Elasticity of Demand – Comprehensive Study Notes
Elasticity of Demand – Comprehensive Study Notes
What elasticity measures
Elasticity of demand = the responsiveness of quantity demanded to a change in price.
Definition in words: the percentage change in quantity demanded divided by the percentage change in price.
Sign convention: price and quantity move in opposite directions for most goods, so elasticity is typically negative due to the law of demand. If a calculation gives a positive number, that indicates a mistake.
We often use the absolute value to categorize elasticity: |ε| > 1 ⇒ elastic, |ε| < 1 ⇒ inelastic, |ε| = 1 ⇒ unit elastic.
Formulas for elasticity (two common forms)
Point or standard percentage change form:
\varepsilon = \frac{\frac{\Delta Q}{Q0}}{\frac{\Delta P}{P0}} = \frac{\Delta Q}{\Delta P} \cdot \frac{P0}{Q0}
where $\Delta Q = Q1 - Q0$, $\Delta P = P1 - P0$, and $(P0, Q0)$ are initial values.
Midpoint (arc) elasticity, used in the examples:
\varepsilon = \frac{\frac{\Delta Q}{\overline{Q}}}{\frac{\Delta P}{\overline{P}}} = \frac{\frac{Q1 - Q0}{Q1 + Q0}}{\frac{P1 - P0}{P1 + P0}}
with arithmetic means: \overline{Q} = \frac{Q1 + Q0}{2}, \quad \overline{P} = \frac{P1 + P0}{2}.
In the transcript’s worked example, A to B:
$Q0 = 5$, $Q1 = 10$, $P0 = 10$, $P1 = 8$.
Numerator: $\frac{Q1 - Q0}{Q1 + Q0} = \frac{10 - 5}{10 + 5} = \frac{5}{15} = \frac{1}{3}$.
Denominator: $\frac{P1 - P0}{P1 + P0} = \frac{8 - 10}{8 + 10} = \frac{-2}{18} = -\frac{1}{9}$.
Elasticity: \varepsilon = \frac{1/3}{-1/9} = -3.n - This shows elastic demand (|ε| = 3 > 1).
How to interpret elasticity values
Elastic (|ε| > 1): quantity responds a lot to price changes; revenue moves in the opposite direction of price changes.
Inelastic (|ε| < 1): quantity responds little to price changes; revenue tends to move with price increases.
Unit elastic (|ε| = 1): quantity responds proportionally to price changes.
Total revenue intuition (with a price rise): if demand is elastic, a price rise lowers total revenue; if demand is inelastic, a price rise increases total revenue.
Revenue implications and examples
Total Revenue (TR) = Price × Quantity, often abbreviated TR.
Example: If price rises by 10% and quantity demanded falls by 20%, elasticity = |ε| = 2 and the revenue falls (since demand is elastic in this case).
If elasticity is elastic (|ε| > 1) and you raise price, TR tends to fall; if you lower price, TR tends to rise (because you gain a larger percentage increase in quantity).
If elasticity is inelastic (|ε| < 1) and you raise price, TR tends to rise (quantity drops little).
Concrete worked examples from the transcript
Example A to B (elasticity calculation with midpoint formula)
Points: $Q0 = 5$, $Q1 = 10$, $P0 = 10$, $P1 = 8$.
Midpoint changes:
Numerator: $\frac{Q1 - Q0}{Q1 + Q0} = \frac{10 - 5}{10 + 5} = \frac{5}{15} = \frac{1}{3}$.
Denominator: $\frac{P1 - P0}{P1 + P0} = \frac{8 - 10}{8 + 10} = \frac{-2}{18} = -\frac{1}{9}$.
Elasticity: \varepsilon = \frac{1/3}{-1/9} = -3.
Interpretation: Demand is elastic (|ε| = 3 > 1).
Example C to D (another midpoint elasticity calculation)
Points: $Q0 = 20$, $Q1 = 25$, $P0 = 4$, $P1 = 2$.
Midpoint changes:
Numerator: $\frac{Q1 - Q0}{Q1 + Q0} = \frac{25 - 20}{25 + 20} = \frac{5}{45} = \frac{1}{9}$.
Denominator: $\frac{P1 - P0}{P1 + P0} = \frac{2 - 4}{2 + 4} = \frac{-2}{6} = -\frac{1}{3}$.
Elasticity: \varepsilon = \frac{1/9}{-1/3} = -\frac{1}{3}.
Interpretation: Demand is inelastic (|ε| = 1/3 < 1).
Takeaways from the two examples: elasticity can move from elastic to inelastic depending on price/quantity changes; the same formula applies with different numbers.
Why we use percentage changes
Percent changes allow comparison across goods with very different price levels (e.g., bread vs. cars).
Example rationale: a $1 change in bread price is huge relative to its base price, while a $1 change in a car is tiny relative to its price; percent changes normalize these differences.
Data usages: firms collect purchaser data (e.g., Kroger Plus cards, online shopping data) to estimate demand and elasticity and tailor pricing to maximize revenue.
Real-world pricing practices influenced by elasticity data: dynamic pricing, targeted discounts, and price discrimination based on observed demand patterns and browser/device data.
Elasticity determinants (factors that affect how elastic or inelastic demand is)
Number of substitutes (the big one)
More substitutes ⇒ more elastic demand.
Example: Starbucks has many substitutes (Dunkin, other coffee shops), leading to higher elasticity for coffee purchases.
Electricity has few substitutes ⇒ highly inelastic demand.
Specificity (narrow vs broad market) and the breadth of substitutes
The more specific the market, the more substitutes you uncover, often increasing elasticity.
Autos example: as you get more specific (car type, model), the set of substitutes grows (from many car brands to nearly infinite specific models), raising elasticity.
Time horizon
More time allows consumers to find substitutes or adjust behavior; elasticity tends to increase with time.
Necessity vs luxury (necessity decreases elasticity)
Necessities (electricity, gasoline, basic services) tend to have inelastic demand.
Luxuries and optional goods tend to have higher elasticity.
Budget share
Goods that take up a larger share of a typical budget tend to have higher elasticity because price changes are more impactful.
If a good is a tiny budget fraction (e.g., a salt shaker), price changes may be barely noticeable; elasticity is low.
Specificity example: substitutes grow as markets become more specific; as you consider many sub-options (e.g., many car makes/models), elasticity rises.
Visual intuition and mnemonics
Demand curves:
Elastic demand: flatter (the “horizontal” portion of the mnemonic idea for the word “elastic”).
Inelastic demand: steeper, near-vertical.
Graphical mnemonic mentioned: lower-case “e” with a horizontal piece helps remember the shape of an elastic demand segment.
Important takeaway: a linear demand curve has a constant slope but elasticity varies along the curve (elasticity is not constant for a linear demand curve).
Real-world and policy examples discussed
UGA football tickets: demand is relatively inelastic, especially when the team is doing well.
Taxes and elasticity: whether a tax raises revenue depends on the elasticity of the taxed good. Inelastic goods (e.g., gasoline, cigarettes) tend to yield higher revenue when taxed because consumption changes little.
NYC soft drink tax: soft-drink consumption declined, illustrating misjudgment when elasticity is not accounted for; consumers substitute toward other beverages like alcohol, potentially offsetting intended effects.
Insulin: near perfectly inelastic demand; price increases have almost no effect on quantity demanded because it is a life-sustaining necessity.
Gasoline: typically inelastic due to lack of close substitutes in the short run; longer-term substitutions exist (public transit, carpooling) but in the short run price changes have limited effect on quantity demanded.
Delta Airlines olives anecdote: a costly, simple cost-cutting insight (eliminate a low-value item like olives) can significantly improve profits; illustrates how small changes guided by cost/benefit analysis affect elasticity and revenue indirectly through costs and demand signals.
Data and pricing: modern firms collect data on consumer behavior (browsers, purchase history) to infer elasticity and optimize pricing; examples include browser-based pricing differentiation and the observation that price can vary by time of day and user characteristics.
Practical implications for exams and practice
Practice problems: use two-number price changes and corresponding quantity changes to compute elasticity and interpret whether demand is elastic or inelastic.
Method for practicing: work two examples (as in the transcript), check math with a calculator, then interpret the results.
Determinants review: be able to explain why a good like electricity is inelastic and a good like Starbucks coffee is more elastic, using substitutes, time, necessity, and budget share.
Exam tips: expect to be given a table of price-quantity pairs and asked to compute elasticity and classify as elastic/inelastic; the formula is the same, the numbers change.
Quick practice prompts you can try
Given a price increase of 12% and a quantity decrease of 18%, compute the elasticity using the midpoint formula and interpret whether demand is elastic or inelastic.
If a good has elasticity |ε| = 0.75 and price falls by 8%, estimate the percentage change in quantity demanded and discuss revenue implications.
Consider a necessity good with a large budget share (e.g., gasoline). Discuss how each determinant mentioned (substitutes, time, necessity, budget share) would tend to affect its elasticity over a longer horizon.
Summary for exam readiness
Know the two key formulas for elasticity (standard percent-change form and the midpoint form).
Be able to classify elasticity as elastic, inelastic, or unit elastic by comparing the absolute value to 1.
Understand the revenue implications of price changes given elasticity.
Memorize the main determinants of elasticity and be able to apply them to real-world examples.
Practice with two-number calculations to build fluency and speed on tests.
Note on teaching style and practice materials
The instructor mentions using old final exams as practice and going through relevant problems during review sessions.
Calculations may be shown step-by-step to ensure memory and understanding; you may be asked to reproduce the calculation on exams with calculator support.
Expect to interpret numerical elasticity results in terms of real-world implications and business strategy.