Walrasian Equilibrium

Transclude of Existence-of-Equilibrium-2024-10-01-09.31.34.excalidraw

Excess demand function, $E(P)=D(P)-S(P)$

There are three possibilities

1. When $E(P)>0$, when price is less than equilibrium price i.e. $P_0<P_e$
2. When $E(P)<0$, when price is more than equilibrium price i.e. $P_0>P_e$
3. When $E(P)=0$, when price is equal to equilibrium price i.e. $P_0=P_e$

• Walrus assumes that if excess demand is positive, then there is a tendency on the part of the consumer to rise the price and if excess demand is negative, there is a tendency on the part of the seller to reduce the price.
• If Walrasian assumption is working in the market, then any reduction in the price, below $P_e$ will make the consumer to rise it till equilibrium is reached.
• If it further rises, then seller will pull it down till equilibrium is reached.
• Thus there will be a mechanism in the market itself to see that equilibrium is maintained.
• If Wa assumption is operating, excess demand is reduced either in the downward direction or in the upward direction.
• Thus $E(P)$ is a decreasing function of price. Thus $\frac{dE}{dP}<0$, which implies that slope of demand function is less than slope of supply function $D’(P)<S’(P)$.
• Thus, according to Walrus, there is a static stability if slope of demand function is less that slope of supply function. This condition is true for normal commodity¹

Footnotes

1. Any exceptional thing will be covered in Marshallian demand functions. ↩