Chapter 5: Elasticity and Its Application

How responsive are buyers and sellers — and why it matters for everything

The Coffee Market

We'll use the market for coffee throughout this chapter. Buyers have a downward-sloping demand (they buy less as price rises), and sellers have an upward-sloping supply (they produce more as price rises).

Demand: P = 8 − 0.4Q buyers' willingness to pay
Supply: P = 2 + 0.2Q sellers' minimum acceptable price
Equilibrium: Q* = 10,  P* = $4.00 where both curves cross

Set demand equal to supply: 8 − 0.4Q = 2 + 0.2Q → 6 = 0.6Q → Q* = 10, P* = $4.00. We'll explore what happens to quantity when price changes — and how to measure that responsiveness precisely.

What Is Elasticity?

Price elasticity of demand measures how much the quantity demanded responds to a change in price. Formally:

Ed = % Change in Qd ÷ % Change in P

To avoid getting different answers depending on which direction we measure, we use the midpoint method:

Ed = |ΔQ / ((Q1+Q2)/2)| ÷ |ΔP / ((P1+P2)/2)|

Five determinants of price elasticity of demand:

  1. Availability of close substitutes — more substitutes means more elastic
  2. Necessities vs. luxuries — necessities tend to be inelastic
  3. Definition of the market — narrow markets (Pepsi) are more elastic than broad ones (soda)
  4. Time horizon — demand is more elastic over longer periods
  5. Share of budget — goods that take a large share of income are more elastic

The same $1 price drop causes a tiny increase in quantity along the inelastic curve but a much larger increase along the elastic curve. That's what elasticity captures: how responsive quantity is to price.

Computing Price Elasticity of Demand

Drag the slider to move along our coffee demand curve (P = 8 − 0.4Q). The midpoint method compares each price to the equilibrium (P* = $4, Q* = 10).

$4.00
P*,Q* 0 $4 $8 0 5 10 15 20 Quantity (cups) Price ($) Demand

Elasticity Calculator

Current P $4.00
Current Q 10.00

Reference P* $4.00
Reference Q* 10.00

%ΔQ (midpoint) 0.00%
%ΔP (midpoint) 0.00%

|Ed|
Move the slider
Key insight: Elasticity varies along a linear demand curve. Near the top (high price, low quantity), demand is elastic. Near the bottom (low price, high quantity), demand is inelastic. At the midpoint, |Ed| = 1.

Total Revenue and the Elasticity Test

Total revenue = P × Q. When price rises on elastic demand, the quantity drop is so large that TR falls. When price rises on inelastic demand, quantity barely budges, so TR rises. This gives us the revenue test for classifying elasticity.

$4.00
TR 0 $3 $4 $5 $8 0 5 10 15 20 Quantity (cups) Price ($) Demand

Revenue Test

Price $4.00
Quantity 10.00
TR = P × Q $40.00

TR at P*=$4 $40.00
ΔTR $0.00

At equilibrium — move the price slider to see the revenue test in action.

Beyond Price Elasticity of Demand

Elasticity isn't just about demand and price. The same logic — percentage change in one variable divided by percentage change in another — applies to supply, income, and cross-price relationships.

Price Elasticity of Supply

Measures how much quantity supplied responds to price changes. The formula mirrors demand elasticity:

Es = % Change in Qs ÷ % Change in P

Key determinant: time horizon. In the short run, firms can't easily adjust production, so supply is relatively inelastic. Over longer periods, firms can build factories, hire workers, and enter/exit the market — making supply more elastic.

Income Elasticity of Demand

Measures how quantity demanded changes when consumer income changes.

Ey = %ΔQd ÷ %ΔIncome

Normal goods (Ey > 0): quantity rises with income. Restaurant meals, new clothes.
Inferior goods (Ey < 0): quantity falls as income rises. Instant noodles, bus rides.

Cross-Price Elasticity of Demand

Measures how the quantity demanded of one good responds to a price change in another good.

Exy = %ΔQd(x) ÷ %ΔP(y)

Substitutes (Exy > 0): if Pepsi's price rises, Coke's quantity demanded rises.
Complements (Exy < 0): if coffee's price rises, cream's quantity demanded falls.

Key Takeaways

  • Elasticity measures responsiveness of quantity to price changes — how much Q moves when P moves.
  • Midpoint formula avoids the direction problem. By averaging the endpoints, you get the same elasticity whether price rises or falls.
  • 5 determinants: substitutes, luxury/necessity, market breadth, time horizon, and budget share all affect how elastic demand is.
  • Revenue test: P↑ + TR↓ = elastic demand; P↑ + TR↑ = inelastic demand. This is the fastest way to classify elasticity in practice.
  • Supply elasticity depends on time horizon and production flexibility. Short-run supply is inelastic; long-run supply is elastic.
  • Cross-price and income elasticity classify goods as substitutes/complements (cross-price) and normal/inferior (income).

Ready to test yourself?

Work through problems on elasticity computation, the revenue test, and cross-price relationships.

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