## Market equilibrium

The competitive market for a good comprises a large number of buyers, which we will generically call consumers, and another large number of sellers, which we will call producers or firms. In a competitive market, both consumers and firms take the price as given.

Each individual, whether consumer or producer, makes his or her decisions independently, according to his or her own objectives, taking the current as the basis for his or her decision.

In a competitive market, there is only one price at which consumers can buy, and vendors can sell.

Will that market work properly?

The market demand curve of a good is a function that tells us the amount that the set of consumers demand (would like to buy) for each possible price.

$Q_{d} = Q_{d}(p)$

Similarly, the supply curve calculates the amount of the good that producers would like to sell (offer) based on the price.

$Q_{s} = Q_{s}(p)$

As can be seen in the example, the demand and supply curves are independent of each other. It can happen that given any price the quantity demanded and offered do not coincide. In that case, some agents cannot make their demand or supply decisions.

If the quantity of product that firms wish to sell is greater than the one demanded by consumers, we say that there is an Excess Supply ($Q_{s} \gt Q_{d}$). If the inequality is in the opposite direction, we say there is an Excess Demand ($Q_{s} < Q_{d}$).

Let's see it graphically (the figure corresponds to the data of the previous example). You can act as a regulator, and use the slider to choose the price that the agents will find in the market.

• When will there be an Excess Supply (ES)? Sol.
When the price is too high; consumers do not demand much, while sellers are interested in selling more.
• What about an Excess Demand (ED)? Sol.
A low price makes companies unwilling to offer much product, while consumers would like to buy a lot.
• Can you find a price at which there is neither too much nor too little product? How can you express it in graphic terms? Sol.
The price at which the quantity demanded matches the quantity offered is that corresponding to the point where the supply and demand curves intersect.

We call the equilibrium price to the price at which the market empties, that is, the quantity demanded is equal to the quantity offered, so there is neither Excess Demand nor Excess Supply. In the equilibrium, all actors (consumers and producers) can make their optimal decisions effective.

### Calculation of the equilibrium

Given the previous definition, to calculate the price corresponding to the equilibrium we pose and solve the equation resulting from equalizing supply and demand:

$Q_d(p) = Q_s(p) \quad \Longrightarrow \quad p^*$

Example

With the above data, $Q_d=100 - 2p$ and $Q_s=p-8$, the equation becomes: $Q_d(p) = Q_s(p) \quad \Longrightarrow \quad 100 - 2p = p - 8$ Solving the equation we have $p^*= \frac{108}{3}= 36$.
At the equilibrium price $p^*=36$, the amount exchanged (it doesn't matter if we use demand or supply to calculate it) will be $q^*=28$.

Who is in charge of calculating the equilibrium price so that the market can work properly?

One of the main appeals of the concept of competitive equilibrium is that no external intervention would be required to achieve it. What will happen in a market if the price is too high and there is Excess Supply? Intuitively we would expect sellers who have not been able to sell their product to be willing to offer it cheaper, to at least sell something. This would encourage consumers to buy more (and in the face of the fierce competition they would be reluctant to pay the initial price). Excess Supply will trigger a process of lowering the price.

In the case of an Excess Demand we would expect a similar effect in the opposite direction. The shortage of product would push the price up. In both cases the process would only stop when the equilibrium price was reached.

The mechanism that in case of imbalance would push the price towards the right level is generically known as

It should be clear that our definition of equilibrium is static. A price is either equilibrium or it is not. Market forces are a dynamic concept, which asks how variables move over time (if 'today' there is an Excess Demand, 'tomorrow' we will see a market response).
The basic model we are building does not contain dynamic elements. When we talk about market forces here, we do so only intuitively. In order to properly talk about equilibrium stability (or instability), it would be necessary to use dynamic models, mathematically more advanced, out of the reach of an intermediate level course.