Supply & Demand — Market Equilibrium

In a competitive market, the demand curve slopes downward (buyers purchase less at higher prices) and the supply curve slopes upward (sellers supply more at higher prices). Equilibrium occurs at price $P^*$ where $Q_D = Q_S$ — the market clears with no surplus or shortage.

Curve shifts move equilibrium:

• Demand shifts right → $P^*$ rises, $Q^*$ rises (e.g., rising incomes, new fashion trend).
• Supply shifts left → $P^*$ rises, $Q^*$ falls (e.g., rising input costs, drought).

Price elasticity of demand measures how sensitive buyers are to price changes:

$E_D = \frac{\%\Delta Q_D}{\%\Delta P}$

Elastic ($|E_D| > 1$): buyers respond strongly — e.g., luxury goods. Inelastic ($|E_D| < 1$): buyers barely change quantity — e.g., essential medicines.

For linear curves $Q_D = a - bP$ and $Q_S = c + dP$, solve $Q_D = Q_S$:

$P^* = \frac{a - c}{b + d}, \qquad Q^* = a - b \cdot P^*$

Point elasticity:

$E_D = \frac{dQ_D}{dP} \cdot \frac{P^*}{Q^*} = -b \cdot \frac{P^*}{Q^*}$

Demand: $Q_D = 100 - 4P$. Supply: $Q_S = 20 + 2P$.

Setting equal: $100 - 4P = 20 + 2P \Rightarrow P^* = ₹\frac{80}{6} \approx ₹13.33$

$Q^* = 100 - 4(13.33) \approx 46.7$ units.

Elasticity at equilibrium: $E_D = -4 \times \frac{13.33}{46.7} \approx -1.14$ — slightly elastic.

When a refinery shuts down, the petrol supply curve shifts left — prices spike but quantity falls only slightly because demand is inelastic. Governments use this analysis to design subsidies (shift supply right to lower price) and minimum support prices for farmers (floor above equilibrium to guarantee income). Businesses use elasticity to decide whether raising prices will increase or decrease total revenue.

1. The government sets a price ceiling below $P^*$. What happens to $Q_D$, $Q_S$, and the market — surplus or shortage?

2. Demand is $Q_D = 60 - 3P$ and supply is $Q_S = 12 + 3P$. Find the equilibrium price and quantity.