In the previous section, we talked about price adjustments and pressure on the price to move in one direction or the other. But what does this actually mean?
A competitive market approaches its market-clearing price as the result of price adjustments. For example, a shortage persists in a market when the price is too low, attracting more units demanded than supplied. Too few sellers for too many buyers. When we say the shortage puts upward pressure on the price in the market, this means that in a sense, a price increase would “solve the problem” of the shortage. Additional quantity supplied would be drawn into the market, as a result of the Law of Supply, which states that as price increases, \(Q_S\) increases as well. At the same time, consumers will be deterred from wanting to buy at the higher price, according to the Law of Demand.
The price increase diminishes the shortage by reducing the gap between \(Q_D\) and \(Q_S\text{.}\) Moreover, the number of units exchanged at the market outcome increases. Therefore, the price increase moves the market closer to equilibrium by increasing both the price and quantity of the market outcome.
Consider the numerical example above, which experiences a shortage at \(P = 5\text{.}\) Quantity demanded is 200, while quantity supplied is 150, leaving a shortage of 50 units. If the price were to increase to, say, 5.50, \(Q_D\) decreases to 190, while \(Q_S\) increases to 165. Notice first that due to the Laws of Supply and Demand, quantity supplied increases while quantity demanded decreases. This shrinks the shortage: now, \(Q_D - Q_S = 25\text{.}\) As predicted, the price increase shrinks the shortage from both ends. The market outcome moves from \((P, Q) = (5, 150)\) to \((P, Q) = (5.50, 165)\text{,}\) and approaches equilibrium which we found earlier as \((P^*, Q^*) = (6, 180)\text{.}\)
Figure5.6.1.The market experiences a shortage at \(P = 5\text{.}\) Upward pressure on the price diminishes the size of the shortage. When the price increases from 5 to 5.50. the market outcome slides along the supply curve, from \((5, 150)\) to \((5.50, 165)\text{.}\) This moves the market outcome closer to equilibrium.
It is possible for the price increase to go too far. If, in response to the shortage at \(P = 5\text{,}\) the price adjusted upward up to $7, this would indeed eliminate the shortage by increasing \(Q_S\) and reducing \(Q_D\text{,}\) but now at \(P = 7\) there is a surplus of 50 units! The surplus would then put downward pressure on the price, since a price reduction would reduce the surplus by encouraging a higher quantity demanded and a lower quantity supplied.
In general, the presence of a shortage or surplus gives the market information about where the equilibrium is. A shortage indicates the current price is too low, and the upward pressure moves the market toward equilibrium; a surplus indicates the current price is too high, generating downward pressure in the direction of equilibrium.
This is particularly important in perfectly competitive markets without regulation. With so many buyers and sellers in the market, and no government to pre-determine what the price should be, how does the market “know” where the market-clearing price is? The information generated by out-of-equilibrium behavior - price adjustments when the market is not in equilibrium - will lead the way. This means equilibrium in perfectly competitive markets is a very unique situation, the result of a continuous series of responses to out-of-equilibrium behavior.
Figure5.6.2.Price adjustment convergence over time. While adjustments may undershoot or overshoot, many adjustments will move the price closer and closer to the market-clearing price.
In practice, the many actors in the market slowly gather information about where equilibrium is. Suppose the market experiences a surplus at a price of $7. We know this puts downward pressure on the price. First, how can the price actually move downward? Given the excess supply (\(Q_S > Q_D\)), sellers with additional units leftover may experiment by lowering the price they charge to $6.99 per unit. Or, buyers who observe merchandise not moving off the shelves may suggest paying only $6.99 per unit. In all likelihood, some combination of both occurs, across the many buyers and sellers in the market, to realize the downward price adjustment. 1
If the price adjustment doesn’t go far enough, there will be continued pressure to move in the same direction until equilibrium is reached. If the price adjustment moves too far, the tide will change, and the pressure reverses. Regardless of the actual price, out-of-equilibrium moves in the direction of equilibrium.
An outcome is said to be dynamically stable if behavior outside of this outcome converges to the outcome over time. 2 We have shown that perfectly competitive equilibrium is dynamically stable, because out-of-equilibrium behavior, if left unchecked, will move toward the equilibrium. 3
The dynamic stability of equilibrium is an important property for many reasons. First and foremost, it means the market will adjust in the direction equilibrium without government intervention. With so many buyers and sellers in the market, one could hypothesize that it will be impossible for those actors to coordinate to reach an equilibrium price and quantity that no one knows! But through dynamic stability, we can be sure that even if the market is not in equilibrium at a given moment in time, it will continue to approach and eventually converge to equilibrium. 4
Dynamic stability also frames equilibrium as a kind of attractor: a point that magnetically attracts behavior. If the market is in equilibrium as some moment in time, it will not have any reason to change. The market outcome will be stable at equilibrium. If, however, the market moves slightly away from equilibrium, dynamic stability will pull the market back in the direction of equilibrium.
This stability is actually critical information for predicting market behavior. What if equilibrium was not dynamically stable? If a market that moved out of equilibrium suddenly went haywire, bouncing to who-knows-where, then equilibrium itself would be much less powerful as a prediction of market behavior, because it would not be robust to slight perturbations or imperfections. If, however, dynamic stability is satisfied, then even if the market strays from equilibrium, behavior will ultimately move back in the direction of equilibrium, and the prediction of equilibrium would remain strong.
Finally, dynamic stability ensures that if some parameter of the model changes, the market will still converge to its equilibrium - even if that equilibrium changes. Consider our numerical example above: demand given by \(Q_D = 300 - 20P\text{,}\) supply by \(Q_S = 30P\text{,}\) and equilibrium at \((P^*, Q^*) = (6, 180)\text{.}\) What if a model parameter changes? Suppose the good is normal, and consumer income increases, leading to higher demand: \(Q'_D = 325 - 20P\text{.}\) How does the model respond?
We can calculate the new equilibrium directly. The new market-clearing price occurs where
\begin{equation*}
Q'_D = Q_S
\end{equation*}
\begin{equation*}
325 - 20P = 30P
\end{equation*}
\begin{equation*}
325 = 50P
\end{equation*}
\begin{equation*}
P^{**} = 6.50
\end{equation*}
At this price, the equilibrium quantity is 195. Therefore, the new market outcome is the new equilibrium \((P^{**}, Q^{**}) = (6.50, 195)\text{.}\) But how does the market respond in real time to the increase in income?
Figure5.6.3.Left: The increase in demand moves equilibrium in the market from \((P^*, Q^*) = (6, 180)\) to \((P^{**}, Q^{**}) = (6.50, 195)\text{.}\) Right: After the shift, the original \(P^* = 6\) does not clear the market, since there is a shortage. By dynamic stability, the resulting upward pressure on the price will lead to an adjustment which ultimately converges to the new equilibrium.
Initially, the market clears at a price of 6, since quantity demanded and quantity supplied are both 180. But when income increases, at a price of 6, \(Q_S\) remains at 180 while \(Q_D\) increases to 205! So now, at the initial equilibrium price, the market no longer clears: there is a shortage of 25 units! Under dynamic stability, the shortage generates upward pressure on the price, and push the price in the market up toward the new equilibrium price of 6.50. Therefore, in response to the income increase, the market doesn’t immediately “jump” to a new equilibrium; rather, the shortage which arises at the initial price generates upward pressure and the price will adjust upward toward the new equilibrium.
Dynamic stability strengthens the concept of competitive equilibrium as a prediction of outcomes in perfectly competitive markets by framing equilibrium as the attractor at the end of a convergence process that does not require any government intervention or prior foresight into what the equilibrium actually is. It ensures equilibrium is robust to any market perturbations, including shifts in supply or demand.
Key terms in this section:
price adjustment
out-of-equilibrium behavior
dynamic stability
In Depth5.6.4.Do we ever reach equilibrium?
In a market with many buyers and many sellers, how can we ever arise at this magical point where quantity supplied equals quantity demanded? How do all of those buyers and sellers know where to go? As we have discussed, the presence of a shortage or a surplus in a competitive market can put upward or downward pressure (respectively) on the price in the market. Surely, if the price were to adjust in the direction of equilibrium, the price would eventually reach equilibrium and the market would clear, no?
Ultimately, it’s unlikely that in practice, we observe real-world markets sitting peacefully at their equilibrium. There are two reasons for this. First, this adjustment to equilibrium could potentially take a long time, with many small adjustments stretching over weeks or months! Moreover, equilibrium is likely a moving target. Supply parameters like wages and technology, as well as demand parameters like consumer preferences and income, are constantly changing in the real world. We know that even small changes in these parameters cause the supply and demand curves to shift, which means equilibrium is changing as well. Even if the price adjustment process over time will move the market in the direction of equilibrium, it may need to change course if the target price is constantly changing!
Even though real-world markets may never reach equilibrium exactly, the existence of equilibrium still matters a great deal! Knowledge about equilibrium can tell us where the market will adjust toward, like knowing the location of the finish line of a marathon. As you watch the runners, you may not know how fast they’ll reach the end of the race, if at all, but you can be sure of the direction they are heading. Equilibrium can also help us better understand the impact of those fluctuations in supply and demand parameters which move equilibrium price around. Price adjustments respond to these changes, so on its journey to equilibrium, the twists and turns in the adjustment process can be seen more clearly with equilibrium as that moving target.
