Supply-demand model

The demand curve shows how much of a good people are willing to buy at a given price. It is generally downward sloping because people are willing to buy more of a good if it is cheaper.

The supply curve shows how much of a good firms are willing to sell for a given price. It is generally upward sloping.

The market equilibrium occurs where the supply and demand curve meet.

$$\varepsilon = \frac{\Delta Q / Q_0}{\Delta P / P_0} \leq 0$$

• $\Delta Q$: change in quantity
• $Q_0$: initial quantity
• $\Delta P$: change in price
• $P_0$: initial price

Perfectly inelastic demand: $\varepsilon = 0$

• No substitute is available
• Demand curve is vertical
• Quantity is fixed

Perfectly elastic demand: $\varepsilon = \infty$

• Perfect substitutes are available
• Demand curve is vertical
• Price is fixed

Elasticity of goods is determined by their substitutability.

$$\gamma = \frac{\Delta Q / Q_0}{\Delta Y / Y_0}$$

• $Q$: quantity of good
• $Y$: income

Engel curve: curve showing relationship between income and quantity of good.

• $\gamma > 0$: normal good
  • $\gamma > 1$: luxuries - spending on these goods goes up as a proportion of income as income increases.
  • $0 < \gamma < 1$: necessitities - spending on these goods goes down as a proportion of income as income increases.
• $\gamma < 0$: inferior good