Price elasticity of demand

1. Overview

Price Elasticity of Demand (PED) measures the responsiveness of the quantity demanded of a product to a change in its price. It is a critical metric for firms determining pricing strategies to maximize total revenue and for governments calculating the impact of indirect taxes or subsidies on consumption and tax yields. Essentially, PED quantifies how "sensitive" or "stretchy" consumer demand is when prices fluctuate.

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Key Definitions

• Price Elasticity of Demand (PED): A numerical measure of the responsiveness of quantity demanded for a product following a change in its price.
• Price Elastic: A situation where the percentage change in quantity demanded is greater than the percentage change in price (PED > 1). Consumers are highly sensitive to price changes.
• Price Inelastic: A situation where the percentage change in quantity demanded is less than the percentage change in price (PED < 1). Consumers are relatively unresponsive to price changes.
• Unitary Elastic: A situation where the percentage change in quantity demanded is exactly equal to the percentage change in price (PED = 1). Total revenue remains constant regardless of price changes.
• Perfectly Inelastic: A situation where quantity demanded remains constant regardless of any change in price (PED = 0). The demand curve is a vertical line.
• Perfectly Elastic: A situation where any increase in price causes quantity demanded to fall to zero (PED = $\infty$). The demand curve is a horizontal line.
• Percentage Change ($% \Delta$): The calculation used to determine the relative change in a variable: $\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100$.

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Core Content

The Concept of PED

PED allows economists to move beyond the basic Law of Demand (which states that as price rises, demand falls) by quantifying how much demand falls.

• If a 10% price increase leads to a 30% drop in demand, the product is elastic.
• If a 10% price increase leads to only a 2% drop in demand, the product is inelastic.

Degree of Elasticity: Inelastic Demand (PED < 1)

• Characteristics: The demand curve is steep. A large change in price results in a proportionately smaller change in quantity demanded.
• Determinants: This occurs for products that are necessities (e.g., basic food), addictive (e.g., tobacco), or have no close substitutes (e.g., specialized medicine).
• Diagram Description: On a P/Q axis, the demand curve (D) drops sharply. If you move from $P_1$ to a much higher $P_2$, the horizontal gap between $Q_1$ and $Q_2$ is very narrow.
• Real-World Example: Electricity. Most households cannot easily switch to an alternative energy source immediately if prices rise, so they continue to consume nearly the same amount.

Degree of Elasticity: Elastic Demand (PED > 1)

• Characteristics: The demand curve is shallow or flat. A small change in price results in a proportionately larger change in quantity demanded.
• Determinants: This occurs for luxury goods (e.g., cruises) or products with many substitutes (e.g., a specific brand of chocolate bar).
• Diagram Description: The demand curve (D) is relatively flat. A tiny vertical increase from $P_1$ to $P_2$ results in a massive horizontal shift from $Q_1$ to $Q_2$ to the left.
• Real-World Example: Foreign Holidays. If one airline raises its prices for flights to Paris, consumers can easily switch to another airline or choose a different destination entirely.

Factors Determining PED (The S.P.L.A.T. Framework)

1. Substitutes: The more close substitutes available, the more elastic demand becomes. If the price of Pepsi rises, consumers switch to Coca-Cola.
2. Proportion of Income: Goods that take up a large % of a consumer's budget (e.g., cars, houses) are more elastic. Goods that cost very little (e.g., matches, salt) are inelastic because consumers hardly notice a 10% price rise.
3. Luxury or Necessity: Necessities (water, bread) are inelastic. Luxuries (designer watches, sports cars) are elastic.
4. Addictiveness: Products that are habit-forming (cigarettes, alcohol, caffeine) have inelastic demand because consumers feel a physical or psychological need to continue buying them despite price hikes.
5. Time: In the short run, demand is often inelastic because it takes time for consumers to find alternatives. In the long run, demand becomes more elastic as consumers adjust their behavior (e.g., switching to electric cars after a permanent rise in petrol prices).

Impact on Decision-Making: Total Revenue (TR)

Firms use PED to decide whether to raise or lower prices to increase their Total Revenue (Price $\times$ Quantity).

• If Demand is Inelastic (PED < 1):

  • Action: Raise the price.
  • Reasoning: The % increase in price is greater than the % decrease in quantity demanded. The firm loses a few customers, but the higher price paid by the remaining customers more than compensates for the loss.
  • Result: Total Revenue increases.

• If Demand is Elastic (PED > 1):

  • Action: Lower the price.
  • Reasoning: The % increase in quantity demanded will be greater than the % decrease in price. The massive influx of new customers outweighs the lower price per unit.
  • Result: Total Revenue increases.

• If Demand is Unitary Elastic (PED = 1):

  • Action: Price changes do not affect revenue.
  • Result: Total Revenue remains unchanged.

Evaluation: Advantages and Disadvantages of PED Knowledge

• For Firms:
  • Advantage: Allows for price discrimination (charging different prices to different groups based on their PED, like peak vs. off-peak train tickets) to maximize profit.
  • Disadvantage: PED is difficult to calculate precisely in the real world as consumer tastes and competitor prices change constantly.
• For Governments:
  • Advantage: Helps in setting tax policy. To raise high tax revenue, governments tax goods with inelastic demand (tobacco, fuel). To discourage consumption of harmful goods, they must understand that if demand is inelastic, a very high tax is needed to significantly reduce quantity.
  • Disadvantage: Taxing inelastic necessities (like salt or heating oil) is regressive, meaning it hurts low-income households more than high-income ones.

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Worked example 1 — Calculating and Interpreting PED

Question: A bakery sells 200 loaves of premium sourdough bread per week at a price of \US$5.00 each. The baker decides to increase the price to \US$6.00. As a result, the quantity demanded falls to 140 loaves per week.

1. Calculate the Price Elasticity of Demand (PED).
2. State whether the demand is elastic or inelastic.

Model Answer:

1. Calculate % Change in Quantity Demanded: $\frac{140 - 200}{200} \times 100 = -30%$
2. Calculate % Change in Price: $\frac{6.00 - 5.00}{5.00} \times 100 = +20%$
3. Calculate PED: $\text{PED} = \frac{-30%}{20%} = -1.5$
4. Interpretation: The PED is 1.5 (ignoring the minus sign). Since 1.5 is greater than 1, the demand for the sourdough bread is price elastic.

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Worked example 2 — PED and Business Strategy

Question: A local bus company is facing a budget deficit and needs to increase its total revenue. An economist informs the company that the PED for bus travel in the area is 0.4. Explain what strategy the bus company should adopt regarding its ticket prices and why.

Model Answer:

• Strategy: The bus company should increase its ticket prices.
• Explanation: A PED of 0.4 indicates that demand is price inelastic (less than 1). This means that the percentage change in quantity demanded will be smaller than the percentage change in price.
• Chain of Reasoning: If the company raises fares, some passengers may switch to walking or cycling, but because the service is likely a necessity for commuting with few immediate substitutes, the majority of passengers will continue to use the bus. The gain in revenue from the higher price per ticket will outweigh the loss in revenue from the small drop in passenger numbers. Therefore, total revenue will increase, helping to reduce the budget deficit.

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Extended Content (Extended Only)

Incidence of Taxation

PED determines who actually pays an indirect tax (like a sales tax or GST).

• Inelastic Demand: If the government imposes a tax on an inelastic good (e.g., cigarettes), the firm can pass most of the tax onto the consumer in the form of higher prices. The consumer burden is greater than the producer burden.
• Elastic Demand: If a tax is imposed on an elastic good (e.g., a specific brand of luxury chocolate), the firm cannot raise the price much without losing almost all its customers. Therefore, the firm must "absorb" most of the tax. The producer burden is greater than the consumer burden.

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Key Equations

1. Price Elasticity of Demand (PED) $$\text{PED} = \frac{% \Delta \text{ Quantity Demanded}}{% \Delta \text{ Price}}$$

2. Percentage Change ($% \Delta$) $$% \Delta = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100$$

3. Total Revenue (TR) $$\text{TR} = \text{Price} \times \text{Quantity Sold}$$

Note: PED is mathematically negative because of the inverse relationship between price and quantity. In the IGCSE exam, you can usually provide the absolute value (e.g., 1.5 instead of -1.5) unless specifically asked for the sign.

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Common Mistakes to Avoid

• Confusing Slope with Elasticity: A straight-line demand curve does not have constant elasticity. PED is higher at the top of the curve (high price, low quantity) and lower at the bottom.
• Mixing up the Formula: Always put Quantity on top and Price on the bottom. A common error is calculating $\frac{% \Delta P}{% \Delta QD}$.
• Ignoring the "Proportionate" Rule: Don't just say "demand changes." You must use the phrase "proportionately more" (for elastic) or "proportionately less" (for inelastic) to get full marks in analysis.
• Perfectly Inelastic vs. Relatively Inelastic: A vertical line is perfectly inelastic (PED=0). A steep curve is relatively inelastic (PED < 1). Do not use these terms interchangeably.

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Exam Tips

• Show Your Workings: In "Calculate" questions, write down the formula and the intermediate percentage changes. If you make a small calculator error but the method is clear, you will still earn "own figure rule" (OFR) marks.
• The Revenue Test: If a question asks how a firm can increase revenue, check the PED.
  • Inelastic? $\rightarrow$ Raise Price.
  • Elastic? $\rightarrow$ Lower Price.
• Use the "SPLAT" acronym: When asked to "Identify factors that influence the PED of a product," use SPLAT to quickly recall Substitutes, Proportion of income, Luxury/Necessity, Addictiveness, and Time.
• Evaluation Command Words: If the question asks you to "Evaluate whether a government should increase tax on petrol," you must look at both sides.
  • Side 1: Yes, because demand is inelastic, so tax revenue will be high.
  • Side 2: However, it might increase costs for businesses (transport) and hurt low-income drivers (regressive impact).
• Time Horizon: Always mention that demand is more inelastic in the short run and more elastic in the long run. This is a high-level evaluative point that examiners look for.

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Exam-Style Questions

Practice these original exam-style questions to test your understanding. Each question mirrors the style, structure, and mark allocation of real Cambridge 0455 papers.

Exam-Style Question 1 — Short Answer [6 marks]

Question:

A small island nation, Isla Paradiso, relies heavily on imported bananas. The government is considering imposing a tax on banana imports.

(a) Define 'price elasticity of demand'. [2]

(b) Explain two factors that might influence the price elasticity of demand for bananas in Isla Paradiso. [4]

Worked Solution:

(a)

1. Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in price. [Understanding the core concept] [B1]
2. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. [Defining the calculation] [B1] $\boxed{PED = \frac{% \Delta Q_d}{% \Delta P}}$

How to earn full marks: Give both the conceptual definition and the formula for PED. Don't just state the formula without explaining what it means.

(b)

1. Availability of substitutes: If there are many readily available substitutes for bananas, such as other fruits grown locally, the demand for bananas will be more price elastic. A small price increase will cause consumers to switch to alternatives. [Identifying a factor] [M1] This is because consumers have alternatives to turn to if the price of bananas increases. [Explaining the impact] [A1]
2. Necessity vs. Luxury: If bananas are considered a staple food or a necessity for the population of Isla Paradiso, the demand will be more price inelastic. Consumers will continue to purchase bananas even if the price increases, as they are essential to their diet. [Identifying a factor] [M1] This is because consumers may not be able to easily reduce their consumption of bananas. [Explaining the impact] [A1]

How to earn full marks: For each factor, clearly identify the factor, then explain how it affects the PED, linking it back to consumer behavior.

Common Pitfall: Many students confuse price elasticity of demand with income elasticity of demand. Remember that PED focuses on how quantity demanded changes in response to price changes, not income changes.

Exam-Style Question 2 — Extended Response [12 marks]

Question:

A large multinational coffee chain, "Brewtopia," is planning to open several new stores in a developing country where coffee consumption is relatively low. Brewtopia is considering two pricing strategies: a high-price strategy targeting wealthier consumers, or a low-price strategy to attract a broader customer base.

(a) Analyse how the price elasticity of demand for coffee in this developing country might influence Brewtopia's choice of pricing strategy. [6]

(b) Discuss the potential advantages and disadvantages for Brewtopia of adopting a low-price strategy, considering the concept of price elasticity of demand. [6]

Worked Solution:

(a)

1. If the price elasticity of demand for coffee is elastic (PED > 1), it means that consumers are very responsive to price changes. [Defining elastic demand] [B1] A small decrease in price will lead to a proportionally larger increase in quantity demanded. Brewtopia could then adopt a low-price strategy to increase sales volume significantly. [Linking to pricing strategy] [M1]
2. Conversely, if the price elasticity of demand for coffee is inelastic (PED < 1), consumers are not very responsive to price changes. [Defining inelastic demand] [B1] Brewtopia could implement a high-price strategy, as a price increase will not substantially reduce the quantity demanded. This would increase revenue. [Linking to pricing strategy] [M1]
3. Market research is needed to determine the PED. If PED is close to 1 (unit elastic), then Brewtopia could consider other factors, such as brand image and competition, for pricing. [Considering unit elasticity] [A1]
4. Brewtopia also needs to consider the income levels of the consumers. If the country is largely low income, then a low-price strategy may be more successful regardless of the PED. [Considering income levels] [A1]

How to earn full marks: Explain both elastic and inelastic scenarios, and directly link each scenario to a specific pricing strategy Brewtopia could use.

(b)

1. Advantages of a low-price strategy: A low-price strategy, if the PED is elastic, can lead to a significant increase in sales volume and market share. [Identifying an advantage] [M1] This can create brand loyalty and economies of scale for Brewtopia. [Explaining the advantage] [A1]
2. Disadvantages of a low-price strategy: A low-price strategy may damage the brand image, associating Brewtopia with lower quality. [Identifying a disadvantage] [M1] It may also attract price-sensitive customers who are not loyal and will switch to competitors if they offer lower prices. If PED is inelastic, the lower price may not significantly increase quantity demanded and will reduce overall revenue. [Explaining the disadvantage] [A1]
3. Conclusion: Whether the low-price strategy is beneficial depends on the actual PED of coffee in the developing country. Brewtopia needs to conduct thorough market research to determine PED. If the PED is elastic, the advantages outweigh the disadvantages. If the PED is inelastic, the high-price strategy is better. [Valid conclusion] [B1] Other factors such as competition and the income distribution of the consumers should also be considered. [Considering other factors] [B1]

How to earn full marks: Give at least one advantage and one disadvantage, explaining why each is an advantage or disadvantage for Brewtopia. End with a clear conclusion that weighs the pros and cons.

Common Pitfall: Don't fall into the trap: elastic demand means total revenue FALLS when prices go up, because the quantity demanded drops by a LARGER percentage than the price increase.

Exam-Style Question 3 — Short Answer [4 marks]

Paper 2: Calculator Allowed

Question:

The price of petrol in a country increased by 10% due to a new government tax. The quantity demanded for petrol decreased by 5%.

(a) Calculate the price elasticity of demand (PED) for petrol. [2]

(b) Is the demand for petrol elastic or inelastic? [2]

Worked Solution:

(a)

1. PED is calculated as percentage change in quantity demanded divided by percentage change in price. [Stating the formula] [M1]
2. $PED = \frac{-5%}{10%} = -0.5$ [Calculating PED] $\boxed{PED = -0.5}$

How to earn full marks: Show the formula you are using, then substitute the values correctly. Include the negative sign in your answer.

(b)

1. Since the PED is -0.5, the absolute value is less than 1 (|-0.5| < 1). [Comparing PED to 1] [B1]
2. Therefore, the demand for petrol is inelastic. [Drawing the correct conclusion] [B1]

How to earn full marks: State why you are classifying the demand as elastic or inelastic, referring to the value of the PED you calculated.

Common Pitfall: When working with Price Elasticity of Demand, don't flip the formula — it's always '% change in quantity demanded' divided by '% change in price'.

Exam-Style Question 4 — Extended Response [10 marks]

Question:

A government is considering increasing the tax on cigarettes to reduce smoking rates.

(a) Explain how the concept of price elasticity of demand can be used to predict the impact of this tax increase on the quantity of cigarettes demanded. [4]

(b) Evaluate the effectiveness of using a tax increase on cigarettes to reduce smoking rates, considering the concept of price elasticity of demand and other factors. [6]

Worked Solution:

(a)

1. If the demand for cigarettes is price inelastic (PED < 1), it means that consumers are not very responsive to price changes. [Defining inelastic demand] [B1] A tax increase will lead to a smaller percentage decrease in the quantity demanded.
2. This means that while the tax increase will generate more tax revenue for the government, it will not significantly reduce smoking rates. [Linking to smoking rates] [M1]
3. Conversely, if the demand for cigarettes is price elastic (PED > 1), a tax increase will lead to a larger percentage decrease in the quantity demanded. This will be more effective at reducing smoking rates. [Linking elastic demand to smoking rates] [M1]
4. Therefore, the government needs to estimate the PED for cigarettes before implementing the tax. They may use surveys or analyze past data. [Understanding the need for PED estimation] [A1]

How to earn full marks: Explain how both elastic and inelastic demand for cigarettes would affect the outcome of the tax, linking directly to the goal of reducing smoking.

(b)

1. Effectiveness of the tax: If demand is inelastic, the tax will be less effective at reducing smoking rates. [Linking effectiveness to inelasticity] [M1] The tax revenue will increase, but smokers will continue to purchase cigarettes, albeit at a higher price. This is especially true for addicted smokers. [Explaining why] [A1]
2. Other Factors: The effectiveness of the tax also depends on other factors, such as the availability of substitutes (e.g., e-cigarettes), the level of addiction among smokers, and the effectiveness of anti-smoking campaigns. [Mentioning other factors] [M1]
3. Limitations: A high tax on cigarettes could lead to increased smuggling and the consumption of illegal cigarettes, which are unregulated and potentially more harmful. [Identifying a limitation] [A1]
4. Conclusion: The effectiveness of a tax increase depends on the price elasticity of demand. If the demand is relatively elastic, the tax may be effective in reducing smoking rates. However, if the demand is inelastic, other measures such as education campaigns and providing access to smoking cessation programs may be more effective. [Valid conclusion] [B1] The government should also consider the potential for unintended consequences, such as increased smuggling. [Considering unintended consequences] [B1]

How to earn full marks: Discuss the effectiveness of the tax, considering both PED and at least two other relevant factors. Offer a balanced conclusion that weighs the different factors.

Common Pitfall: Remember that the demand for addictive goods like cigarettes tends to be price inelastic, especially among regular smokers. This means that taxes may not be as effective at reducing consumption as policymakers hope.