4.1 Market Demand and Supply in Equilibrium

A perfectly The famous experiment by Vernon Smith, one of the founders of experimental economics (Nobel Prize in Economics 2002), made Adam Smith’s invisible hand “visible”: even with few participants and limited information, markets tend to converge rapidly toward the competitive equilibrium predicted by theory. competitive market is composed of a large number of buyers and sellers, each acting as a price taker, that is, accepting the market price as given and unable to influence it individually. Every economic agent pursues only their own interest: consumers seek to maximize their utility, while firms aim to maximize their profit. Yet, from the interaction of these individual choices emerges a collective outcome that no one has centrally planned: the market price is determined as if an “invisible hand” were coordinating consumers and firms, bringing the economy to a point where the total quantity demanded and the total quantity supplied coincide. In equilibrium, what is the result of the pursuit of personal interest also ends up promoting the general interest: the traded quantity is exactly the one that maximizes collective welfare.

Market Demand

The market demand curve represents the relationship between the price of a good and the quantity that consumers are collectively willing to purchase. It is obtained by aggregating individual demand curves horizontally, that is, by summing the quantities demanded by individual consumers at each price level.

The figure below illustrates an example. To simplify the analysis, we assume that consumers are identical and therefore have the same individual demand function. Moreover, we assume that this function is linear — a simplification we will often adopt in the remainder of these notes to facilitate graphical and analytical reasoning.

As shown in the figure, the market demand curve shifts to the right or to the left as the number of consumers in the market increases or decreases. Since it results from the horizontal summation of individual demand curves, the market demand curve also shifts in response to changes in the factors that affect individual demand. In particular, it is easy to see (although we do not show it in the figure) that:

• When all consumers regard the good as normal (an assumption always valid given the type of preferences discussed in Chapter 2), a change in income shifts the market demand curve to the right if income increases, or to the left if income decreases.

• Similarly, a change in the price of a substitute good causes the market demand curve to shift to the right if the price of the substitute rises, or to the left if it falls.

Short-Run Supply and Equilibrium

In the short run, a situation in which the number of firms in the market is fixed, the short-run market supply curve represents the relationship between the price of the good and the quantity that the firms present in the market are collectively willing to sell. It is obtained in a way analogous to market demand, that is, by horizontally summing the individual short-run supply curves. The example in the figure below uses data from Figure 3.19.

The short-run market supply curve shifts to the right or left respectively as the number of firms in the market increases or decreases. It is appropriate here to make considerations similar to those previously made regarding market demand. Being the result of the horizontal summation of individual supply curves, the market supply also shifts in response to changes in factors that affect individual supply. In particular, it is easy to see (and we will show in Figure 4.3 below) that:

• A reduction in firms’ marginal cost (due to an increase in the productivity parameter $A$, or a decrease in the price of labor, $W$) causes a rightward shift of the short-run market supply curve. Conversely, an increase in marginal cost causes a leftward shift.

• The short-run market supply curve does not depend on firms’ fixed costs. This is obvious given that the firms’ optimal short-run choice does not depend on those costs.

In a short-run equilibrium, the market price is such that the quantity demanded by consumers equals the quantity supplied by the firms operating in the market. The right-hand graph in the figure below illustrates the equilibrium and shows how it depends on As in Figure 4.1, we are holding constant consumers’ income and the price of substitute goods. (some of the) factors that determine demand and supply. The left-hand graph, instead, shows the individual firm’s supply function, highlighting the presence of profits or losses.

How do the factors that determine demand and supply influence market equilibrium? The figure allows us to observe the following:

• An increase in the number of consumers causes a rightward shift of the market demand curve and thus a movement of the equilibrium point toward northeast along the supply curve. Both the equilibrium price and quantity increase. The same effect occurs (not shown in the figure) if consumer income increases or the price of a substitute good rises.

• An increase in firms’ productivity ($A$) causes a rightward shift of the market supply curve and thus a movement of the equilibrium point to the southeast along the demand curve. The equilibrium price falls, while the equilibrium quantity increases. The same happens in response to a decrease in the wage rate ($W$) or with a larger number of firms.

• In equilibrium, each firm maximizes its profit by taking the market price as given. The maximum profit can be positive, but it can also be negative. In particular, firms incur losses when there is a large number of firms, when their fixed costs are high, or when demand is low (e.g., due to a low number of consumers).

Long-Run Supply and Equilibrium

As we saw in Section 3.3, in the long run, firms operating in a market may choose to shut down and exit. One of the key assumptions underlying perfect competition is that, likewise, new firms that are initially inactive can choose to enter the market. There is therefore a potenatially infinite number of sellers.

To compute the long-run market supply curve we proceed just like in the short run, that is, summing horizontally the individual long-run supply curves. However, unlike the short run, the long run presents a potentially infinite number of firms, so we need to sum an infinite number of curves. The construction is illustrated in the next figure.

When incumbent firms earn positive economic profits, new firms have an incentive to enter. The entry of new firms increases overall supply: the market moves to a new short-run equilibrium in which the price is lower and the quantity higher. Conversely, when profits are negative, some firms will choose to exit the market, reducing total supply and causing the equilibrium price to rise.

The process of entry and exit continues until profits become zero — that is, when the market price equals the minimum average cost. At this point, the short-run equilibrium is also a long-run equilibrium: no new firm has an incentive to enter, being indifferent between entering or staying out; and no incumbent firm has an incentive to exit, as it is covering exactly its costs. The long-run equilibrium is found at the intersection between the demand curve and the long-run supply curve, as illustrated in the right diagram of the figure below.

The figure allows us to draw some important conclusions:

• In the long run, the price in a competitive market is determined solely by the industry's cost structure, which in turn depends on productivity ($A$), the wage rate ($W$), and the cost of production units ($FC$). Specifically, in the long run, the price tends to equal the minimum average cost. As shown in Chapter 3, this cost is given by $AC_{\text{min}} = (2/A)\sqrt{FC}\sqrt{W}$.

• Production takes place at the lowest possible unit (average) cost: all firms produce at their efficient scale of production, $Q^{\text{eff}}$.

• As one would expect (and as is clear from the formula for minimum average cost), the long-run equilibrium price increases if fixed costs or wages rise, or if productivity falls (i.e., a decrease in $A$).

• The quantity exchanged in the long run depends, in addition to the minimum average cost, on the market demand for the good. All else being equal, this quantity increases with a higher number of consumers, greater income, or a higher price of a substitute good.

We conclude this section with a purely technical curiosity. In long-run equilibrium, each firm produces at the efficient output level, $Q^{\text{eff}}$. However, it may happen that the equilibrium quantity is not an exact multiple of $Q^{\text{eff}}$. For example, from Figure 4.5, we can observe that if there are 1000 consumers and the parameters are $A = 70$, $W = 64$, and $FC = 100$, then $Q^{\text{eff}}$ equals $87.5$, while the equilibrium quantity is (approximating to the nearest hundredth of an output unit) $2714.29$, which we obtain by equating demand and long-run supply: \(5-Q/1000 = 2.2857... \; (=AC_{\text{min}})\) So, does this mean that in the long run there will be a fractional number of firms — that is, $2714.29 / 87.5 = 31.02$ firms? We can think of many reasons why the answer is: obviously not! One reason, for instance, could be the presence of a small fixed entry cost in the market. The thirty-first firm found it profitable to pay that cost, attracted by the profit it would earn once operating. The thirty-second did not, because with 31 firms already in the market, profits are already extremely low (since with “31.02 firms”, profits would be zero). In this case, it seems appropriate to take the long-run number of firms in the market to be 31.