Difficulty: Introductory to Intermediate | Prerequisites: Basic algebra, understanding of supply and demand curves.
Price elasticity measures how sensitive buyers and sellers are to price changes. It sits at the heart of every policy question in microeconomics: who bears a tax, whether a price ceiling causes a shortage, how trade affects domestic markets. You need to be comfortable calculating percentage changes before anything else in the course will click. This topic draws directly on the supply-and-demand framework from your first weeks and feeds into consumer theory, taxation, and welfare analysis later.
Price elasticity of demand (or supply) equals the percentage change in quantity divided by the percentage change in price. When curves are not straight lines, you must use this basic definition at each segment rather than a shortcut formula. Elasticity can differ at every point along the same curve.
Price elasticity of demand (PED)
The percentage change in quantity demanded divided by the percentage change in price. It is normally negative (demand falls as price rises) but is often reported as an absolute value.
In simple terms, this measures how much buyers cut back when the price goes up.
Price elasticity of supply (PES)
The percentage change in quantity supplied divided by the percentage change in price. It is normally positive (supply rises as price rises).
Think of it as how eagerly producers ramp up output when they can charge more.
Elastic demand/supply
When the absolute value of elasticity is greater than 1. Quantity responds more than proportionally to a price change.
In simple terms, buyers (or sellers) are very sensitive to the price.
Inelastic demand/supply
When the absolute value of elasticity is less than 1. Quantity responds less than proportionally to a price change.
Think of it as buyers (or sellers) barely reacting to a price move.
Unit elastic
When the absolute value of elasticity equals exactly 1. Percentage changes in price and quantity are the same size.
Kink (in a demand or supply curve)
A point where the curve changes slope. At a kink, elasticity must be calculated from one direction (the direction of the price change you are analysing), not by averaging both sides.
In simple terms, the curve bends sharply, so you pick a direction and stick with it.
When demand or supply curves are not straight lines, you cannot use a single slope-based shortcut. Instead, apply the basic definition directly at each price interval.
Pick two price points and note the quantity at each.
Compute the percentage change in price: (change in P) / (starting P).
Compute the percentage change in quantity: (change in Q) / (starting Q).
Divide: elasticity = %ΔQ / %ΔP.
The direction of the price change matters. Moving from P = 25 to P = 30 gives a different percentage base than moving from P = 30 to P = 25. At kink points, state clearly which direction you are calculating from.
Price rises from 25 to 30. That is a change of 5 on a base of 25, so %ΔP = 5/25 = 20%.
Quantity demanded falls by 8 from a starting quantity of 38, so %ΔQ = -8/38 = -21.1%.
Demand elasticity at P = 25: -21.1% / 20% = -1.05.
At the next segment:
Price rises from 30 to 40. That is 10/30 = 33.3%.
Quantity demanded falls by 20 from 30, so %ΔQ = -20/30 = -66.7%.
Demand elasticity at P = 30: -66.7% / 33.3% = -2.
Notice the same curve produces different elasticities at different prices. The curve is more elastic at higher prices here.
Price rises from 25 to 30 (%ΔP = 20%). Quantity supplied rises by 5 from 25, so %ΔQ = 20%.
Supply elasticity at P = 25: 20% / 20% = 1 (unit elastic).
Price rises from 30 to 40 (%ΔP = 33.3%). Quantity supplied rises by 20 from 30, so %ΔQ = 66.7%.
Supply elasticity at P = 30: 66.7% / 33.3% = 2 (elastic).
Equilibrium is the price where quantity demanded equals quantity supplied. In Q1c, that occurs at P = 30, where both demand and supply equal 30 million units.
If the price is forced below equilibrium, demand exceeds supply. In Q1d, the result is excess demand of 20 million units.
\varepsilon_P^D = \frac{\%\Delta Q_D}{\%\Delta P} = \frac{\Delta Q_D / Q_D}{\Delta P / P}\varepsilon_P^S = \frac{\%\Delta Q_S}{\%\Delta P} = \frac{\Delta Q_S / Q_S}{\Delta P / P}For a linear demand function Q_D(P) = a - bP, the point elasticity formula is:
\varepsilon_P^D = \frac{-bP}{a - bP}For a linear supply function Q_S(P) = a + bP, the point elasticity formula is:
\varepsilon_P^S = \frac{bP}{a + bP}These linear shortcuts only work when the curve is a straight line across the interval. For kinked or non-linear curves, fall back to the basic percentage-change definition.
Governments use elasticity estimates to predict how much revenue a cigarette tax will raise (inelastic demand means revenue climbs; elastic demand means people just stop buying). Firms use it to set prices: if demand for your product is elastic, a price hike loses you more in sales than it gains in margin.
Students often think elasticity and slope are the same thing. They are not. Slope is constant along a straight-line demand curve, but elasticity changes at every point.
Students often think a steeper curve is always more inelastic. Steepness depends on the units on the axes. Elasticity is unit-free, which is the whole reason we use it.
Students sometimes calculate percentage changes using the wrong base (the ending quantity instead of the starting quantity). The homework solutions use the starting value as the base.
At kink points, students forget to specify the direction of the price change. The elasticity from 20 to 25 is not the same as the elasticity from 25 to 20.
⚠️ You will almost certainly be asked to calculate elasticity from a table or a non-linear curve. Know the basic definition cold.
⚠️ At kink points, state the direction of your price change. Marks are lost for ambiguity here.
⚠️ Understand what elastic vs. inelastic implies for total revenue. This links directly to taxation questions later in the course.
True or False: Elasticity is the same as the slope of the demand curve. (False.)
Fill in the blank: If quantity demanded falls by 10% when price rises by 5%, the price elasticity of demand is ______. (-2.)
True or False: At a kink in the demand curve, you may calculate elasticity from either direction and get the same answer. (False, you will generally get different values.)
Fill in the blank: Demand is called elastic when the absolute value of PED is ______ than 1. (Greater.)
True or False: A supply elasticity of 1 means quantity supplied changes by the same percentage as price. (True.)
Q: A non-linear demand curve shows Q = 38 at P = 25 and Q = 30 at P = 30. What is the price elasticity of demand when the price rises from 25 to 30?
A: %ΔQ = -8/38 = -21.1%. %ΔP = 5/25 = 20%. PED = -21.1%/20% = -1.05.
Q: Using the same curve, Q = 30 at P = 30 and Q = 10 at P = 40. What is PED when price rises from 30 to 40?
A: %ΔQ = -20/30 = -66.7%. %ΔP = 10/30 = 33.3%. PED = -66.7%/33.3% = -2.
Q: Supply is 25 at P = 25 and 30 at P = 30. What is the price elasticity of supply for this interval?
A: %ΔQ = 5/25 = 20%. %ΔP = 5/25 = 20%. PES = 20%/20% = 1 (unit elastic).
Q: At P = 30, both demand and supply equal 30. What is the equilibrium price, and what happens if price is set below this level?
A: Equilibrium price is 30. Below that price, quantity demanded exceeds quantity supplied, creating excess demand (a shortage).
Elasticity feeds directly into tax incidence analysis: who actually pays a tax depends on the relative elasticities of demand and supply. It also underpins the analysis of price ceilings and floors (whether they create shortages or surpluses and how large those are). Later in the course, you will see elasticity again when studying monopoly pricing and international trade.
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