Price elasticity, income elasticity and cross elasticity of demand

Welcome to Elasticity Central!

Hi there! This chapter is one of the most practical and useful parts of microeconomics. If you understand elasticity, you understand how businesses and governments predict reactions in the market. It is essentially the science of measuring how sensitive people are to changes in prices, income, or the price of related goods.

Don't worry if the formulas look scary. We are dealing with percentages, which makes everything straightforward! Elasticity is simply a ratio of how much one thing changes relative to another.

Key Concept: Elasticity measures responsiveness.

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1. Price Elasticity of Demand (PED)

Price Elasticity of Demand (PED) measures how much the quantity demanded (\(Q_d\)) of a good responds to a change in its own price (\(P\)).

1.1 The PED Formula and Calculation

The calculation uses percentage changes, not absolute changes, so we can compare the sensitivity of different products (like yachts vs. bread).

Definition and Formula

Definition: The ratio of the percentage change in quantity demanded to the percentage change in price.

\( \text{PED} = \frac{\%\Delta Q_d}{\%\Delta P} \)

A Quick Note on Sign: Since demand curves are generally downward sloping (Law of Demand), the PED coefficient will always be negative. When price goes up (+), quantity demanded goes down (–). However, for simplicity and analysis, economists usually use the absolute value of PED (ignore the negative sign).

How to Calculate Percentage Change

If you need to calculate the percentage change for a numerical question:

\( \text{\% Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100 \)

(Tip: The syllabus covers the significance of relative percentage changes. If the numerator – \(\%\Delta Q_d\) – is larger than the denominator – \(\%\Delta P\) – then the result will be greater than 1, meaning demand is elastic.)

1.2 Interpreting the PED Coefficient (The Size of the Number)

The size of the PED coefficient tells us whether demand is sensitive (elastic) or insensitive (inelastic).

• Elastic Demand (\(\text{PED} > 1\)): Buyers are highly responsive. If the price changes by 1%, the quantity demanded changes by more than 1%. (Example: Cereal – if the price goes up, people easily switch brands.)
• Inelastic Demand (\(\text{PED} < 1\)): Buyers are not very responsive. If the price changes by 1%, the quantity demanded changes by less than 1%. (Example: Essential medicine or fuel – you need it regardless of a small price hike.)
• Unitary Elasticity (\(\text{PED} = 1\)): Quantity demanded changes by exactly the same percentage as the price change.

Extreme Cases

• Perfectly Elastic (\(\text{PED} = \infty\)): Consumers will only buy at one specific price. If the price rises even slightly, demand drops to zero (horizontal demand curve).
• Perfectly Inelastic (\(\text{PED} = 0\)): Quantity demanded does not change at all, regardless of the price change (vertical demand curve). (Example: Life-saving drug with no substitutes.)

1.3 Variation in PED Along a Straight-Line Demand Curve

A common misconception is that a straight-line (linear) demand curve has constant elasticity because its slope is constant. However, slope and elasticity are not the same thing.

Because PED is calculated using percentage changes rather than absolute changes, the value of PED changes continuously along the length of a downward-sloping linear demand curve:

• Top Half (High Prices, Low Quantities): Demand is price elastic (\(\text{PED} > 1\)). At high price levels, a small absolute change in price is a small percentage change, but starting from a low quantity, the change in quantity represents a large percentage change.
• Midpoint of the Demand Curve: Demand has unitary elasticity (\(\text{PED} = 1\)). Total revenue is maximized at this point.
• Bottom Half (Low Prices, High Quantities): Demand is price inelastic (\(\text{PED} < 1\)). At low price levels, a small absolute change in price is a large percentage change, while from a large quantity base, the change in quantity represents a small percentage change.

1.4 Factors Affecting PED (A-N-I-S-E Mnemonic)

The level of elasticity depends on several factors. A good mnemonic to remember these is A-N-I-S-E:

1. A: Availability of Substitutes: This is the most important factor. The more substitutes available, the easier it is for consumers to switch when the price rises. Demand will be elastic. (Example: If Brand A coffee raises its price, consumers can easily buy Brand B.)
2. N: Necessity vs. Luxury: Necessities (like basic food or water) tend to have inelastic demand because consumers must buy them. Luxuries (like sports cars) tend to have elastic demand because purchases can be postponed.
3. I: Income Proportion: The greater the proportion of consumer income spent on the good, the more elastic the demand. (Example: A 10% price rise on a car feels significant; a 10% rise on salt feels negligible.)
4. S: Scope (or Definition) of the Market: Demand for a narrowly defined market (e.g., Puma running shoes) is more elastic than a broadly defined market (e.g., all footwear), as there are more substitutes within the narrow category.
5. E: Time Period: Demand is generally more elastic in the long run. Given more time, consumers can find new substitutes or adjust their consumption habits. (Example: If petrol prices rise today, people still need to drive. But over several years, they might switch to electric vehicles or public transit.)

1.5 PED and Total Expenditure (Total Revenue)

For a firm, understanding PED is critical because it tells them whether raising or lowering the price will increase their Total Revenue (TR), which is calculated as Price (\(P\)) \(\times\) Quantity (\(Q\)).

• If Demand is Elastic (\(\text{PED} > 1\)): A price increase leads to a proportionally larger drop in quantity demanded. Therefore, to increase TR, the firm must lower the price.
• If Demand is Inelastic (\(\text{PED} < 1\)): A price increase leads to a proportionally smaller drop in quantity demanded. Therefore, to increase TR, the firm must raise the price.
• If Demand is Unitary (\(\text{PED} = 1\)): Changing the price will leave total revenue unchanged.

Quick Memory Aid:
If demand is Elastic, price movement and revenue movement are opposite (\(P\uparrow, \text{TR}\downarrow\)).
If demand is Inelastic, price movement and revenue movement are in sync (\(P\uparrow, \text{TR}\uparrow\)).

Key Takeaway (PED)

PED tells a firm how effective a price change will be in achieving revenue goals. Firms selling inelastic goods have greater pricing power (e.g., monopolies).

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2. Income Elasticity of Demand (YED)

Income Elasticity of Demand (YED) measures how much the quantity demanded (\(Q_d\)) of a good responds to a change in consumer income (\(Y\)).

2.1 The YED Formula and Calculation

Definition and Formula

Definition: The ratio of the percentage change in quantity demanded to the percentage change in income.

\( \text{YED} = \frac{\%\Delta Q_d}{\%\Delta Y} \)

2.2 Interpreting the YED Coefficient (The Sign and Size)

Unlike PED, the sign of the YED coefficient is crucial, as it tells us what type of good we are analyzing.

1. Normal Goods (\(\text{YED} > 0\), or Positive)

If income rises, demand for the good rises. Most goods are normal goods.

• Necessity Goods (\(0 < \text{YED} < 1\)): Demand rises with income, but less than proportionally. Consumers don't spend drastically more on necessities like bread or utility bills as their income increases.
• Luxury Goods (\(\text{YED} > 1\)): Demand rises with income more than proportionally. These goods (e.g., overseas holidays, designer clothes) are highly income-sensitive. A 10% rise in income could lead to a 20% rise in demand.

2. Inferior Goods (\(\text{YED} < 0\), or Negative)

If income rises, demand for the good falls. Consumers switch to higher-quality substitutes as they get richer.

Example: Generic supermarket brands, basic instant noodles, or bus transport (passengers switch to purchasing their own cars).

2.3 Factors Affecting YED

The primary factor affecting YED is the degree of necessity. Goods considered essential for basic living have a low, positive YED, while goods representing status or discretionary spending have a high, positive YED.

2.4 Implications of YED for Decision Making

• Firms (Forecasting): Companies use YED to forecast future sales based on expected economic growth (changes in national income). Firms selling luxury goods (high positive YED) thrive during economic expansions but experience sharper drops during recessions.
• Government (Taxation/Planning): Governments can evaluate how economic cycles affect living standards and demand for public services across different socio-economic groups.

Key Takeaway (YED)

YED determines if a product is a necessity, luxury, or inferior good, and predicts how sensitive sales will be to economic growth and downturns.

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3. Cross Elasticity of Demand (XED)

Cross Elasticity of Demand (XED) measures how much the quantity demanded (\(Q_d\)) of one good (Good A) responds to a change in the price (\(P\)) of a different good (Good B).

3.1 The XED Formula and Calculation

Definition and Formula

Definition: The ratio of the percentage change in quantity demanded of Good A to the percentage change in price of Good B.

\( \text{XED} = \frac{\%\Delta Q_d \text{ of Good A}}{\%\Delta P \text{ of Good B}} \)

3.2 Interpreting the XED Coefficient (The Sign and Size)

The sign of the XED coefficient determines the relationship between the two goods.

1. Substitute Goods (\(\text{XED} > 0\), or Positive)

If the price of Good B rises, the demand for Good A rises (as consumers switch). They are substitutes.

• Example: Tea and Coffee. If the price of coffee rises (+), the demand for tea rises (+). A positive/positive ratio gives a positive XED.
• The larger the positive number, the closer the substitutes.

2. Complementary Goods (\(\text{XED} < 0\), or Negative)

If the price of Good B rises, the demand for Good A falls (because they are consumed together). They are complements.

• Example: Printers and Ink Cartridges. If the price of ink cartridges rises (+), people buy fewer printers (–). A negative/positive ratio gives a negative XED.
• The larger the negative number (further below zero), the closer the complements.

3. Unrelated Goods (\(\text{XED} \approx 0\))

If the XED is zero or very close to zero, the goods are largely independent of one another. (Example: The price of car tyres and the demand for milk.)

3.3 Factors Affecting XED

The main factor is the closeness of the relationship. Are the goods easily swapped (close substitutes)? Or must they be used together (strong complements)?

3.4 Implications of XED for Decision Making

• Firms (Competition): Firms use XED to monitor competitors. If XED for their product relative to a rival's product is high and positive, they are close substitutes and the firm must react swiftly to rival price adjustments.
• Mergers/Antitrust: Competition authorities use XED to determine whether a merger between two companies creates excessive market dominance. A high XED indicates that the merging firms are strong direct competitors.

Key Takeaway (XED)

XED reveals market structure by identifying competitive (substitute) and joint-consumption (complementary) relationships between products.

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4. Summary of Elasticities and Decision Making (2.2.8)

4.1 Implications for Firms

Firms use elasticity estimates to make crucial operational decisions:

Pricing Strategy (PED)

• If a firm wants to maximize revenue, it must identify if its demand is elastic or inelastic.
• For inelastic goods (like monopolized utility services), the firm has the power to raise prices without a severe loss of sales.
• For elastic goods (like fast fashion), price reductions can attract sales and boost total revenue.

Product Mix and Recession Planning (YED)

• Firms selling high YED (luxury) goods must plan for sales to drop sharply during recessions.
• Firms that sell a mix of normal and inferior goods are more resilient, as sales of inferior product lines rise during economic downturns.

Competitive Strategy (XED)

• If XED is high and positive, the firm knows it is in direct competition and must closely monitor competitors' pricing.
• If XED is high and negative (complements), a firm selling a primary product (e.g., games console) might lower its price to stimulate demand for its complementary product (e.g., video games).

4.2 Implications for Government Policy

Governments rely heavily on PED and YED when implementing taxes, subsidies, and other regulatory measures.

Tax Revenue (PED)

• Governments place indirect taxes on goods with inelastic demand (e.g., alcohol, tobacco, fuel) to maximize tax yield. Because demand is inelastic, the higher price leads to only a small reduction in quantity demanded.
• Taxing goods with highly elastic demand causes a substantial contraction in output and generates less tax revenue.

Tax Burden (Incidence) (PED)

The incidence (who bears the economic burden of the tax) depends on elasticity:

• If demand is highly inelastic, consumers bear the majority of the tax burden (higher price passed on).
• If demand is highly elastic, producers bear the majority of the tax burden (producers cannot easily pass on the tax without losing most sales).

Welfare and Public Health (PED)

If the government aims to discourage consumption of harmful goods (demerit goods), knowing PED is essential. When demand is price inelastic, tax increases must be substantial to achieve a meaningful reduction in consumption.