Price Elasticity of Demand (PED) (AQA A Level Economics)

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The Definition & Calculation of PED

  • The law of demand states that when there is an increase in price, there will be a fall in the quantity demanded
    • Economists are interested by how much the quantity demanded will fall
  • Price elasticity of demand reveals how responsive the change in quantity demanded is to a change in price
    • The responsiveness is different for different types of products

Calculation of PED

  • PED can be calculated using the following formula

text PED =  end text fraction numerator percent sign space change space in space quantity space demanded over denominator percent sign space change space in space price end fraction space equals space fraction numerator percent sign triangle space in thin space QD over denominator percent sign triangle in space straight P end fraction

 

  • To calculate a % change, use the following formula

begin mathsize 16px style percent sign space Change space equals space fraction numerator new space value space minus space old space value over denominator old space value end fraction space cross times space 100 end style 

Worked example

A firm raises the price of its products from $10 to $15. Its sales fall from 100 to 40 units per day. Calculate the PED of its products 

 

Step 1:  Calculate the % change in QD

  begin mathsize 14px style percent sign triangle QD space equals space fraction numerator 40 minus 100 over denominator 100 end fraction space cross times 100

percent sign triangle QD space equals space minus 60 percent sign end style 


Step 2: Calculate the % change in P

percent sign triangle straight P space equals space fraction numerator 15 space minus space 10 over denominator 10 end fraction space straight x space 100

percent sign triangle straight P space equals space 50 percent sign


Step 3: Insert the above values in the PED formula

PED space equals space fraction numerator percent sign triangle space in thin space QD over denominator percent sign triangle in space straight P end fraction

PED space equals space fraction numerator negative space 60 over denominator space space space space 50 end fraction

PED space equals space minus 1.2
 

Step 4: Final answer = 1.2

  
The PED value will always be negative so economists ignore the sign and present the answer as 1.2

Exam Tip

In Paper 3 you are occasionally given the PED value and the %Δ in Price - you are then asked to find the %Δ in Qd. Follow the standard math procedure as follows:

1. Substitute the values provided into the equation

2. Substitute X for %Δ in Qd

3. Solve for X

Worked example

The price elasticity of demand for smart phones is -2. It can be concluded that a 10% reduction in their price would be a percentage change in demand of:

A. -7.4%

B. -20.0%

C. +7.4%

D. +20.0%

Step 1: Substitute the values provided into the equation

   PED space equals space fraction numerator percent sign space increment in space QD over denominator percent sign space increment space in space straight P end fraction

Step 2: Substitute X for %Δ in Qd

   plus 2 space equals space fraction numerator straight X over denominator negative 10 percent sign end fraction

Step 3. Solve for X

   X space equals space 20 percent sign

Quantity demanded increases by 20%

Interpreting PED Values

PED Classifications


Value


Name and Diagram


Explanation

0

 

  • Perfectly Inelastic

2-7-1-calculation-and-determination-of-ped--perfectly-inelastic

 
  • The QD is completely unresponsive to a change in P (very theoretical value e.g. heart transplant is extremely inelastic but possibly not perfectly)

0 →1

  • Relatively Inelastic

2-7-1-calculation-and-determination-of-ped--relatively-inelastic


  • The %∆ in QD is less than proportional to the %in P (e.g. addictive products)

1

  • Unitary Elasticity

2-7-1-calculation-and-determination-of-ped---unitary-elasticity


  • The % ∆ in QD is exactly equal to the %∆ in P

1 → ∞

  • Relatively Elastic

2-7-1-calculation-and-determination-of-ped---relatively-elastic


  • The %∆ in QD is more than proportional to the % in P (e.g. luxury products)

  • Perfectly Elastic

2-7-1-calculation-and-determination-of-ped---perfectly-elastic


  • The %∆ in QD will fall to zero with any %∆ in P (highly theoretical elasticity)

PED & Total Revenue

  • Knowledge of PED is important to firms seeking to maximise their revenue
  • Sales revenue will be maximised 
    • If their product is price inelastic in demand, they should raise their prices
    • If their product is price elastic in demand, then they should lower their prices
  • This rule is used when firms choose to use [popover id="F_vUGukEe4aWRck1" label="price discrimination"] to maximise their revenue
    • They lower their prices for elastic sections of their market e.g. off peak train travel
    • They increase prices for inelastic sections of their market e.g. peak hour train trave
  • The benefits of this rule can be illustrated using a demand curve
    • A shallow curve represents a price-elastic product
    • A steep curve represents a price inelastic product

Diagram: Elastic Demand Curve 

3-3-1-elastic-ar_edexcel-al-economics

A small decrease in price from P1 → Pcauses a large increase in quantity demanded from Q1 → Q2

Diagram analysis

  • When a good/service is price elastic in demand, there is a greater than proportional increase in the quantity demanded to a decrease in price
    • A small decrease in price leads to a larger increase in QD
  • TR is higher once the price has been decreased
    • begin mathsize 14px style left parenthesis straight P subscript 2 cross times straight Q subscript 2 right parenthesis space greater than space left parenthesis straight P subscript 1 cross times straight Q subscript 1 right parenthesis end style

Diagram: Inelastic Demand Curve 

3-3-1-inelastic-ar_edexcel-al-economics

A large increase in price from P1 → Pcauses a small decrease in quantity demanded from Q1 → Q2

Diagram analysis

  • When a good/service is price inelastic in demand, there is a smaller than proportional decrease in the quantity demanded to an increase in price
    • A large increase in price leads to a smaller decrease in QD
  • TR is higher once the price has been increased
    • begin mathsize 14px style left parenthesis straight P subscript 2 cross times straight Q subscript 2 right parenthesis space greater than space left parenthesis straight P subscript 1 cross times straight Q subscript 1 right parenthesis end style

The Factors that Influence PED

  • Some products are more responsive to changes in prices than other products
  • The factors that determine the responsiveness are called the determinants of PED and include:
    • Availability of substitutes: good availability of substitutes results in a higher value of PED (relatively elastic)
    • Addictiveness of the product: addictiveness turns products into necessities, resulting in a low value of PED (relatively inelastic)
    • Price of product as a proportion of income: the lower the proportion of income the price represents, the lower the PED value will be. Consumers are less responsive to price changes on cheap products (relatively inelastic)
    • Time period: In the short term, consumers are less responsive to price increases, resulting in a low value of PED (relatively inelastic). Over a longer period of time, consumers may feel the price increase more and will then look for substitutes, resulting in a higher value of PED (relatively elastic)

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Lorraine Clancy

Author: Lorraine Clancy

Lorraine brings over 12 years of dedicated teaching experience to the realm of Leaving Cert and IBDP Economics. Having served as the Head of Department in both Dublin and Milan, Lorraine has demonstrated exceptional leadership skills and a commitment to academic excellence. Lorraine has extended her expertise to private tuition, positively impacting students across Ireland. Lorraine stands out for her innovative teaching methods, often incorporating graphic organisers and technology to create dynamic and engaging classroom environments.