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Elasticity: Using Formulas - Activity

This Activity is designed to get you used to using the formulas for the various elasticities you will come across in your studies. Examiners rarely ask you to do specific calculations such as these, but you are expected to be able to understand and manipulate the formulas and understand the consequences of the elasticity figure you are presented with. Write down the formula and show your working for EACH example. The reason for this is that it helps to embed your knowledge of the formula and is good practice, as examiners will often reward you for showing your workings!

In the Activity, the following abbreviations are used:

  • Ped = Price Elasticity of Demand
  • Pes = Price Elasticity of Supply
  • Yed = Income Elasticity of Demand
  • Xed = Cross Elasticity of Demand
  • Δ = change

Task 1

Calculate the price elasticity of demand in each of the following examples:

  • The change in demand is 5%, the change in price is 7%
  • The change in demand is 12%, the change in price is 3%
  • The change in demand is 9%, the change in price is 4%
  • The change in demand is 13%, the change in price is 25%
  • The change in demand is 6%, the change in price is 8%

In each case say whether the price elasticity is inelastic or elastic.


Task 2

Calculate the percentage change in demand in each of the following cases:

  • Yed is 2.4 and the % Δ P is 5%
  • Xed is -1.5 and the % Δ Price of good y is 20%
  • Ped is -0.6 and the % Δ P is 18%
  • Pes is 1.2 and the % Δ P is 6%
  • Yed is - 3.1 and the % Δ P is 8%

Where appropriate say whether the good is a normal good or an inferior good, or whether it is a substitute or complement.


Task 3

Calculate the percentage change in price or income in each of the following cases:

  • Yed is 1.7 and the % ΔQ is 2%
  • Ped is -0.75 and the % ΔQ is 25%
  • Pes is 2.5 and the % ΔQ is 3%
  • Yed is -0.35 and the % ΔQ is 3%
  • Ped is 1.6 and the % ΔQ is 4%

Task 4

Say whether revenue will rise or fall (or stay the same) in each of the following cases:

  • Ped is inelastic and a firms raises its price
  • Ped is elastic and a firm lowers its price
  • Ped is elastic and a firm raises its price
  • Ped is -1.3 and the firm raises price by 2%
  • Ped is -0.7 and the firm raises its price by 25%
  • Ped is -0.45 and the firm raises its price by 6%
  • Ped is -3.5 and the firm lowers its price by 14%

Task 5

In each of the following say whether the products are normal or inferior goods. Explain your answer.

  • Yed = -0.4
  • Yed = 2.8
  • Yed = -1.3
  • Yed = -3.4
  • Yed = +0.6
Hot Tubs - luxury or necessity?

Image: Hot Tubs - luxury or necessity? Price elastic or inelastic? Income elastic or inelastic? Normal good or inferior good?


Task 6

In each of the following cases say whether the goods are substitutes or complements and whether the relationship is elastic or inelastic:

  • Xed = -2.3
  • Xed = -0.6
  • Xed = +4.1
  • Xed = -1.67
  • Xed = + 0.74

Task 7

Look at the following information:

'The authors find that a 1 percent price increase at Amazon reduces sales there by about 0.5 percent, but a 1 percent price increase at Barnes & Noble means a 4 percent sales decline - eight times as large.'

Source: Hal Varian, New York Times

  • Calculate the price elasticity of demand for both Amazon and Barnes & Noble.
  • What would happen to the total revenue in each case if the businesses concerned decided to drop price by 1%?
  • How do you explain the difference in the demand elasticity for the two companies?