Cross-Price Elasticity and Income Elasticity

Cross-Price Elasticity and Income Elasticity Price elasticity of demand is only one type of elasticity. Demand depends not only on the price of the good itself, but also on the prices of other goods and on the income of consumers. These relationships are measured by cross-price elasticity and income elasticity.

Cross-price elasticity of demand

Cross-price elasticity of demand (XED) measures how the demand for good A responds to a change in the price of good B:

$ \text{XED} = \frac{%\ \text{change in } Q_d \text{ of good } A}{%\ \text{change in } P \text{ of good } B} $

The sign of XED determines the relationship between goods:

• XED

  gt; 0$ — substitute goods: an increase in B's price raises demand for A
  Consumers switch from the more expensive good
  Examples: Coca-Cola and Pepsi, butter and margarine, bus and metro
  The higher the XED, the closer the substitutes

• XED

  lt; 0$ — complementary goods: an increase in B's price lowers demand for A
  Goods are consumed together
  Examples: cars and gasoline, printers and cartridges, smartphones and applications

• XED $\approx 0$ — independent goods: No link between demand for A and price of B
  Examples: bread and automobiles

Practical significance of XED

• Market definition: antitrust authorities use XED to determine market boundaries.
  High positive XED = one market (goods are competing). Low XED = different markets.
• Competitive strategy: understanding substitutes and complements is critical for business. Who are the real competitors? Whose price increases help/hurt?
• Complement pricing: classic strategy — low price on the main product, high price on complements (printers and ink, razors and blades).

Income elasticity of demand

Income elasticity of demand (YED) measures how demand responds to changes in consumer income:

$ \text{YED} = \frac{%\ \text{change in } Q_d}{%\ \text{change in income}} $

The sign of YED determines the type of good:

• YED
  gt; 0$ — normal goods: Rising income increases demand
  Most goods are normal
• YED
  lt; 0$ — inferior goods: Rising income reduces demand
  Consumers "outgrow" the good
  Examples: cheap food, public transport (for some), used goods

Classification of normal goods

• $0 < \text{YED} < 1$: Demand grows slower than income
  Share of budget decreases as income rises
  Examples: food, basic clothing, utilities
  Engel's Law: the share of food expenditures falls as income grows
• YED
  gt; 1$ — luxury goods:
  Demand grows faster than income
  Share of budget increases as income grows
  Examples: restaurants, travel, designer clothing, jewelry

Practical applications of YED

• Demand forecasting: in economic growth, demand for luxury rises faster than for the economy as a whole. In recessions — it falls faster.
• Sectoral analysis:
  • Defensive sectors (low YED): food, utilities, healthcare — stable demand during recessions
  • Cyclical sectors (high YED): automobiles, consumer electronics, tourism — volatile demand
• Positioning: companies can choose segments with different YED. Mass market vs. luxury — different sensitivity to economic cycles.

Price Elasticity of Supply

Price Elasticity of Supply (PES) measures the supply response to a change in price:

$ \text{PES} = \frac{%\ \text{change in } Q_s}{%\ \text{change in } P} $

PES is usually positive (law of supply).

Factors determining PES:

• Time:
  • Immediate period: PES $\approx 0$ (fixed stock)
  • Short run: low PES (limited capacity)
  • Long run: high PES (new capacity, new firms)
• Resource mobility:
  Easy to reallocate resources $\rightarrow$ high PES
  Specific assets $\rightarrow$ low PES
• Inventories:
  Ability to store $\rightarrow$ high short-term PES
  Perishable goods $\rightarrow$ low PES
• Excess capacity:
  Underutilization $\rightarrow$ high PES
  Full capacity $\rightarrow$ low PES

Elasticity and tax burden

The combination of demand and supply elasticity determines the distribution of the tax burden:

• Rule: the less elastic side bears the greater share of the tax.
• If demand is inelastic, supply is elastic: consumers pay most of the tax (producers readily exit).
• If supply is inelastic, demand is elastic: producers pay most (consumers readily exit).

For the investor

A comprehensive XED analysis helps to understand:

• Who are the company's competitors?
• How does a change in competitors’ prices affect sales?
• Which complementary markets are critical?

YED helps to understand:

• How cyclical is the company?
• How will economic growth/recession affect revenue?
• Is this a defensive or growth investment?

PES helps to understand:

• How quickly does the industry respond to price changes?
• Are high prices sustainable or will supply quickly increase?
• Are there barriers to expansion?