Cambridge IGCSE0455

Price elasticity of demand (PED)

Economics 0455 Chapter Notes

What this chapter covers

Price elasticity of demand (PED) - Definition of PEDPrice elasticity of demand (PED) - Calculation of PEDPrice elasticity of demand (PED) - Determinants of PEDPrice elasticity of demand (PED) - PED, consumer expenditure and firms’ revenuePrice elasticity of demand (PED) - Significance of PED
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In this chapter

  1. 1Defining and Calculating PED
  2. 2Interpreting PED Values
  3. 3PED and Total Revenue
  4. 4Determinants of PED
  5. 5Special Cases of Elasticity

1. Defining and Calculating PED

Price elasticity of demand (PED) measures how much the quantity demanded of a product changes in response to a change in its price. In simple terms, it tells us how 'sensitive' consumers are to price changes. If a small price change causes a large change in demand, we call it 'price elastic'. If a price change has little effect on demand, it's 'price inelastic'. We calculate it by comparing the percentage change in quantity demanded to the percentage change in price that caused it.

PED = (% Change in Quantity Demanded) / (% Change in Price)

% Change in Quantity Demanded = [(New Quantity - Original Quantity) / Original Quantity] × 100

% Change in Price = [(New Price - Original Price) / Original Price] × 100

Key term

Price Elasticity of Demand (PED): A measure of the responsiveness of the quantity demanded of a good to a change in its price.

Examiner insight

Examiners look for the correct application of the formula, including showing the working for calculating the percentage changes. Simply stating the final answer will not earn full marks.

Common pitfall

A common mistake is to divide the change in price by the change in quantity, or to forget to calculate the changes in percentage terms. Always use the formula: %ΔQd / %ΔP.

Worked example 13 marks

The price of a smartphone rises from $500 to $550. As a result, weekly demand falls from 1,000 units to 850 units. Calculate the price elasticity of demand.

  1. 1

    Step 1: Calculate the percentage change in price. Change in price = $550 - $500 = $50. % Change in Price = ($50 / $500) × 100 = 10%.

  2. 2

    Step 2: Calculate the percentage change in quantity demanded. Change in quantity = 850 - 1,000 = -150. % Change in Quantity Demanded = (-150 / 1,000) × 100 = -15%.

  3. 3

    Step 3: Calculate PED using the formula. PED = (% Change in Qd) / (% Change in Price) = -15% / 10% = -1.5.

Recap

  • PED measures the responsiveness of quantity demanded to a price change.
  • The formula for PED is the percentage change in quantity demanded divided by the percentage change in price.
  • Always use the original price and quantity as the base for your percentage calculations.
  • A negative sign in the result simply shows the inverse relationship between price and quantity demanded.

Quick check

  1. If the price of a good increases by 20% and the quantity demanded falls by 10%, what is the PED?2 marks

2. Interpreting PED Values

The numerical value of PED tells us the type of price elasticity. We usually ignore the negative sign (using the absolute value) when interpreting it. There are three main categories:

  1. Price Elastic (PED > 1): The percentage change in quantity demanded is greater than the percentage change in price. Demand is highly responsive to price changes.
  2. Price Inelastic (PED < 1): The percentage change in quantity demanded is less than the percentage change in price. Demand is not very responsive to price changes.
  3. Unitary Elastic (PED = 1): The percentage change in quantity demanded is exactly the same as the percentage change in price.

Key term

Price Inelastic Demand: A situation where the percentage change in quantity demanded is smaller than the percentage change in price, resulting in a PED value between 0 and 1.

Worked example 13 marks

A product has a PED of 0.6. If the firm increases its price by 15%, what will be the effect on quantity demanded? Is the demand for this product price elastic or price inelastic?

  1. 1

    Step 1: Interpret the PED value. Since 0.6 is less than 1, the demand for the product is price inelastic.

  2. 2

    Step 2: Calculate the percentage change in quantity demanded. Rearrange the formula: %ΔQd = PED × %ΔP.

  3. 3

    Step 3: Substitute the values: %ΔQd = 0.6 × 15% = 9%.

  4. 4

    Step 4: State the final effect. The quantity demanded will fall by 9%.

Worked example 22 marks

The demand curve for a product is relatively flat. Does this suggest its demand is price elastic or price inelastic? Explain your answer.

  1. 1

    Step 1: Relate the curve's shape to elasticity. A relatively flat demand curve indicates that demand is price elastic.

  2. 2

    Step 2: Explain why. A flat curve shows that a small percentage change in price (a small vertical change on the graph) leads to a large percentage change in quantity demanded (a large horizontal change).

Recap

  • If PED > 1, demand is price elastic.
  • If PED < 1, demand is price inelastic.
  • If PED = 1, demand has unitary elasticity.
  • A steep demand curve represents inelastic demand, while a flat demand curve represents elastic demand.
  • For interpretation, we typically use the absolute value of PED, ignoring the minus sign.

Quick check

  1. A good has a PED of 2.4. Is its demand price elastic or inelastic?1 mark

3. PED and Total Revenue

Understanding PED is crucial for firms when making pricing decisions, as it directly impacts their total revenue (TR = Price × Quantity). The relationship is key:

  • If demand is Price Elastic (PED > 1): A price cut leads to a proportionally larger increase in quantity sold, so Total Revenue increases. A price rise causes TR to fall.
  • If demand is Price Inelastic (PED < 1): A price rise leads to a proportionally smaller decrease in quantity sold, so Total Revenue increases. A price cut causes TR to fall.
  • If demand is Unitary Elastic (PED = 1): A change in price leads to an equal proportional change in quantity, so Total Revenue remains unchanged.

Total Revenue (TR) = Price (P) × Quantity Demanded (Qd)

Key term

Total Revenue: The total income a firm receives from the sale of its output, calculated by multiplying the price per unit by the quantity of units sold.

Fun fact

Airlines are experts at using PED. They charge high prices for last-minute flights to business travellers, who have inelastic demand, and offer lower prices for advance-booked holidays to leisure travellers, who have elastic demand. This is called price discrimination.

Worked example 15 marks

A cinema sells 500 tickets per night at a price of $12 each. It estimates the PED for tickets is 1.8. To increase total revenue, should the cinema raise or lower its price? Explain your answer with calculations.

  1. 1

    Step 1: Identify the type of elasticity. PED is 1.8, which is greater than 1, so demand is price elastic.

  2. 2

    Step 2: State the rule for elastic demand and revenue. When demand is price elastic, a firm should lower its price to increase total revenue.

  3. 3

    Step 3: Demonstrate with an example. Let's assume a 10% price cut. New Price = $12 × 0.90 = $10.80.

  4. 4

    Step 4: Calculate the effect on quantity. %ΔQd = PED × %ΔP = 1.8 × 10% = 18%. New Quantity = 500 × 1.18 = 590 tickets.

  5. 5

    Step 5: Compare old and new revenue. Old TR = 500 × $12 = $6,000. New TR = 590 × $10.80 = $6,372.

  6. 6

    Step 6: Conclude. Since the new total revenue ($6,372) is higher than the old revenue ($6,000), the cinema should lower its price.

Recap

  • For elastic demand, price and total revenue move in opposite directions.
  • For inelastic demand, price and total revenue move in the same direction.
  • For unitary demand, total revenue is maximised and does not change with price.
  • Firms can use knowledge of PED to set prices that will help them achieve their revenue goals.

Quick check

  1. A train company operates a route with highly inelastic demand. If it wants to increase its revenue, what should it do to its ticket prices?1 mark

4. Determinants of PED

The PED for a product is not random; it is determined by several factors. Understanding these helps to predict whether demand for a good will be elastic or inelastic. The key determinants are:

  1. Availability of Substitutes: The more close substitutes a good has, the more elastic its demand. If the price of one brand of coffee rises, consumers can easily switch to another.
  2. Necessity vs. Luxury: Necessities (e.g., bread, water, medicine) tend to have inelastic demand because people need them regardless of price. Luxuries (e.g., sports cars, designer watches) have more elastic demand.
  3. Proportion of Income: Goods that take up a large proportion of a person's income (e.g., a car, a holiday) tend to have more elastic demand. Goods that are very cheap (e.g., a box of matches) have inelastic demand.
  4. Time Period: Demand tends to be more elastic over a longer period. If petrol prices rise, people may not change their habits overnight (inelastic), but over time they might buy a more fuel-efficient car or move closer to work (elastic).

Key term

Substitutes: Goods that can be used in place of one another to satisfy a consumer's want, such as different brands of cola.

Examiner insight

Top-level answers don't just list the determinants. They select the most relevant ones for the specific product in the question and explain precisely *how* they affect consumer responsiveness to price changes.

Worked example 14 marks

Explain why the PED for table salt is likely to be very low (highly inelastic).

  1. 1

    Step 1: Identify relevant determinants. The key factors for salt are that it is a necessity, has few direct substitutes, and represents a very small proportion of a person's income.

  2. 2

    Step 2: Explain the 'necessity' factor. Salt is considered a basic food item by most households, so they will continue to buy it even if the price increases slightly.

  3. 3

    Step 3: Explain the 'proportion of income' factor. A box of salt is very cheap. Even if its price doubles, the impact on a household's budget is tiny, so consumers are unlikely to change their purchasing behaviour.

  4. 4

    Step 4: Explain the 'substitutes' factor. While there are other seasonings, there are no perfect substitutes for salt itself, making it difficult for consumers to switch.

Recap

  • More substitutes means more elastic demand.
  • Necessities tend to be inelastic; luxuries tend to be elastic.
  • Goods that are a large part of one's budget have more elastic demand.
  • Demand becomes more elastic over longer periods of time.
  • Habit-forming or addictive goods, like cigarettes, tend to have very inelastic demand.

Quick check

  1. Name two factors that would make the demand for a specific brand of car, like a Ford Focus, relatively price elastic.2 marks

5. Special Cases of Elasticity

Besides the main categories, there are three theoretical special cases of PED, which are represented by unique demand curves.

  1. Perfectly Inelastic Demand (PED = 0): Quantity demanded does not change at all, no matter what happens to the price. This is shown by a vertical demand curve. While rare in reality, a life-saving drug might come close.
  2. Perfectly Elastic Demand (PED = ∞): Consumers will buy all they can at one specific price, but any increase in price, no matter how small, will cause demand to drop to zero. This is shown by a horizontal demand curve. This applies to individual producers in a perfectly competitive market, like a single farmer selling wheat.
  3. Unitary Elastic Demand (PED = 1): The percentage change in quantity demanded is exactly equal to the percentage change in price. As a result, total revenue remains constant when price changes. The curve is a rectangular hyperbola.

PED = 0 (Perfectly Inelastic)

PED = ∞ (Perfectly Elastic)

PED = 1 (Unitary Elastic)

Key term

Perfectly Inelastic Demand: A situation where quantity demanded shows no response whatsoever to a change in price, represented by a vertical demand curve and a PED value of 0.

Common pitfall

Confusing a very steep (highly inelastic) curve with a perfectly vertical (perfectly inelastic) curve. An exam question asking for a 'perfectly inelastic' curve requires a line that is exactly vertical.

Worked example 13 marks

A diagram shows a horizontal demand curve for a firm's product at a price of $5.(a) What is the PED for this product?(b) What would happen to the firm's sales if it raised its price to $5.01?

  1. 1

    Step 1 (a): Identify the curve shape. A horizontal demand curve represents perfectly elastic demand.

  2. 2

    Step 2 (a): State the PED value. For perfectly elastic demand, the PED is infinite (∞).

  3. 3

    Step 3 (b): Explain the consequence of a price change. With perfectly elastic demand, consumers are only willing to buy at the market price of $5. If the firm raises its price to $5.01, its quantity demanded and sales would fall to zero as consumers would switch to identical products from other firms.

Recap

  • A vertical demand curve means demand is perfectly inelastic (PED = 0).
  • A horizontal demand curve means demand is perfectly elastic (PED = ∞).
  • A rectangular hyperbola curve means demand is unitary elastic (PED = 1).
  • These are theoretical extremes but help in understanding the concept of elasticity.

Quick check

  1. What is the value of PED for a good with a vertical demand curve?1 mark

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Define 'price elasticity of demand' and state the formula used to calculate it.3 marks
  2. The price of a bus ticket rises from $2.00 to $2.50. As a result, the number of passengers per day falls from 1,200 to 1,000. Calculate the PED for bus tickets and state whether demand is price elastic or price inelastic.4 marks
  3. A business selling luxury watches knows that the PED for its product is 2.2. Explain the pricing strategy it should use if it wishes to increase its total revenue.4 marks
  4. Explain two reasons why the demand for petrol is price inelastic in the short run.4 marks
  5. Draw a fully labelled diagram showing a perfectly elastic demand curve. Give an example of a market where a firm might face such a curve.3 marks
  6. A government wants to reduce the consumption of sugary drinks by 15%. If the PED for these drinks is estimated to be 0.75, by what percentage must the price of the drinks increase to meet this target?3 marks
  7. Analyse why the PED for a foreign holiday is likely to be significantly different from the PED for a loaf of bread.6 marks
  8. A rock band sells 20,000 tickets for its concert at a price of $80 per ticket. It decides to lower the price to $70 and finds that it sells 25,000 tickets. a) Calculate the PED for the concert tickets. b) Did the decision to lower the price increase the band's total revenue?5 marks
  9. Explain how the passage of time affects the price elasticity of demand for a product.3 marks
  10. Using the concepts of PED and total revenue, explain why a shop might put a '50% off' sale on last season's fashion clothing but would not do the same for milk.6 marks

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