Static Equilibrium

Existence of Equilibrium

Transclude of Existence-of-Equilibrium-2024-10-01-09.15.43.excalidraw

Let the demand function $D=D(P)$, supply function be $S=S(P)$;

• If they intersect in the first quadrant at one point, the equilibrium exists and it is unique. ($I$)
• If they intersect in any other quadrant then equilibrium doesn’t exist. ($II$, $III$, & $IV$)
• If more than one point intersect, then equilibrium exists , but its not unique.

Static Equilibrium¹

Suppose there is disturbance in the equilibrium either due to change in demand or change in supply. But the disturbance results in coming back to the original position, due to adjustment of market forces. Then the equilibrium is said to be stable, otherwise it is said to be unstable. This is called static stability.²

If the stability is achieved through several periods of times in the long run, then it is said to be in dynamic stability. In dynamic stability, $P_t$³ $\to P_e$⁴ as $t\to \infty$.

Footnotes

1. Equilibrium is the state of an object where it stays without motion in the absence of a disturbance ↩

2. Once we disturb the ball in a bowl, it will still achieve its equilibrium ↩

3. Price in time period $t$ ↩

4. Equilibrium price ↩