seller reduces production.

(2) If the seller charges $P_1>P^e$ no one buys from him and he makes a loss for the unsold units. The seller reduces production.

The seller realizes that the seller must adhere to the price charged by the market at which point the seller realizes that the optimum quantity produced by the seller is such that $P^e = MC(q_i^e)$

(2) requires, I believe, homogeneous products, large number of buyers and sellers.

When the seller (as discussed above) realizes the overproduction, the seller must adjust back to the output level sold in the market. There are two features while this process happens (i) till the seller adjusts back, there is excess supply, and (ii) there are two prices in the market - $P^e$ and $P_1$. The price that "falls" to the equilibrium level is $P_1$.

Now instead of a single seller, imagine that a group of sellers make this type of overproduction - ultimately all of them will come back to the equilibrium quantity level.

• Thanks for this answer. My question, however, was not why (under perfect competition) firms produce until the point when price equals marginal cost. My question, rather, was why and when we would expect supply to equal demand (i.e. starting from any non-equilibrium price/quantity, why we would we converge over time to the equilibrium price/quantity?) Can you spell out the links between your answer and my question? – user17900 Aug 13 '18 at 13:58
• Hi. I made an edit, I hope it helps. – erik Aug 14 '18 at 3:56

The way I like to think about it is in form of this universally true relationship.

Value of Goods sold = Value of Goods bought

For every seller, there is a corresponding buyer (in terms of value) otherwise trade is not possible.

This is nothing but the essence of general equilibrium theory. Forgive me, I won't go into the algebra or the language of the answer would change from English to Greek.

Now the question why does the demand equal supply. If we assume that the agents are rational, then obviously they would maximize their profit / utility / welfare.

Now if demand does not equal supply, then the agents being rational would calibrate their parameter of price which would make BOTH of them better off. In Economics this is known as Pareto improvement.

This Pareto improvement will continue till the demand equals supply.

PS I am sorry that I did not supplement my answer with mathematical rigour which I could have done to show that in equilibrium net demand = net supply. But I believe, the essence could be understood.

• It is certainly true that 'value of goods sold = value of goods bought'. Indeed, this is an accounting identity. However, this is true at any price, so fails to pin down a unique price that we might expect to prevail in a market. In other words, this accounting identity makes no predictions whatsoever about the market price (or quantity). So this is not the supply/demand model, which does make predictions about price and quantity. – user17900 Nov 26 '18 at 11:07
• As an aside, supply and demand are usually defined as quantities, not values. However, this is not the main problem with your answer. – user17900 Nov 26 '18 at 11:10
• The point which I wanted to make is as long as the markets are efficient, the price will reflect true equilibrium of demand and supply – DrStrangeLove Nov 27 '18 at 17:11
• Any fluctuations in demand and supply would change the relative scarcity and hence the parameter of price. I interpreted your question spatially regarding the market mechanism. I think your question centres more on the time horizon regarding expectations of future prices. – DrStrangeLove Nov 27 '18 at 17:15
• What I stated was more specifically "the walras law", rather than an accounting identity. – DrStrangeLove Feb 2 '19 at 15:03

This is actually a very important question in the field of macroeconomic theory. Basically as you stated most focus on the standard framework of competitive equilibrium at the undergrad level shows that at a given equilibrium price supply and demand will equal, with demand/supply being adjusted in order to eliminate excess demand/ excess supply that appears at non-equilibrium prices. Now first clarification that might have gotten you some downvotes is that taking prices as given does not relate to fixing a price, but rather to the assumption that "small" individuals cannot exert any influence on the price of a commodity (suggest you read up on the law of large numbers, which is a basic assumption of such models). Now, if you are really interested in understanding the pure theoretical perspective of the existence and uniqueness of a competitive equilibrium price I suggest you look further into fixed point theorems and the concept of the possibility of free-disposal equilibria. As far as the assumptions go in these models, the basic ones will relate to the convexity of preferences and free-disposal.

Here is a suggestion: http://math.uchicago.edu/~may/REU2014/REUPapers/Jung.pdf

Now at a less advanced level, consumers and firms take prices as given (because they are small relative to a large number of individuals). Now, a competitive equilibrium is reached when the demand of consumers (assuming a certain form of preferences and budget set), and the supply of firms (assuming a certain production function) are equal. There is no excess anything. Now, from this situation a price will be determined, which is known as the equilibrium price. Competitive equilibria simply require that the budget constraint for the economy is "respected" so to speak. In more advanced micro excess demand and excess supply under competitive equilibria is in fact allowed, so I suggest you read up on this (any exchange or production economy set-up a la Arrow-Debreu-Mckensie.

• Thanks for the answer. However, my question was not whether there exists a set of prices at which supply equals demand (i.e. whether a competitive equilibrium exists). Rather, the question was whether there is any reason to expect a competitive equilibrium to come about, assuming that one exists (e.g. since starting from an arbitrary price, there are reasons why the price will converge to the equilibrium price). So the reference you provide is not relevant. – user17900 Dec 11 '18 at 12:05
• Moreover, it is false that 'Competitive equilibria simply require that the budget constraint for the economy is "respected" so to speak'. In fact, the budget constraints of the agents can be satisfied at many prices, not just the equilibrium price. (You may wish to verify this with a simple example.) – user17900 Dec 11 '18 at 12:11
• You might also want to check out a proof of Walras Law, e.g. math.stackexchange.com/questions/139584/… As you will see, the law holds at ALL prices, not just the equilibrium price. So you cannot be right in claiming that budget constraints imply competitive equilibrium. – user17900 Dec 11 '18 at 12:13
• Actually, a competitive equilibrium is a pair price vector and an allocation such that this consumption bundle is consistent with consumer preferences at the given endowment level and such that the sum nominal consumptions is equal to the sum of nominal endowments (less or equal to in a competitive equilibrium with free disposal). Whether the price equilibrium vector is a unique solution or not does not mean that the competitive equilibrium holds for ALL prices. I suggest you read on any standard intermediate microeconomics book (e.g. Mas-Colell). – user20105 Dec 12 '18 at 12:02
• Next to this your question on whether a competitive equilibrium comes about is not relevant as you appear to infer that the contrary might hold, that is that the competitive equilibrium may not come about (can you find a set-up for any economy for which this may arise?) – user20105 Dec 12 '18 at 12:02

I have just discovered an essay by Dixon in which he claims that supply equals demand is not an equilibrium! He writes:

Firms will want to raise price at the competitive equilibrium (see Dixon, 1987, theorem 1). The reason is simple. At the competitive price, firms are on their supply function: price equals marginal cost. This can only be optimal for the firm if the demand curve it faces is actually horizontal. But if the firm raises its price (a little), it will not lose all its customers since, although consumers would like to buy from firms still setting the competitive price, those firms will not be willing to expand output to meet demand (their competitive output maximizes profits at the competitive price). Those customers turned away will be available to buy at a higher price. Thus if a firm raises its price above the competitive price, it will not lose all its customers but only some of them . . .

Apparently, then, the premise of the question was wrong: we should not expect supply to equal demand (except perhaps with constant marginal costs, as Dixon discusses).

• That sounds quite similar to what Steve Keen writes and publishes in this regards, for example in this video. – gwr Aug 16 '18 at 11:26

In the classical assumption of perfect competition you should make a distinction b/w Supply and Demand curves, and the Quantity Supplied and the Quantity Demanded at any one point on those curves. I'd argue that this statement

buyers could therefore pay a lower price to these sellers while still buying all the units that they want to purchase

is not true in the perfect competition framework. Buyers will demand a different quantity at every price point. The theory is that the intersection of S and D curves represents the equilibrium that will eventually happen. The market would only bear one price at a time. If some sellers are willing to lower their price, but not all then new sellers will enter the market if necessary to meet the Quantity Demanded (perfect competition assumes no barriers to entry).

You can easily change the informal explanation to a "quantity-based" approach, using a dynamic approach. Assume that firms in the market produce this period $S_1$ but the consumers that show up buy only $D_1<S_1$. What would you do if you were a producer, for period $2$, given the information you have about where demand stands?

Assume the good is perishable. Then the unsold quantity from period $1$ is destroyed. In period $2$ are you going to produce the same amount, or something less? I would say less, to reduce somehow the quantity that will go to waste and your loss from that fact.

Assume the good is not perishable, so you have inventories left over from the first period. Now, the tendency is to produce even less than when the good is perishable, because you can sell during period $2$ the inventories from period $1$.

So we see, that starting from a quantity supplied above quantity demanded, it is reasonable to expect lower quantity supplied next period. One can easily make the analogous argument starting with quantity demanded higher than quantity supplied. This is a gradual adjustment towards "market equilibrium", where quantity supplied will equal quantity demanded, or approximately so.

...and I didn't mention prices anywhere. You can think that this is a local market where the producers are forced to sell at a specific price, "imposed" on them by other similar markets and the expectations of consumers. In other words, what I described above can roll out while the price remains fixed from period to period.

The above was just an informal description. The benchmark approach to the dynamic adjustment towards market equilibrium is the Cobweb Theorem, see Ezekiel 1938.

• Thanks for the answer. However, I would think that this story cannot be right since, if it works, it works for any price (not just the 'equilibrium' price). – user17900 Aug 10 '18 at 13:18
• Can you think of a story why, starting from any price, we will converge to the equilibrium price (where supply equals demand)? – user17900 Aug 13 '18 at 13:53
• @Afreelunch: Alecos mentioned prices not coming into it. if you want prices coming into it, ( as your comment suggests ) then just takes Alecos's argument and then the price that ends up being reached in that environment is the equilbrium price. In essence, the price stops moving when the supplier figures out what amount he should supply. So, equilibrium of price and equilibrium of supply are tied together ( same for demand ). – mark leeds Aug 14 '18 at 17:32
• @mark leeds. I'm afraid I don't understand your suggestion. We want to show that, over time, the price will end up such that the quantity supplied equals quantity demanded. Alecos has argued that, independently of the price, supply will tend to equal demand. However, this fails to pin down a unique price. It is also false: at many prices, supply does not equal demand. – user17900 Aug 15 '18 at 16:58
• @afreelunch: I'm no expert at this ( last formal economics course was 30 years ago ) but I think the idea is the price will go to a value such that supply does equal demand. Hopefully Alecos can clarify or add to his nice example. – mark leeds Aug 15 '18 at 22:32