Unit 8 Economic dynamics: Financial and environmental crises

8.5 Modelling a house price bubble and collapse

Before you start

In this section and the next, we put the microeconomic supply and demand framework together with the concepts of positive feedback and tipping points to build a model of the dynamics of the housing market. If you are not familiar with supply and demand diagrams, you should first read Sections 8.2 and 8.3 of the microeconomics volume.

Positive and negative feedback processes in the housing market

If the housing market is in equilibrium, the price of housing remains at the same level from period to period—the price at which supply and demand are equal. What happens when the price is not at the equilibrium level depends on whether buyers and sellers are concerned not only about the current price, but also about future prices—that is, about how the value of their asset might change in future.

When decisions depend only on the current price

If buyers and sellers were concerned only with current prices (as in the case of food prices, because food is not an asset), we would expect a negative feedback process to restore equilibrium. The housing market equilibrium, like the equilibrium in the bread market, would be stable.

Figure 8.9 explains the dynamic process of price adjustment in this case. The left-hand panel shows the supply and demand curves for housing. The market is in equilibrium at point E, where supply and demand are equalized at price $P^*$. We can illustrate what happens when prices are changing using the diagram on the right, with the price in period t, $P_{t}$, on the horizontal axis and the price in the next period, $P_{t+1}$, on the vertical axis. We have marked the point where $P_{t}= P^*$: at this price, the market is in equilibrium so the price remains the same next period: $P_{t+1} = P^*$. Therefore, the equilibrium corresponds to a point on the 45-degree line.

What happens if the market is not in equilibrium? Suppose the price in period t is $P_a$, above $P^*$. Work through Figure 8.9 to analyse what happens, and how to derive the price dynamics curve.

$There are two diagrams. In the first diagram, the horizontal axis shows quantity, denoted as Q, and the vertical axis shows price, denoted as P. The coordinates are (quantity, price). The downward-sloping line is labeled as demand, and the upward-sloping line is labeled as supply. Their intersection is labeled as E, with a horizontal coordinate of Q^. The second diagram illustrates the adjustment process. The horizontal axis displays the price in period t, denoted as P_t, and the vertical axis shows the price in period t+1, denoted as P_{t+1}. The coordinates are (price in period t, price in period t+1). There is a 45-degree upward-sloping straight line from the origin, labeled ‘price unchanged from year to year’. The point E from the first diagram is mirrored on this line, with a horizontal coordinate of P^.$

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Figure 8.9 Deriving a price dynamics curve.

$At the market equilibrium: There are two diagrams. In the first diagram, the horizontal axis shows quantity, denoted as Q, and the vertical axis shows price, denoted as P. The coordinates are (quantity, price). The downward-sloping line is labeled as demand, and the upward-sloping line is labeled as supply. Their intersection is labeled as E, with a horizontal coordinate of Q^. The second diagram illustrates the adjustment process. The horizontal axis displays the price in period t, denoted as P_t, and the vertical axis shows the price in period t+1, denoted as P_{t+1}. The coordinates are (price in period t, price in period t+1). There is a 45-degree upward-sloping straight line from the origin, labeled ‘price unchanged from year to year’. The point E from the first diagram is mirrored on this line, with a horizontal coordinate of P^.$

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At the market equilibrium

Supply is equal to demand when the housing price is $P^*$. If $P_{t} = P^*$, then $P_{t+1}= P^*$, too. In the right-hand diagram, this is a point on the price dynamics curve. It is on the 45-degree line.

$Suppose the price in period t is Pa: There are two diagrams. In the first diagram, the horizontal axis shows quantity, denoted as Q, and the vertical axis shows price, denoted as P. The coordinates are (quantity, price). The downward-sloping line is labeled as demand, and the upward-sloping line is labeled as supply. Their intersection is labeled as E, with a horizontal coordinate of Q^* and a vertical coordinate of P^. When the price is at P_a, a price higher than P^, the gap between the demand and supply that appears is denoted as excess supply. The quantity demanded is Q_a, positioned to the left of Q^. When the price is at P_b, which is lower than P_a but higher than P^, the gap between demand and supply decreases. The second diagram illustrates the adjustment process. The horizontal axis displays the price in period t, denoted as P_t, and the vertical axis shows the price in period t+1, denoted as P_{t+1}. The coordinates are (price in period t, price in period t+1). There is a 45-degree upward-sloping straight line from the origin, labeled ‘price unchanged from year to year’. The point E from the first diagram is mirrored on this line, with a horizontal coordinate of P^. An additional dot appears, where the price P_a is mirrored as the horizontal coordinate (price in period t), and the price P_b is mirrored as the vertical coordinate (price in period t+1). The new dot is positioned to the upper right of the original point, E.$

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Suppose the price in period t is P_a

At the high price $P_a$, supply exceeds demand. There is excess supply, so some sellers realise that they will not be able to sell all they would like at the going price, and they cut the price they are asking. So the price begins to fall.
Tracing $P_a$ across to the right-hand diagram we can use the 45-degree line to find $P_{t} = P_{a}$ on the horizontal axis. Suppose the price falls to $P_{t+1} = P_{b}$ in the next period. The point ($P_a$, $P_b$), below the 45-degree line, is a point on the price dynamics curve.

$The price falls again to Pc: There are two diagrams. In the first diagram, the horizontal axis shows quantity, denoted as Q, and the vertical axis shows price, denoted as P. The coordinates are (quantity, price). The downward-sloping line is labeled as demand, and the upward-sloping line is labeled as supply. Their intersection is labeled as E, with a horizontal coordinate of Q^* and a vertical coordinate of P^. When the price is at P_a, a price higher than P^, the gap between the demand and supply that appears is denoted as excess supply. The quantity demanded is Q_a, positioned to the left of Q^. When the price is at P_b, which is lower than P_a but higher than P^, the gap between demand and supply decreases. Similarly, when the price is at P_c and P_d, which are lower than P_b but higher than P^*, the gap between demand and supply decreases. The second diagram illustrates the adjustment process. The horizontal axis displays the price in period t, denoted as P_t, and the vertical axis shows the price in period t+1, denoted as P_{t+1}. The coordinates are (price in period t, price in period t+1). There is a 45-degree upward-sloping straight line from the origin, labeled ‘price unchanged from year to year’. The point E from the first diagram is mirrored on this line, with a horizontal coordinate of P^. An additional dot appears, where the price P_a is mirrored as the horizontal coordinate (price in period t), and the price P_b is mirrored as the vertical coordinate (price in period t+1). The new dot is positioned to the upper right of the original point, E. Two more dots are depicted, whose coordinates are (P_b, P_c) and (P_c, P_d).$

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The price falls again to P_c

The price $P_b$ is still above the equilibrium price. Again there is excess supply and sellers continue to cut their prices, competing for buyers, so the price falls again. If the new price is $P_c$, we can again find $P_b$ on the horizontal axis on the right, and plot the point ($P_b$, $P_c$) on the price dynamics curve. As the price falls further, we can plot more points until it reaches equilibrium at $P^*$.

$The PDC: There are two diagrams. In the first diagram, the horizontal axis shows quantity, denoted as Q, and the vertical axis shows price, denoted as P. The coordinates are (quantity, price). The downward-sloping line is labeled as demand, and the upward-sloping line is labeled as supply. Their intersection is labeled as E, with a horizontal coordinate of Q^* and a vertical coordinate of P^. When the price is at P_a, a price higher than P^, the gap between the demand and supply that appears is denoted as excess supply. The quantity demanded is Q_a, positioned to the left of Q^. When the price is at P_b, which is lower than P_a but higher than P^, the gap between demand and supply decreases. Similarly, when the price is at P_c and P_d, which are lower than P_b but higher than P^, the gap between demand and supply decreases. The second diagram illustrates the adjustment process. The horizontal axis displays the price in period t, denoted as P_t, and the vertical axis shows the price in period t+1, denoted as P_{t+1}. The coordinates are (price in period t, price in period t+1). There is a 45-degree upward-sloping straight line from the origin, labeled ‘price unchanged from year to year’. The point E from the first diagram is mirrored on this line, with a horizontal coordinate of P^. An additional dot appears, where the price P_a is mirrored as the horizontal coordinate (price in period t), and the price P_b is mirrored as the vertical coordinate (price in period t+1). The new dot is positioned to the upper right of the original point, E. Two more dots are depicted, whose coordinates are (P_b, P_c) and (P_c, P_d) respectively. An additional upward-sloping line labeled as PDC passes through the four points, with a slope flatter than the 45-degree line. Its intersection with the 45-degree line corresponds to the point E mirrored from the first diagram.$

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The PDC

Joining the points gives us the price dynamics curve (PDC). In this example, it turns out to be a straight line. The PDC is flatter than the 45-degree line.

price dynamics curve: The price dynamics curve is a graph of the relationship between the price of a good in period $t$ (on the horizontal axis) and the price in period $t + 1$ (on the vertical axis). A point where the graph crosses the 45-degree line represents a market equilibrium: at this price demand = supply so the price stays constant from one period to the next. At other prices excess demand or excess supply leads to a change in price.

The price dynamics curve is flatter than the 45-degree line, and the intersection of the two is an equilibrium price (being on the 45-degree line means that the price will be the same in the two periods, that is, unchanging, as is required in an equilibrium). When prices are above the equilibrium level (in the left panel of the figure), the PDC (in the right panel) lies below the 45-degree line. If you start at a price below $P^*$ and repeat the derivation you will find that (as shown in the figure) the PDC is above the 45-degree line while the price rises up to the equilibrium level.

The price dynamics curve in Figure 8.9—flatter than the 45-degree line—corresponds to the case of a stable equilibrium. If due to a shock the price moves away from its equilibrium level, a process of negative feedback along the PDC restores equilibrium in the market.

We have illustrated this process by a shock that raised the price above the equilibrium price, so the negative feedback lowered the price. But this is not why we call the feedback negative. The feedback is ‘negative’ because the actions of buyers and sellers work against (‘negate’) the initial shock. If the shock resulted in a price lower than $P^*$, this would result in the price increasing back to the equilibrium level.

When beliefs about future prices matter

Since housing—unlike bread—is an asset, it is more realistic to assume that supply and demand for houses depends not only on the current price, but also on what people believe will happen to prices in future. Think about what might then happen if people observe that houses are selling for higher prices than usual. News spreads that the market seems to be heating up.

Depending on beliefs, equilibrium may be restored through a negative feedback process. But it is possible that a positive feedback process arises that is strong enough to result in instability—a house price bubble. Figure 8.10 illustrates these two alternative scenarios for the house price, $P$.

The price shock leads some people to believe that future prices will be higher, so houses are becoming a more valuable asset and the demand curve for houses goes up. But if people believe that the price rise is just a blip, then as shown in the left-hand panel, the negative feedback process described above in Figure 8.10 will restore the equilibrium.

There are two flowcharts. The first flowchart illustrates the negative feedback process where beliefs dampen price rises. The news that housing market is heating up causes price to rise, making some people to think price will continue to rise, thereby demand rises. But others believe price will fall again, eventually resulting in falling demand and stabilized price. The second flowchart illustrates the positive feedback process where beliefs amplify price rises. This scenario is also known as a bubble. The news that housing market is heating up causes price to rise, causing people to widely believe price will rise further, driving demand to rise. Such belief leads to price to rise, confirming expectations of further rises. As a result, demand goes up and price rises further. In turn, such price rises again confirms expectations of further price rises. Hence a cycle forms, which is often called as a bubble.

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Figure 8.10 Positive and negative feedback in the housing market.

The right panel illustrates a positive feedback process. A bubble can happen if the view that prices are likely to be higher in future spreads widely. Individuals interpret a price rise to mean that other people have received news that they hadn’t heard themselves, and adjust their own expectations upwards. Or they may think there is an opportunity for speculation: to buy the house now and sell to other buyers at a higher price later. Either way, the increase in demand is large enough to put further upward pressure on prices creating a positive feedback, with further increases in demand and price.

The price dynamics curve for housing assets

We can model the two alternative scenarios as we did before, using a diagram of demand and supply and deriving the price dynamics curve. The important difference is that the demand curve depends not only on the current price, which is on the vertical axis as usual, but also on expected future prices. If the expected future price increases, demand will be higher at each level of the current price. So the demand curve will shift outwards (to the right).

excess supply: A situation in which the quantity of a good supplied is greater than the quantity demanded at the current price. See also: excess demand.

A price shock raises the price of houses from the equilibrium price $P^*$ to $P_a$. In Figure 8.9, excess supply at $P_a$ led to a process of dynamic adjustment back to the equilibrium price. But now, some people believe that the price rise is the beginning of a period of rising prices, shifting out the demand curve.

Figure 8.11 shows what might happen next. The new demand curve is D_a. In this case, the increase in demand is relatively small—perhaps because the majority of people don’t expect prices to rise further—so there is still excess supply at price $P_a$. This means that prices will begin to fall, as before. The process of negative feedback operates similarly to the one in Figure 8.9, although with smaller price adjustments as the demand shift puts some upward pressure on prices, producing less excess supply. As prices fall and people realise that the rise in price was temporary, the demand curve will shift back to where it was before. Prices will stabilize again at $P^*$.

$There are two diagrams. In the first diagram, the horizontal axis shows quantity, denoted as Q, and the vertical axis shows price, denoted as P. The coordinates are (quantity, price). One downward-sloping line is labeled as demand, and the other parallel downward-sloping line is labelled as D_a, with D_a positioned above demand. The upward-sloping line is labeled as supply. Their intersection is labeled as E, with a horizontal coordinate of Q^* and a vertical coordinate of P^. When the price is at P_a, a price higher than P^, the gap between D_a and supply that appears is denoted as excess supply, smaller than the gap of demand and supply. The second diagram illustrates the adjustment process. The horizontal axis displays the price in period t, denoted as P_t, and the vertical axis shows the price in period t+1, denoted as P_{t+1}. The coordinates are (price in period t, price in period t+1). There is a 45-degree upward-sloping straight line from the origin, labeled ‘price unchanged from year to year’. The point E from the first diagram is mirrored on this line, with a horizontal coordinate of P^*. Another upward-sloping line labeled as PDC with a flatter slope intersects with the 45-degree line at point E mirrored from the first diagram.$

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Figure 8.11 The price shock is dampened: negative feedback and stable equilibrium.

The price dynamics curve is similar to the previous one. We have drawn a steeper curve, representing smaller price adjustments, but it is still flatter than the 45-degree line. The housing market equilibrium is stable.

Positive feedback and amplification of a house price shock

But if many people believe that the initial price rise signals further increases, the shift in the demand may be bigger, in turn causing further price rises. Figure 8.12 models this case of runaway price increases. (To show prices above $P_a$, we have used a different scale on the vertical axis.)

excess demand: A situation in which the quantity of a good demanded is greater than the quantity supplied at the current price. See also: excess supply.

When the price $P_a$ is observed, the demand curve shifts to D_a. There is now excess demand for houses. So the price begins to rise above $P_a$, reaching $P_b$ in the next period. This is the first point marked above $P^*$ on the PDC in the right-hand panel. The rise to $P_b$ reinforces beliefs that prices are rising and the demand curve shifts again to D_b. Again there is excess demand, leading to more price rises and demand shifts.

$There are two diagrams. In the first diagram, the horizontal axis shows quantity, denoted as Q, and the vertical axis shows price, denoted as P. The coordinates are (quantity, price). A downward-sloping line is labeled as demand, and three additional parallel downward-sloping lines are labeled as D_a, D_b, and D_c, with D_c positioned highest and demand positioned lowest. An upward-sloping line is labeled as supply, intersecting with demand at point E, with a horizontal coordinate of Q^* and a vertical coordinate of P^. D_c and the supply curve intersect at a point with a vertical coordinate of P_d. When the price is at P_c, the gap between D_c and supply is denoted as excess demand. The gaps between supply and D_b at price P_b, and supply and D_a at price P_a, are also highlighted. P_d is positioned highest and P_a lowest on the vertical axis. The second diagram illustrates the adjustment process. The horizontal axis displays the price in period t, denoted as P_t, and the vertical axis shows the price in period t+1, denoted as P_{t+1}. The coordinates are (price in period t, price in period t+1). A 45-degree upward-sloping straight line from the origin is labeled ‘price unchanged from year to year.’ The point E from the first diagram is mirrored on this line, with a horizontal coordinate of P^. Other intersections from the first diagram are also mirrored, lying on an upward-sloping line labeled as PDC, which has a slope steeper than the 45-degree line. This PDC line intersects the 45-degree line at the mirrored point E from the first diagram. These mirrored points have horizontal coordinates of P_a, P_b, and P_c, with P_a positioned closest to P^*, and P_c furthest.$

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Figure 8.12 The price shock is amplified: positive feedback and instability.

In Figure 8.12, price rises lead to further price rises—a process of positive feedback—magnifying the initial price shock rather than working against it and taking us further and further from equilibrium. Likewise, a decrease in price below $P^*$ would set in motion a set of positive feedbacks magnifying the initial price fall setting off a process of runaway falling prices (as Exercise 8.2 will discuss). Both of these cases correspond to a PDC that passes through $P^*$ and is steeper than the 45-degree line. The equilibrium at E is unstable.

Figure 8.12 describes the beginning of a bubble of runaway increases in house prices. In this scenario the positive feedback process will continue until something happens to change the expectation of continuously rising prices.

For a mathematical model of a bubble as shown in Figure 8.12, read this mathematical supplement.

Exercise 8.2 Modelling a bust in the housing market

Construct a diagram similar to Figure 8.12 and provide a step-by-step explanation of how a housing market bust can occur. As the starting point, assume a negative shock: a fall in price resulting from causes external to the model.

The dynamics of house prices: Boom-bust cycles

Figure 8.13 summarizes the price dynamics curves for stable and unstable equilibria. In an unstable equilibrium, the PDC is steeper than the 45-degree line; in a stable equilibrium, it is flatter than the 45-degree line.

$There are two diagrams. In the first diagram, labeled ‘Unstable equilibrium,’ the horizontal axis displays price in period t, denoted as P_t, and the vertical axis shows the price in period t+1, denoted as P_{t+1}. The coordinates are (price in period t, price in period t+1). A 45-degree upward-sloping straight line from the origin is labeled ‘price unchanged from year to year.’ An additional upward-sloping line with a steeper slope labeled as PDC intersects the 45-degree line at the point where both the horizontal and vertical coordinates are P_0. The points P_0, P_1, P_2, and P_3 are marked on the horizontal axis, and their corresponding points on the vertical axis illustrate the adjustment process. When the horizontal coordinates are P_1 and P_2, their corresponding vertical coordinates on the PDC line are P_2 and P_3, respectively. The process continues with P_3, with each step moving further away from the 45-degree line. In the second diagram, labeled ‘Stable equilibrium,’ the horizontal axis also displays the price in period t, denoted as P_t, and the vertical axis shows the price in period t+1, denoted as P_{t+1}. The coordinates are (price in period t, price in period t+1). Similarly, a 45-degree upward-sloping straight line from the origin is labeled ‘price unchanged from year to year.’ An additional upward-sloping line with a flatter slope labeled as PDC intersects the 45-degree line at the point where both the horizontal and vertical coordinates are P_0. Points P_0, P_1, P_2, and P_3 are marked on the horizontal axis, and their corresponding points on the vertical axis show the adjustment process. When the horizontal coordinates are P_1 and P_2, their corresponding vertical coordinates on the PDC line are P_2 and P_3, respectively. The process continues with P_3, with each step converging to the 45-degree line.$

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Figure 8.13 Unstable and stable equilibria in the housing market.

So far, we have drawn PDCs as straight lines for convenience, but there is no reason why they should not be curves (as we named them). And if so, they may cross the 45-degree line more than once, representing a situation in which there is more than one equilibrium in the housing market with different levels of prices that are unchanging from year to year.

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Figure 8.3

We can use PDCs to model what we observe, with periods of stability around more than one equilibrium house price, and other unstable periods of boom and bust. It appears that both stable and unstable equilibria coexist. In Figure 8.14, we model the housing market like the ‘hill’ in Section 8.2, with two stable equilibria, and an unstable equilibrium—the tipping point at the top of the hill—between them. This gives us an S-shaped PDC, as shown in Figure 8.14.

There is a stable equilibrium with a low price at point C. Here, the PDC is flatter than the 45-degree line, so the equilibrium is stable. A small price shock would result in dynamic adjustment with negative feedback working against the shock and moving the price along the curve back to point C. Point D is stable for the same reason.

Point T is also an equilibrium, but it is an unstable tipping point. This means that a small price shock would set off positive feedbacks leading either to prices falling towards C (if the shock was a fall in price), which is a stable equilibrium at a low price, or rising towards D (if the shock was a rise in price), which is a stable equilibrium at a high price.

Unlike the poverty trap, in this case—the housing market—we do not have a ‘good’ and a ‘bad’ equilibrium. Whether high or low house prices are preferable depends on whether you are owning a house and would like to sell, or without a house and would like to buy. The problem in the housing market is that prices can change dramatically—boom or bust—imposing substantial uncertainty on all households.

To understand why the equilibrium at T is unstable, at T the PDC is steeper than the 45-degree line, whose slope is equal to 1. This means that along the 45-degree line, a change in the price in time t is associated with the same magnitude of price change in period $t + 1 (\Delta P_\text{t} = \Delta P{_\text{t+1}})$. If the PDC has a slope greater than 1, this means that a change in the price in period t is associated with a price change in period t + 1 that is greater than the change in period t. In other words, the reaction to a price shock at point T (either up or down) does not dampen but instead magnifies the shock. An important insight from Figure 8.13, is that we would expect to observe the economy much more frequently close to a stable than an unstable equilibrium.

Follow the steps through Figure 8.14 to understand how, starting from the low-price equilibrium at C, a housing boom could occur.

$The diagram illustrates the dynamics of price adjustments over time. The horizontal axis displays the price in period t, denoted as P_t, and the vertical axis shows the price in period t+1, denoted as P_{t+1}. The coordinates are (price in period t, price in period t+1).A 45-degree upward-sloping straight line from the origin is labeled ‘price unchanged from year to year.’ An upward-sloping, S-shaped line labeled PDC intersects this 45-degree line at three points: C, T, and D. Point C, located at a lower price level, represents a stable equilibrium at a low price. Point T, located at a middle price level, represents an unstable equilibrium. Point D, located at a higher price level, represents a stable equilibrium at a high price. Arrows indicate the direction of price adjustments, pointing either from T to C or from T to D.$

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Figure 8.14 Price dynamics, multiple equilibria, and the S-shaped PDC.

$One unstable and two stable equilibria: The diagram illustrates the dynamics of price adjustments over time. The horizontal axis displays the price in period t, denoted as P_t, and the vertical axis shows the price in period t+1, denoted as P_{t+1}. The coordinates are (price in period t, price in period t+1). A 45-degree upward-sloping straight line from the origin is labeled ‘price unchanged from year to year.’ An upward-sloping, S-shaped line labeled PDC intersects this 45-degree line at three points: C, T, and D. Point C, located at a lower price level, represents a stable equilibrium at a low price. Point T, located at a middle price level, represents an unstable equilibrium. Point D, located at a higher price level, represents a stable equilibrium at a high price.$

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https://www.core-econ.org/macroeconomics/08-financial-environmental-crises-05-model-house-price-bubble.html#figure-8-14a

One unstable and two stable equilibria

An S-shaped PDC that crosses the 45-degree line three times gives us a model of the housing market with three equilibria—a stable equilibrium at a low and at a high price and an unstable equilibrium between the two.

$The unstable equilibrium is called a tipping point: The diagram illustrates the dynamics of price adjustments over time. The horizontal axis displays the price in period t, denoted as P_t, and the vertical axis shows the price in period t+1, denoted as P_{t+1}. The coordinates are (price in period t, price in period t+1). A 45-degree upward-sloping straight line from the origin is labeled ‘price unchanged from year to year.’ An upward-sloping, S-shaped line labeled PDC intersects this 45-degree line at three points: C, T, and D. Point C, located at a lower price level, represents a stable equilibrium at a low price. Point T, located at a middle price level, represents an unstable equilibrium. Point D, located at a higher price level, represents a stable equilibrium at a high price.$

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The unstable equilibrium is called a tipping point

Any price shock at the unstable equilibrium—no matter how small—produces price movements in the same direction as the shock (positive feedback). This is a tipping point.

$A price shock: The diagram illustrates the dynamics of price adjustments over time. The horizontal axis displays the price in period t, denoted as P_t, and the vertical axis shows the price in period t+1, denoted as P_{t+1}. The coordinates are (price in period t, price in period t+1). A 45-degree upward-sloping straight line from the origin is labeled ‘price unchanged from year to year.’ An upward-sloping, S-shaped line labeled PDC intersects this 45-degree line at three points: C, T, and D. Point C, located at a lower price level, represents a stable equilibrium at a low price. Point T, located at a middle price level, represents an unstable equilibrium, namely the tipping point. Point D, located at a higher price level, represents a stable equilibrium at a high price. Arrows are depicted, pointing from T to D.$

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A price shock

The starting point is the low-price stable equilibrium C. A price shock large enough to move the price beyond the tipping point takes the market onto the steep part of the PDC above the 45-degree line. A positive feedback process occurs, which produces ever-larger price rises.

$Positive feedbacks cumulate, continuing to magnify the shock: The diagram illustrates the dynamics of price adjustments over time. The horizontal axis displays the price in period t, denoted as P_t, and the vertical axis shows the price in period t+1, denoted as P_{t+1}. The coordinates are (price in period t, price in period t+1). A 45-degree upward-sloping straight line from the origin is labeled ‘price unchanged from year to year.’ An upward-sloping, S-shaped line labeled PDC intersects this 45-degree line at three points: C, T, and D. Point C, located at a lower price level, represents a stable equilibrium at a low price. Point T, located at a middle price level, represents an unstable equilibrium, namely the tipping point. Point D, located at a higher price level, represents a stable equilibrium at a high price. Arrows are depicted, pointing from T to D. Additional small arrows are depicted to highlight the convergence to high-price stable equilibrium from T towards D.$

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Positive feedbacks cumulate, continuing to magnify the shock

This process continues until the housing market converges to the stable equilibrium at a high price level.

Similarly, a large fall in the price of housing can produce a collapse from the high-price equilibrium to the low-price equilibrium.

Exercise 8.3 Differences between equilibrium and stability

Explain in your own words, giving examples, the difference between the terms ‘equilibrium’ and ‘stability’.

Question 8.4 Choose the correct answer(s)

Read the following statements and choose the correct option(s).

Positive feedback processes in response to a price shock can lead to prices falling.
At any given time, the economy is more likely to be at a stable than an unstable equilibrium.
For the case of housing, the low-price equilibrium is stable because it does not disappear if the price dynamics curve shifts.
A housing price boom occurs when people do not treat price changes as a source of information.

Positive feedback processes reinforce the initial shock (movement away from equilibrium), so if the initial shock causes prices to fall, then positive feedback processes will cause the price to continue to fall.
If the economy is at a stable equilibrium, any small movement away from this equilibrium will eventually result in prices returning to the same equilibrium, so the economy will remain at this equilibrium unless there is a large shock. However, if the economy is at an unstable equilibrium, any small movement away from this equilibrium will result in the economy moving further and further away, so it is more difficult to sustain an unstable equilibrium.
The low-price equilibrium is stable because any small movement away from this equilibrium will eventually result in prices returning to the same equilibrium. The stability of the equilibrium is unrelated to whether or not it still exists when the price dynamics curve shifts.
The opposite is true: a housing price boom occurs because people treat current changes in price as information telling them that prices will continue to rise.