# Equilibrium quantity

The equilibrium quantity of a good is that which corresponds to the point where the supply and demand curves intersect in a market, at a given price. Therefore, we can say that it is the amount that producers are willing to sell and consumers are willing to buy. All this at a price that allows the agreement of both parties. This, in turn, is the equilibrium price of a perfectly competitive market. In this theoretical situation there is no shortage or surplus in the market. But the reality is very different, as we will see below.

## How the equilibrium quantity is calculated

We start from a market in perfect competition. In it, there is a supply curve (O) and a demand curve (D). For simplicity, equations of lines are used. Both represent all producers and consumers. Therefore, they are the production and consumption preferences of a type of good. As seen in the image, they are supply and demand functions. At the end we will see a numerical example to clarify possible doubts.

In equilibrium, the producer and the consumer will agree on a certain price, the equilibrium or market price (Pe). At that point, the producer will want to offer a quantity and the consumer will be willing to buy it. This is the equilibrium quantity (Qe), as it appears on the graph. Analytically, it is calculated by equating the function of Qo and Qd to a price (P) that is equivalent to that market equilibrium price and clearing this out of the equation.

## Situations that may arise, surplus and shortage

Perfect markets do not exist and reality is always imperfect. Let’s see what would happen in four situations. In almost all of them there is an intervention of the State in prices. This can set a maximum or minimum price. The theoretical goal is to avoid possible speculation. An example is the coronavirus crisis in 2020 with the price of masks and gloves. There are governments that have intervened in these sectors.

• What happens when we have a market equilibrium price below the intervened price? The maximum price at which we can sell, for example, a pack of gloves, is six monetary units (um). The market price, on the other hand, is CU5 per box of gloves. We see that what would happen is that these would be sold at that market price (5) and nothing would happen.
• What happens if the market price is above the intervened price? Now the maximum price is five CU, but the market price is six. In this case there will be many producers who are not compensated to sell cheaper. Consumers would want more at a lower price. There would be a shortage in the market.
• What happens if the minimum price intervened is below the market price? In this case, as in the first, the producer and consumer would agree on that market price. Nothing would happen.
• Finally, what happens if the minimum price is above the market price? This situation allows the producer to sell above the equilibrium price, obtaining a premium. But the consumer does not demand the entire equilibrium quantity at that higher price. Therefore there will be a surplus.

## Let’s see an example

Let us imagine two functions of supply and demand. These are calculated through past data of the good to be analyzed. For the purposes of the example, let’s imagine two equations of simple lines. If we look closely, the first one on the left is the quantity supplied. We see that the sign that accompanies the price is positive, since the higher the price, the bidders will produce more quantity. This line is increasing. With demand, the opposite happens, the sign is negative and decreasing.

To calculate the equilibrium quantity, we first equal both and solve for the value of Pe or P. In this case it is two. Now we substitute this in either of the two functions, for example the offer. The Qe would be five. We prepare the graph as seen in the figure. First without the green line. Where O and D intersect is the equilibrium point.

Now let’s imagine that the maximum intervened price is one (green line). We see that this is below equilibrium. If we follow the straight line, we see that it cuts the supply by 5 units. However, the cut-off point with demand is 7. That is, consumers want seven but suppliers only manufacture five. Therefore there would be a shortage.

As we can see, the intervention can only be done once the market equilibrium price and quantity are known. Otherwise, it could cause a bigger problem.