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Elasticity of Demand and Supply

Elasticity and total revenue

  • 2 things to know
  • Unit AS 1

Overview

Total revenue.

What you need to know

Answer each one before you reveal it.

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Numbers

A rail operator raises a season ticket from £25.00 to £27.50 and monthly sales fall from 4,000 to 3,400. Calculate the change in total revenue.

Key term

A firm cuts its price, sees total revenue rise, and concludes it should keep cutting. What is wrong with that reasoning?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is total revenue, how is it calculated, and why is it the same thing as consumers' total expenditure?

    Model answer

    Total revenue is the total amount a firm receives from selling its output over a period, calculated as price multiplied by quantity sold. It is identical to the total expenditure of consumers on that good, because every pound a buyer hands over is a pound the seller receives - the two are the same transaction viewed from opposite sides. This is why the same calculation answers both a firm's question about its sales income and a government's question about how much households are spending on a product.

  2. 2

    State the rule linking price elasticity of demand to the effect of a price change on total revenue, and explain why it works.

    Model answer

    If demand is price inelastic, raise price to increase total revenue; if demand is price elastic, cut price to increase total revenue. It works because total revenue is price multiplied by quantity, so a price change pulls the two components in opposite directions and the larger percentage change wins. When demand is inelastic the percentage fall in quantity is smaller than the percentage rise in price, so revenue rises. When demand is elastic the percentage rise in quantity from a price cut outweighs the percentage price reduction, so revenue rises. At unit elasticity the two exactly cancel and revenue is unchanged.

  3. 3

    A rail operator raises a fare from £12.00 to £13.20 and weekly passenger journeys fall from 50,000 to 47,500. Calculate the price elasticity of demand and the change in total revenue.

    Model answer

    Percentage change in price: +£1.20 divided by 12.00, multiplied by 100, gives +10%. Percentage change in quantity: -2,500 divided by 50,000, multiplied by 100, gives -5%. Price elasticity of demand is -5 divided by +10, which is -0.50, so demand is inelastic. Total revenue before is £12.00 multiplied by 50,000, which is £600,000. Total revenue after is £13.20 multiplied by 47,500, which is £627,000. Revenue rises by £27,000, exactly as the rule predicts for a price rise where demand is inelastic.

  4. 4

    An airline cuts a fare from £120 to £96 and seats sold on the route rise from 300 to 420 per week. Calculate the price elasticity of demand and the effect on total revenue.

    Model answer

    Percentage change in price: -£24 divided by 120, multiplied by 100, gives -20%. Percentage change in quantity: +120 divided by 300, multiplied by 100, gives +40%. Price elasticity of demand is +40 divided by -20, which is -2.00, so demand is elastic. Total revenue before is £120 multiplied by 300, which is £36,000. Total revenue after is £96 multiplied by 420, which is £40,320. Revenue rises by £4,320. Cutting price where demand is elastic raises revenue, because the extra seats sold more than compensate for the lower fare on each.

  5. 5

    A bakery raises the price of a loaf from £1.50 to £1.80 and weekly sales fall from 4,000 to 3,000 loaves. Calculate the price elasticity of demand and show what happens to total revenue.

    Model answer

    Percentage change in price: +£0.30 divided by 1.50, multiplied by 100, gives +20%. Percentage change in quantity: -1,000 divided by 4,000, multiplied by 100, gives -25%. Price elasticity of demand is -25 divided by +20, which is -1.25, so demand is elastic. Total revenue before is £1.50 multiplied by 4,000, which is £6,000. Total revenue after is £1.80 multiplied by 3,000, which is £5,400. Revenue falls by £600. Raising price where demand is elastic is self-defeating, because the loaves lost outweigh the extra received on each one sold.

  6. 6

    A streaming service raises its monthly subscription from £9.00 to £10.80 and subscriber numbers fall from 2,000,000 to 1,800,000. Calculate the price elasticity of demand and the change in monthly total revenue.

    Model answer

    Percentage change in price: +£1.80 divided by 9.00, multiplied by 100, gives +20%. Percentage change in quantity: -200,000 divided by 2,000,000, multiplied by 100, gives -10%. Price elasticity of demand is -10 divided by +20, which is -0.50, so demand is inelastic. Total revenue before is £9.00 multiplied by 2,000,000, which is £18.00 million. Total revenue after is £10.80 multiplied by 1,800,000, which is £19.44 million. Monthly revenue rises by £1.44 million, because the 10% of subscribers lost is outweighed by the 20% more paid by those who stayed.

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Key Economic Concepts
The Basic Economic Problem of Scarcity and Choice
Demand and Supply in Product Markets
Markets and Equilibrium

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AThe initial spending becomes income for those who receive it.
BPart of that income is spent again, generating further income.
CThe total effect on demand exceeds the original injection.

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