Market equilibrium and price determination

• Market equilibrium occurs when planned purchases (demand) equal planned sales (supply).
• Equilibrium is reached at the market-clearing price, where there is no tendency for price to change.
• In equation form: \(Q_d(P)=Q_s(P)\), where \(Q_d\) is quantity demanded and \(Q_s\) is quantity supplied.

Key definitions

• Excess demand (shortage): demand > supply at a given price. Measured as \(\text{shortage} = Q_d(P) - Q_s(P)\) when positive.
• Excess supply (surplus): supply > demand at a given price. Measured as \(\text{surplus} = Q_s(P) - Q_d(P)\) when positive.

How price adjusts

• If price is below equilibrium (too low), demand exceeds supply (shortage). Firms raise prices and increase quantity supplied; consumers reduce quantity demanded until equilibrium is restored.
• If price is above equilibrium (too high), supply exceeds demand (surplus). Firms cut prices to sell excess stock; quantity demanded rises and quantity supplied falls until equilibrium is restored.
• These adjustments describe a self-correcting mechanism that pushes the market toward the market-clearing price.

Shifts and their effects

• A rightward shift in demand (increase in demand) or a leftward shift in supply (decrease in supply) tends to create excess demand at the original price and raises the equilibrium price and quantity (depending on elasticities).
• A rightward shift in supply (increase in supply) or a leftward shift in demand (decrease in demand) tends to create excess supply at the original price and lowers the equilibrium price and quantity (again depending on elasticities).

Reading a typical supply-demand diagram (labels used in class)

• Equilibrium labelled as \((P_1, Q_1)\): price \(P_1\) clears quantity \(Q_1\).
• If price is at \(P_2<P_1\), quantity demanded exceeds quantity supplied (shortage); the gap equals \(Q_d(P_2)-Q_s(P_2)\).
• If price is at \(P_2>P_1\), quantity supplied exceeds quantity demanded (surplus); the gap equals \(Q_s(P_2)-Q_d(P_2)\).

Quick procedure to find and check equilibrium

1. Write demand function \(Q_d(P)\) and supply function \(Q_s(P)\).
2. Solve \(Q_d(P)=Q_s(P)\) for the equilibrium price \(P^*\).
3. Compute equilibrium quantity \(Q^*=Q_d(P^*)=Q_s(P^*)\).
4. For any other price \(P\), compute \(Q_d(P)-Q_s(P)\) to determine shortage (positive) or surplus (negative).

Important points to remember

• Equilibrium is stable when price adjustments eliminate shortages or surpluses.
• Shifts in demand or supply change the equilibrium; the direction of change depends on whether curves shift left or right.
• The size of price and quantity changes depends on the slopes (elasticities) of the supply and demand curves.

Summary example (conceptual)

• Start at \((P_1,Q_1)\) in equilibrium.
• Demand increases (right shift): at the original price there is a shortage; price rises to new equilibrium, raising \(P\) and usually raising \(Q\).
• Supply increases (right shift): at the original price there is a surplus; price falls to new equilibrium, lowering \(P\) and usually raising \(Q\).