# Backward bending supply curve

The following says that the point $$(q_b,p_b)$$ is an unstable equilibrium while $$(q_a, p_a)$$ is a stable equilibrium. May I know what that means and why that is the case?

Here's the original paper, for your reference.

Equilibrium is considered unstable when small disturbance might evoke further disturbance so that original equilibrium is lost.

Equilibrium is considered stable when small disturbances do not matter values always revert back to the original equilibrium.

To understand this consider an analogy with physical equilibrium. You can balance a ball on top of a hill (meaning the ball is in its equilibrium), but if you push it ever so slightly it will start rolling down to hill. Hence this would be unstable equilibrium, the ball is at an equilibrium if balanced but any small perturbation will disturb it.

Now suppose you put the same ball on the bottom of a valley (again ball is at equilibrium). Now even if you try to push the ball it will always just roll back to its original equilibrium at the bottom of the valley. This is stable equilibrium, you perturb the ball yet the ball goes back to its original equilibrium.

In your particular case $$(q_a, p_a)$$ is stable because left to the point there is incentive to supply more labor (people are paid more which attracts more people) at higher price (until the supply intersects demand) and reverse holds for point right to $$(q_a, p_a)$$.

However, when we consider point $$(q_b, p_b)$$ if you move to the left of the point, the price will get higher but people will supply less labor to the market (since richer workers might prefer to get more leisure time) so the quantity supplied to market goes to zero at some very high wage. If you move to the right of $$(q_b, p_b)$$ the market forces will drive $$q$$ and $$p$$ to the stable equilibrium $$(q_a, p_a)$$.

• Very very helpful. So this is indeed related to the notion of backward bending labour supply. Thank you.
– Isa
Commented Sep 7, 2022 at 21:46
• Can you please tell me one basic thing: If $(q,p)$ is a point on the supply curve, does $q$ denote the total supply possible at price $€ \ p$? That is, the price of each item is $€ \ p/q$ (instead of $€ \ p$).
– Isa
Commented Sep 7, 2022 at 21:51
• @Isa no it denotes per unit price, that is p per 1 q supplied
– 1muflon1
Commented Sep 7, 2022 at 22:08
• There is a subtle difference between stable and asymptotically stable. You give the latter's definition for stable. Commented Sep 7, 2022 at 23:33
• @Giskardas as far as I remember asymptotic stability requires that all initial values converge to some equilibrium. Here q_a and p_a is not asymptotically stable because values right of q_b and p_b do not converter but diverge
– 1muflon1
Commented Sep 8, 2022 at 7:32