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

The substitution effect is the change in the quantity of a good as price changes holding utility constant.

$$ \left.\frac{dQ}{dP}\right|_{\bar{U}} $$

The income effect is the change in the quantity of a good as income changes.

$$ \frac{dQ}{dY} $$