Why does supply equal demand?

Question

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).

Answer 1

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.

EDIT Adjustment process for (2).
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.

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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).

Answer 6

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).