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

Key idea · Exam recipe: demand, supply and equilibrium (memorise this)

Choke price: Set $q_x = 0$ in the demand function $q_x = a - bP_x \implies P_{\text{choke}} = a/b$ . No consumer buys above this price.
Inverse demand: Solve $q_x = a - bP_x$ for price: $P_x = \frac{a}{b} - \frac{1}{b}q_x$ . The vertical intercept is $a/b$ , and the slope on the graph is $-1/b$ .
Market equilibrium: Set $Q^d(P^*) = Q^s(P^*)$ . Solve for equilibrium price $P^*$ , then plug $P^*$ into $Q^d$ to get $Q^*$ . Always verify $Q^s(P^*) = Q^*$ .
Shifts vs movements: A change in the good’s own price $P$ causes a movement along the curve ( $\Delta Q$ ). A change in any exogenous variable ( $I, T, P_s, P_c, \text{input costs}, \text{tech}$ ) causes a shift of the entire curve ( $\Delta D$ or $\Delta S$ ).
Elasticity: Point price elasticity is $\epsilon = \frac{dQ}{dP} \cdot \frac{P}{Q}$ . If $|\epsilon| \gt 1$ demand is elastic ( $P \uparrow \implies TR \downarrow$ ); if $|\epsilon| \lt 1$ demand is inelastic ( $P \uparrow \implies TR \uparrow$ ).

How the exam asks it: three core exam templates

Exam questions on demand and supply test your ability to convert between direct and inverse demand, solve market equilibrium algebraically, and calculate point elasticities.

Exam template 1: Linear demand intercepts and choke price

Question: A market demand equation is estimated as: $q_x = 35 - 0.008P_x$ where $q_x$ is quantity demanded and $P_x$ is unit price in TL.
a) Find the quantity demanded at a price of zero.
b) Calculate the choke price (the vertical intercept).
c) Derive the inverse demand equation $P_x = f(q_x)$ .

Exam template 2: Market equilibrium and point elasticity

Question: In a market, demand is given by $Q^d = 120 - 2P$ and supply is given by $Q^s = -20 + 3P$ .
a) Find the market equilibrium price $P^*$ and equilibrium quantity $Q^*$ .
b) Compute the price elasticity of supply $\epsilon_s$ at equilibrium.
c) Compute the point price elasticity of demand $\epsilon_d$ at equilibrium and classify demand as elastic, inelastic, or unit elastic.

Exam template 3: Recovering linear demand from a point and elasticity

Question: At the current price of 10 TL, consumers buy 200 units of a good, and the price elasticity of demand at this point is $\epsilon_d = -0.5$ .
a) Find the parameters $a$ and $b$ of the linear demand equation $Q = a - bP$ .
b) State the full linear demand equation.
c) If the seller increases the price from 10 TL to 11 TL (a 10% increase), will total revenue rise or fall? Explain without calculating the exact new revenue.

Cheat-sheet & the 4-step method

· Cheat-sheet: demand, supply and elasticity formulas

Concept	Equation / Rule	When to use it	How to write the exam answer
Linear demand	$Q^d = a - bP$	Given direct quantity as function of price	State horizontal intercept $a$ and slope coefficient $-b$
Inverse demand	$P = \frac{a}{b} - \frac{1}{b}Q$	Plotting on graph with $P$ on vertical axis	Solve for $P$ ; vertical intercept is $a/b$ , graph slope is $-1/b$
Choke price	$P_{\text{choke}} = \frac{a}{b}$	Finding price where quantity drops to 0	Set $Q^d = 0$ , solve for $P$ ; state that above this price $Q=0$
Equilibrium condition	$Q^d(P^) = Q^s(P^)$	Finding market price and quantity	Set equations equal, solve $P^$ , plug into $Q^d$ for $Q^$ , verify with $Q^s$
Point price elasticity	$\epsilon = \frac{dQ}{dP} \cdot \frac{P}{Q}$	Measuring responsiveness at a point	Multiply slope $dQ/dP$ by $P/Q$ ; state sign and whether $\lvert\epsilon\rvert \gtrless 1$
Income elasticity	$\epsilon_I = \frac{dQ}{dI} \cdot \frac{I}{Q}$	Classifying normal vs inferior	$\epsilon_I \gt 0 \implies$ normal; $\epsilon_I \lt 0 \implies$ inferior; $\epsilon_I \gt 1 \implies$ luxury
Cross-price elasticity	$\epsilon_{xy} = \frac{dQ_x}{dP_y} \cdot \frac{P_y}{Q_x}$	Classifying substitutes vs complements	$\epsilon_{xy} \gt 0 \implies$ substitutes; $\epsilon_{xy} \lt 0 \implies$ complements
Total revenue test	$TR = P \cdot Q$	Price change effect on seller revenue	Inelastic ( $\lvert\epsilon\rvert \lt 1$ ): $P\uparrow \implies TR\uparrow$ ; Elastic ( $\lvert\epsilon\rvert \gt 1$ ): $P\uparrow \implies TR\downarrow$

Key idea · The 4-step method for demand, supply and equilibrium questions

Step 1: Identify given equations and the required target.
- Is demand in direct form ( $Q = f(P)$ ) or inverse form ( $P = f(Q)$ )?
- Are you solving for an intercept, an equilibrium point, an elasticity, or a curve shift?
Step 2: State the formal rule.
- Choke price: $Q^d = 0$ .
- Equilibrium: $Q^d = Q^s$ .
- Elasticity: $\epsilon = \dfrac{dQ}{dP} \cdot \dfrac{P}{Q}$ .
- Shift: identify whether own price moved (movement along) or an exogenous factor moved (shift).
Step 3: Solve one arithmetic operation per line.
- Set up the equality and isolate the variable cleanly.
- For point elasticity, compute $dQ/dP$ first, then the ratio $P/Q$ , then multiply.
Step 4: Check and conclude in bold.
- For equilibrium, verify both $Q^d(P^*)$ and $Q^s(P^*)$ give the identical quantity.
- State economic meaning clearly (elastic vs inelastic, normal vs inferior, substitute vs complement).

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_x^d = f(P_x,\; \bar{I},\; \bar{T},\; \bar{P}_s,\; \bar{P}_c,\; \bar{N}_c,\; \bar{P}^E,\; \bar{I}^E)

$P_x$: own price
$I$: income
$T$: tastes
$P_s$: price of a substitute
$P_c$: price of a complement
$N_c$: number of consumers
$P^E$: expected future price
$I^E$: expected future income. A bar means the variable is held constant.

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

This is the notation used in lecture. The bars are the whole idea of ceteris paribus: freeze every determinant except the good’s own price and demand collapses to a function of $P_x$ alone, $q_x^d = f(P_x)$ , which in the linear case is $q_x = a - bP_x$ . Unfreeze any barred variable and the curve itself moves.

Which way does each determinant shift demand?

Event	Demand shifts	Why
Income $I \uparrow$ , normal good	right	richer buyers want more
Income $I \uparrow$ , inferior good	left	richer buyers switch to better goods
Tastes $T \uparrow$	right	the good became more popular (red roses on 14 February)
Price of a substitute $P_s \uparrow$	right	the alternative got expensive, buyers switch to this good
Price of a complement $P_c \uparrow$	left	the good used together with it got expensive
Number of consumers $N_c \uparrow$	right	more buyers at every price
Expected future price $P^E \uparrow$	right	buy now before it gets more expensive
Expected future income $I^E \uparrow$	right	buyers spend more today

Reverse the arrow and the shift reverses: a fall in the price of a substitute shifts demand left, and so on.

Demand equation and inverse demand equation

The same line can be written two ways, and exam questions switch between them without warning.

Demand vs inverse demandFormula sheet →

q_x^d = a - bP_x \quad\Longleftrightarrow\quad P_x = \frac{a}{b} - \frac{1}{b}\,q_x

$q_x^d$: left side, the demand equation: quantity as a function of price
$P_x$: right side, the inverse demand equation: price as a function of quantity (what you plot, since price is on the vertical axis)

Use it when a problem gives demand in one form and you need the other, for example to read the vertical intercept off a graph.

The choke price

The choke price is the price at which quantity demanded falls to zero: the vertical intercept of the demand curve. Set $q_x = 0$ in $q_x = a - bP_x$ :

Choke priceFormula sheet →

q_x = 0 \;\Rightarrow\; P_x = \frac{a}{b}

$a, b$: coefficients of the linear demand equation q_x = a - bP_x

Use it when you need the price above which nobody buys the good, or the vertical intercept of a linear demand curve.

Slide the price on the lecture line and watch the quantity fall to zero exactly at the choke price.

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.

Determinants of supplyWhat shifts supplyFormula sheet →

q_x^s = f(P_x,\; \overline{\text{tech}},\; \bar{P}_I,\; \bar{N}_f,\; \bar{t},\; \overline{\text{sub}})

$P_x$: own price
$\text{tech}$: technology
$P_I$: input prices
$N_f$: number of firms
$t$: taxes on the good
$\text{sub}$: subsidies. A bar means the variable is held constant.

Use it when you need to decide whether an event moves the market along the supply curve or shifts it.

Holding the barred variables fixed gives $q_x^s = f(P_x)$ , the law of supply: $P_x \uparrow \Rightarrow q_x^s \uparrow$ and $P_x \downarrow \Rightarrow q_x^s \downarrow$ . Compare the law of demand, where they move oppositely.

Change	Curve	Direction
Better technology	supply	right
Input price $P_I$ rises	supply	left
More firms $N_f$	supply	right
Tax $t$ rises	supply	left
Subsidy rises	supply	right

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.

How the market gets there: excess supply and excess demand

Equilibrium $E_0$ is not just where the lines cross. It is the only price where nobody has a reason to change what they do.

Price above equilibrium ( $P_1 \gt p^e$ ): buyers want only $q_1$ (point A on demand) but sellers offer $q_2$ (point B on supply). The gap $q_2 - q_1$ is excess supply. Unsold stock piles up, sellers cut prices, and $P$ falls back toward $p^e$ .
Price below equilibrium ( $P_2 \lt p^e$ ): buyers want more than sellers offer. The gap is excess demand (a shortage). Buyers bid the price up and $P$ rises toward $p^e$ .

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

Pick a case and press Show shift. The dashed line is where the curve was; follow the equilibrium from $E_0$ to $E_1$ .

Lecture examples

Event	What moves	Result
Income $I$ rises (normal good)	demand shifts right	$P \uparrow$ , $q \uparrow$
Tastes $T$ rise: red roses on 14 February	demand shifts right	$P \uparrow$ , $q \uparrow$
Input price $P_I$ rises	supply shifts left	$P \uparrow$ , $q \downarrow$

These are the three board diagrams, drawn the same way as in class.

When both curves move

If two events hit the market together, one of $P$ and $q$ is certain and the other depends on which shift is bigger. The two board examples:

Hibiscus: a tax rises ( $t \uparrow$ ) and tastes shift toward it ( $T \uparrow$ ). Supply shifts left, demand shifts right. Both push the price up, so $P \uparrow$ for sure. Quantity is ambiguous. In the board diagram the supply shift was larger, so $q \downarrow$ .
Oranges: the price of a substitute rises ( $P_s \uparrow$ ) and a subsidy is introduced ( $\text{sub} \uparrow$ ). Demand shifts right, supply shifts right. Both push quantity up, so $q \uparrow$ for sure. Price is ambiguous. In the board diagram the supply shift was larger, so $P \downarrow$ .

Show the shift, then switch which shift is bigger. One variable keeps its direction in both versions (certain), the other flips (ambiguous).

The whole topic fits in one table. Find the variable both shifts push the same way: that one is certain.

Demand	Supply	Certain	Ambiguous
right	right	$q \uparrow$	$P$
left	left	$q \downarrow$	$P$
right	left	$P \uparrow$	$q$
left	right	$P \downarrow$	$q$

Derived demand

Some goods are demanded mainly as inputs into something else. The demand for oranges, for example, depends partly on the demand for orange juice. This is derived demand: when demand for the final good rises, demand for the input shifts right too. Bad weather in orange-growing regions works the other way, through supply: fewer oranges at every price, so the orange supply curve shifts left.

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.

Elasticity along a straight demand line

For a linear demand $q = a - bP$ the slope is constant ( $dq/dP = -b$ ), so the formula becomes:

Elasticity of linear demandFormula sheet →

E_d = -b\,\frac{P}{q}

$a, b$: coefficients of q = a − bP
$P, q$: the point on the curve where you measure

Use it when demand is a straight line and you need the elasticity at a specific price.

The slope never changes, but $P/q$ does. Near the choke price $P$ is large and $q$ is tiny, so $|E_d|$ is huge. Near the horizontal intercept $P$ is tiny, so $|E_d|$ is close to 0. Exactly halfway, at $P = \frac{a}{2b}$ (half the choke price), $|E_d| = 1$ .

Special demand shapes

Exam questions love the two extremes, so learn their pictures: a vertical demand curve is perfectly inelastic ( $E = 0$ ) and a horizontal one is perfectly elastic ( $|E| = \infty$ ). Between them, a straight line has a different elasticity at every point, and a constant-elasticity curve has the same elasticity everywhere.

Constant elasticity demandFormula sheet →

Q = aP^{-b} \quad\Longrightarrow\quad E_d = -b \text{ at every point}

$a$: a positive constant that sets the level of demand
$b$: the elasticity, in absolute value

Use it when demand is given as a power of price and you need its elasticity: read it straight off the exponent.

Arc (midpoint) elasticity

When you only have two observed points instead of a demand equation, use the arc elasticity. It divides each change by the average of the two values, so you get the same answer whether the price rises or falls.

Arc elasticityFormula sheet →

E_d = \frac{\Delta Q / \left(\frac{Q_1 + Q_2}{2}\right)}{\Delta P / \left(\frac{P_1 + P_2}{2}\right)}

$P_1, Q_1$: first observed point
$P_2, Q_2$: second observed point
$\Delta Q$: Q_2 - Q_1
$\Delta P$: P_2 - P_1

Use it when you are given two price-quantity pairs and no demand equation.

What makes demand more or less elastic?

Substitutes: the more close substitutes a good has, the more elastic its demand.
Market vs brand: demand for one brand (one cola) is more elastic than demand for the whole market (all soft drinks), because other brands are close substitutes.
Share of the budget: goods that take a large share of income (a car) tend to be more elastic than tiny purchases (salt).
Necessities vs luxuries: necessities are less elastic.
Time: most goods are more elastic in the long run, because buyers find substitutes over time. Durable goods (cars) are the exception: their demand is more elastic in the short run, since buyers can postpone replacing them.

Price elasticity of supply

Price elasticity of supplyFormula sheet →

E_s = \frac{\%\Delta Q^s}{\%\Delta P} = \frac{P}{Q}\cdot\frac{dQ^s}{dP}

$E_s$: price elasticity of supply, positive because supply slopes upward

Use it when you need to measure how strongly quantity supplied responds to price.

Fitting a linear demand curve from an elasticity

Besanko and Braeutigam show a back-of-the-envelope trick: if you know the current price $P^*$ , quantity $Q^*$ and elasticity $E$ , you can recover the straight line $Q = a - bP$ through that point.

Elasticity and total revenue

Total revenue is $TR = P \cdot q$ . When the price rises, $P$ goes up but $q$ goes down, and elasticity tells you which effect wins.

Demand at this point	Price rises	Price falls
Elastic, $\lvert E_d\rvert \gt 1$	$TR$ falls	$TR$ rises
Inelastic, $\lvert E_d\rvert \lt 1$	$TR$ rises	$TR$ falls
Unit elastic, $\lvert E_d\rvert = 1$	$TR$ unchanged (at its maximum)	$TR$ unchanged

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.
Along a straight demand line elasticity changes: elastic above the midpoint, inelastic below it, unit elastic at half the choke price.
Elastic demand: price and revenue move oppositely. Inelastic demand: they move together.
Vertical demand: $E = 0$ . Horizontal demand: $|E| = \infty$ . $Q = aP^{-b}$ : $E = -b$ everywhere.
With two observed points and no equation, use the arc (midpoint) elasticity.
From one point and its elasticity you can rebuild a linear demand curve: $b = -EQ/P$ , $a = Q + bP$ .