Useful Notes on Unstable Equilibrium in Economics (With Case Studies)

Equilibrium is said to be unstable, if an initial disturbance or displacement in equilibrium leads to movements away from the original equilibrium.

The equilibrium is not self-adjusting and is not restored to its initial equilibrium position. These are rare cases.

Case 1: Upward Sloping Demand Curve Upward and Downward Sloping Supply Curve

In Fig 11.9, the demand curve DD is upward sloping as in the case of Giffen goods. The supply curve DD is downward sloping may be due to distress selling. These two curves intersect each other at point ‘E’. The equilibrium price is OP and the equilibrium quantity is OQ. Suppose, due to the initial disturbance the price rises to OP₁.

At this price, the consumers are prepared to purchase OQ₁ quantity, while the sellers are willing to sell only OQ₂ quantity. Thus, trade is profitable because the maximum price that buyers are willing to pay is greater than the minimum price acceptable to sellers. In this situation of excess demand, the consumers will be willing to offer a higher price to meet their unfulfilled demand.

This will push up the price further, resulting in a movement further and further away from the equilibrium point ‘E’. On the other hand, when the price falls to OP₁, the consumers are willing to buy only OQ₃ quantity, while the sellers are prepared to sell OQ₄ quantity.

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This situation of excess supply will induce sellers to reduce the price in order to clear their stocks. Thus, the price will fall and there will be ‘movement’ further away from the equilibrium point. This depicts the case of Walrasian unstable equilibrium. If quantity were to rise to OQ₁, demand price would be higher than the supply price.

This would induce larger trade, and quantity would continue to rise. Likewise, if quantity were to fall to OQ₂, supply price would be higher than demand price, and quantity would continue to fall, as less trade would take place because the minimum price acceptable to sellers is greater than the maximum price that buyers are willing to pay. This is the case of Marshallian unstable equilibrium.

Fig. 11.9: Downward Sloping Demand and Supply Curves

Case 2: Downward Sloping Demand and Supply Curves

In Fig 11.10, demand curve DD has a normal negative slope, while supply curve SS has a an unusual negative slope. The equilibrium is established at point ‘E’, where the two curves intersect each other. The equilibrium price is OP and the equilibrium quantity is OQ.

In Fig 11.10, negative slope of supply curve is more than the negative slope of demand curve, i.e., the supply curve is relatively less elastic than the demand curve. Here, the supply curve cuts the demand curve from above. Suppose, the price rises to OP, due to some disturbance. This will lead to excess supply.

Given the negatively sloped supplied curve, sellers will tend to supply less until it falls to OP. Likewise, at any other price lower than OP₁ say OP₂, there will be excess demand and the buyers will be willing to pay a higher price. Ultimately the original equilibrium price is restored. Now, if the quantity rises to OQ₁ making demand price higher than the supply price.

This will tend to increase the trade and quantity will continue to rise. If quantity were to fall to OQ₂, supply price would be higher than the demand price, continuously reducing the trade and hence quantity. Thus, in Fig 11.10, we have Walrasian stable equilibrium and Marshallian unstable equilibrium.

Fig. 11.10: Less Elastic Supply Curve with Downward Sloping Demand and Supply Curves (Unstable Marshalian Equilibrium)

In Fig 11.11, supply curve is relatively more elastic, as negative slope of supply curve is less than that of demand curve. Here, the demand curve cuts the supply curve from above. If price rises to OP₁, there will be an excess demand. With the negatively sloped supply curve, the seller will sell less, when price increases. This will cause a further and further rise in price, resulting in a movement away from the equilibrium point ‘E’.

Fig. 11.11: More Elastic Supply Curve with Downward Sloping Demand and SupplyCurves (Unstable Walrasian Equilibrium)

If the price falls to OP₂, the sellers, given the negatively sloped demand curve, will like to sell more. This also results in movement away from the equilibrium. However, when quantity moves away from the equilibrium (to OQ₁ or OQ₂), the correcting forces come into operation and it returns to the equilibrium. Thus, in Fig 11.11, there is Walrasian unstable equilibrium and Marshallian stable equilibrium.

Case 3: Upward Sloping Demand and Supply Curves

In Fig 11.12, both demand curve DD and supply cause SS are upward sloping, which intersect each other at point ‘E’. The equilibrium price and equilibrium quantity are OP and OQ respectively. Positively sloped demand curve indicates the case of a Giffen commodity. In Fig 11.12, negative slope of supply curve is more than the negative slope of the demand curve, i.e., the supply curve is relatively less elastic than the demand curve.

Here, the upward sloping supply curve cuts the upward sloping demand curve from below. Suppose, the price drifts away from the equilibrium to OP₁. There will be excess demand which causes the price to rise further. This will mean a movement away from the equilibrium point.

On the other hand, if the initial disturbance causes the price to fall to OP₂, there will be excess supply. This will further reduce the price and the movement will be away from the equilibrium point ‘E’. Further, if quantity moves away from the equilibrium to OQ₁, supply price will be more than the demand price.

This will lead to a fall in trade till OQ quantity is attained. If quantity falls to OQ₂, then demand price will be more than the supply price leading to a rise in trade till OQ quantity is attained. Thus, in Fig 11.12, the equilibrium is Walsarian unstable and Marshallian stable.

Fig. 11.12: Less Elastic Supply Curve with upward Sloping Demand and Supply Curves (Unstable Walrasian Equilibrium)

In Fig 11.13, upward sloping demand curve cuts the upward sloping supply curve from below. Here, if price moves away from the equilibrium to OP, or OP₂, it will return to equilibrium on account of correcting forces. However, if quantity drifts away from the equilibrium, it will continue to move farther and farther. Thus, in Fig 11.13, equilibrium is Walsarian stable and Marshallian unstable.

Fig. 11.13: More Elastic Supply Curve with Upward Sloping Demand and Supply Curves (Unstable Marshallian Equilibrium