Economics (9708) | 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’s 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 (The Easiest Way)

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 (2.2.3). 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 (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 (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 (PED = 1): Quantity demanded changes by exactly the same percentage as the price change.

Extreme Cases

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

1.3 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, I can easily buy Brand B.)
2. N: Necessity vs. Luxury: Necessities (like basic food or water) tend to have inelastic demand because you must buy them. Luxuries (like sports cars) tend to have elastic demand because you can easily postpone the purchase.
3. I: Income Proportion: The greater the proportion of a consumer's income spent on the good, the more elastic the demand. (Example: A 10% price rise on a house feels massive; a 10% rise on chewing gum 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 broad 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, you still need to drive. But over five years, you might buy an electric car.)

1.4 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 (\(P\)) x Quantity (\(Q\)).

• If Demand is Elastic (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 (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 (PED = 1): Changing the price will not change the total revenue.

Quick Memory Aid:

If demand is Elastic, price movement and revenue movement are opposite (P↑, TR↓).
If demand is Inelastic, price movement and revenue movement are in sync (P↑, TR↑).

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 (YED > 0, or Positive)

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

• Necessity Goods (0 < 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 (YED > 1): Demand rises with income more than proportionally. These goods (e.g., holidays, designer clothes) are very income-sensitive. A 10% rise in income could lead to a 20% rise in demand.

2. Inferior Goods (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, instant noodles, or public transport (people switch to driving their own car).

2.3 Factors Affecting YED

The primary factor affecting YED is the degree of necessity. Goods considered essential for basic living will have a low, positive YED, while goods representing status or discretionary spending will 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) will thrive during economic booms but suffer greatly during recessions.
• Government (Taxation/Planning): Governments can understand how living standards might change for different groups. For example, a recession (falling income) will disproportionately increase the demand for inferior goods.

Key Takeaway (YED)

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

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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 (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 (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 from zero), the closer the complements.

3. Unrelated Goods (XED ≈ 0)

If the XED is zero or very close to zero, the goods are largely unrelated. (Example: The price of car tires 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 their competition. If XED for their product with a rival's product is high and positive, they know they are close substitutes and must react swiftly to the rival's pricing strategies.
• Mergers/Antitrust: Governments often use XED to determine if a potential merger between two companies would create a monopoly. If the XED between them is high, they are strong competitors, and merging would significantly reduce competition.

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), heavy discounting or lowering prices is necessary to attract sales and capture market share.

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 may be more economically stable, as sales of their inferior lines may rise during downturns.

Competitive Strategy (XED)

• If XED is high and positive, the firm knows it is in direct competition and must match or beat rivals' price cuts immediately.
• If XED is high and negative (complements), a firm selling the primary product (e.g., games console) might lower its price to boost demand for the complementary product (e.g., 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 want to impose indirect taxes on goods with inelastic demand (e.g., alcohol, tobacco, fuel). This is because the rise in price due to the tax will cause a small drop in quantity demanded, ensuring the government collects maximum tax revenue.
• Conversely, taxing goods with elastic demand causes a huge reduction in consumption, making it an ineffective way to raise revenue.

Tax Burden (Incidence) (PED)

The incidence (who pays the tax) is determined by elasticity:

• If demand is highly inelastic, consumers bear most of the tax burden (they keep buying the product anyway).
• If demand is highly elastic, producers bear most of the tax burden (they cannot easily pass the cost onto the consumer).

Welfare and Public Health (PED)

If the government wants to discourage consumption (e.g., smoking), they must determine the PED. If the good is inelastic, taxation alone may not be effective unless the tax is extremely high.