Price Elasticity of Demand: Concept and Measurement

Price Elasticity of Demand: Concept and Measurement
We know that when the price rises, demand falls—the law of demand. But by how much does it fall? Elasticity answers this question—a measure of the sensitivity of one variable to changes in another. This is one of the most practically important tools in microeconomics.

The Concept of Elasticity

Elasticity shows the percentage change of one quantity in response to a one-percent change in another. It is a dimensionless measure—it does not depend on units of measurement.

Price Elasticity of Demand (PED — Price Elasticity of Demand):

$ PED = \frac{% \text{ change in } Q_d}{% \text{ change in } P} $

Or in differential form:

$ PED = \frac{dQ}{dP} \times \frac{P}{Q} $

Why percentages? Absolute changes depend on the units of measurement. “Demand increased by 100 units”—is that a lot or a little? It depends on the scale. “Demand increased by 10%”—is universally clear.

Sign of PED: according to the law of demand, $P$ and $Q$ move in opposite directions. PED is usually negative. Often, the absolute value $|PED|$ is taken for convenience.

Midpoint Formula (Midpoint Method)

When calculating elasticity between two points, a problem arises: from which point should the percentage be calculated? The midpoint formula solves this problem:

$ PED = \frac{(Q_2 - Q_1) / \left( \frac{Q_1 + Q_2}{2} \right)}{(P_2 - P_1) / \left( \frac{P_1 + P_2}{2} \right)} $

Or, more simply:

$ PED = \frac{(Q_2 - Q_1) / (Q_1 + Q_2)}{(P_2 - P_1) / (P_1 + P_2)} $

Example: the price increased from $4 to $6, the quantity decreased from 100 to 80.
$\Delta Q = -20$, average $Q = 90$
$\Delta P = 2$, average $P = 5$

$ PED = \frac{-20/90}{2/5} = \frac{-0.222}{0.4} = -0.56 $

Classification by Elasticity

• $|PED| > 1$ — elastic demand:
  The percentage change in $Q$ is greater than the percentage change in $P$
  Consumers are sensitive to price
  Examples: luxury goods, goods with close substitutes

• $|PED| < 1$ — inelastic demand:
  The percentage change in $Q$ is less than the percentage change in $P$
  Consumers are not very sensitive to price
  Examples: necessities, goods without substitutes, goods associated with addiction

• $|PED| = 1$ — unit elasticity:
  Percentage changes are equal
  Revenue does not change when the price changes

• $|PED| = 0$ — perfectly inelastic demand:
  Quantity does not react to price
  The demand curve is vertical
  Rarely occurs: life-saving medications

• $|PED| = \infty$ — perfectly elastic demand:
  Any price increase eliminates demand
  The demand curve is horizontal
  Perfect competition: firm is a price taker

Elasticity Along a Linear Demand Curve

An important insight: elasticity changes along a linear demand curve, even if the slope is constant!

• At the upper part of the curve (high price, small quantity): demand is elastic.
  A small change in $Q$ is a large percentage of a small $Q$.
• At the lower part (low price, large quantity): demand is inelastic.
  A large change in $Q$ is a small percentage of a large $Q$.
• In the middle: unit elasticity.

Slope ≠ Elasticity: slope is the absolute change ($\Delta Q / \Delta P$), elasticity is relative.
Constant slope, variable elasticity.

Factors Determining Elasticity

• Availability of Substitutes:
  Many close substitutes → elastic demand
  Unique product → inelastic demand
  Butter vs a specific brand of butter: the latter is more elastic

• Share in the Budget:
  Larger share of expenditures → more elastic
  Small expenses—we do not pay attention to price

• Necessity vs Luxury:
  Necessities—inelastic
  Luxuries—elastic

• Time:
  Short term—more inelastic (hard to adapt)
  Long term—more elastic (can find substitutes, change habits)

• Market Definition:
  Narrowly defined market (Coca-Cola)—more elastic
  Broadly defined (soft drinks)—more inelastic

Elasticity and Revenue

A key relationship for business:

$ \text{Total Revenue (TR)} = P \times Q $

When the price changes:
$P$ increases → direct positive effect on TR
$Q$ falls → opposing negative effect on TR
The result depends on elasticity.

• Elastic demand ($|PED| > 1$):
  Price increase → TR falls (Q drops more than P rises)
  Price decrease → TR rises

• Inelastic demand ($|PED| < 1$):
  Price increase → TR rises (P rises more than Q falls)
  Price decrease → TR falls

• Unit elasticity:
  TR does not change when the price changes

Practical conclusion: if demand is inelastic—you can raise the price and increase revenue. If it is elastic—a price reduction will increase revenue.

For the Investor

• Pricing power: companies with inelastic demand have pricing power—they can raise prices without a substantial loss in sales. This is margin protection in an inflationary environment. Examples: brands with loyal audiences, companies with network effects, monopolists, producers of necessity goods.

• Competitive analysis: demand elasticity for a firm's product depends on industry competitive structure. High competition = high elasticity = price and margin pressure.