Lecture 2 · Week 3 · Besanko & Braeutigam ch. 2 · about 50 min

Demand and Supply Analysis

The workhorse model of microeconomics: demand and supply curves, market equilibrium, the four comparative-statics cases, and the elasticities that measure how strongly quantity responds to price, income and the price of related goods.

By the end you can

Distinguish a movement along a demand or supply curve from a shift of the curve
Solve for market equilibrium price and quantity algebraically
Predict the direction of change in equilibrium P and Q from a shift in demand or supply
Compute and interpret price, income and cross-price elasticities

The demand curve

The law of demand: holding everything else fixed (ceteris paribus), quantity demanded falls as price rises. This gives a downward-sloping demand curve.

Linear demand functionFormula sheet →

Q^d = a - bP

$a$: quantity demanded at a price of zero
$b$: how strongly quantity responds to price (the slope's magnitude)

Use it when a demand relationship is given as a straight line in price, the most common form in problem sets.

Price is not the only thing that affects demand. Other determinants — income, the price of related goods, tastes, expectations, the number of buyers — cause the entire curve to shift, which is a fundamentally different event from a movement along the curve caused by price itself changing.

Determinants of demandWhat shifts demandFormula sheet →

Q^d = f(P,\; Y,\; P_{\text{related}},\; \text{tastes},\; \text{expectations},\; \text{number of buyers})

Use it when you need to decide whether a described event moves demand along the curve (price changed) or shifts the whole curve (anything else changed).

The supply curve

The law of supply: holding everything else fixed, quantity supplied rises as price rises, giving an upward-sloping supply curve.

Linear supply functionFormula sheet →

Q^s = c + dP

$c$: quantity supplied at a price of zero (often negative, meaning suppliers need a minimum price before entering)
$d$: how strongly quantity responds to price

Use it when a supply relationship is given as a straight line in price.

Supply shifts with input prices, technology, the number of sellers, expectations, and the prices of related goods a firm could produce instead.

Market equilibrium

Equilibrium conditionConditionFormula sheet →

Q^d(P^*) = Q^s(P^*)

$P^*$: equilibrium price
$Q^*$: the common quantity demanded and supplied at P^*

Use it when you need to find the price and quantity where a market clears — no shortage, no surplus.

Comparative statics: four cases

Once you know which curve shifts and which direction, the effect on equilibrium price and quantity is mechanical.

Event	Demand	Supply	P*	Q*
Demand increases	shifts right	unchanged	rises	rises
Demand decreases	shifts left	unchanged	falls	falls
Supply increases	unchanged	shifts right	falls	rises
Supply decreases	unchanged	shifts left	rises	falls

Try it: shift demand and supply

Price elasticity of demand

Price elasticity of demandKey formulaFormula sheet →

E_d = \frac{\%\Delta Q^d}{\%\Delta P} = \frac{P}{Q}\cdot\frac{dQ}{dP}

$E_d$: price elasticity of demand, typically negative (report the absolute value when classifying)

Use it when you need to measure how strongly quantity demanded responds to a price change, in percentage terms, independent of units.

By convention, economists usually quote $|E_d|$ : values above 1 are elastic, below 1 are inelastic, and exactly 1 is unit elastic — the same classification developed with the calculus definition in the Mathematics I course, applied here directly to Besanko and Braeutigam’s notation.

Income and cross-price elasticity

Income elasticity of demandFormula sheet →

E_Y = \frac{\%\Delta Q^d}{\%\Delta Y}

$Y$: consumer income

Use it when you need to classify a good as normal or inferior from how demand responds to income.

Cross-price elasticity of demandFormula sheet →

E_{XY} = \frac{\%\Delta Q_X^d}{\%\Delta P_Y}

$Q_X$: quantity of good X demanded
$P_Y$: price of a related good Y

Use it when you need to classify the relationship between two goods as substitutes or complements.

Sign of elasticity	Classification
$E_Y \gt 0$	Normal good (demand rises with income)
$E_Y \lt 0$	Inferior good (demand falls with income)
$E_{XY} \gt 0$	Substitutes (price of Y up, demand for X up)
$E_{XY} \lt 0$	Complements (price of Y up, demand for X down)

Exam practice

Summary and review

A change in the good’s own price moves you along the demand or supply curve; anything else shifts the whole curve.
Equilibrium: $Q^d(P^*) = Q^s(P^*)$ .
Demand shift: price and quantity move together. Supply shift: price and quantity move oppositely.
$E_d = (P/Q)(dQ/dP)$ ; $|E_d| \gt 1$ elastic, $\lt 1$ inelastic.
$E_Y \gt 0$ normal good, $E_Y \lt 0$ inferior good.
$E_{XY} \gt 0$ substitutes, $E_{XY} \lt 0$ complements.
Simultaneous shifts in both curves make one of price or quantity ambiguous without knowing relative magnitudes.