Elasticity Of Demand

Cross price elasticity of demand

The ratio of a percentage change in quantity demanded of a good to a percentage change in the price of a related good is termed cross elasticity of demand.They are substitutes and complements in cross price elasticity of demand. When an increase in the price of a related good increases demand for another good, we say then that they are substitute goods. An increase in the price of one will lead consumers to purchase more of the other. The cross price elasticity of demand of substitute goods is positive eg homogenous products like cds manufactured by different producers. An increase in the demand of one leads to an increase in the demand of the other.

For complements, an increase in the price of one leadfs to a decrease in the demand of the other.The cross price elasticity of demand is negative. Eg for automobile and gasoline, an increase in the price of automobiles would lead to a decrease in the demand for gasoline.

 

Formulas:

Price elasticity :

=     

Where Po = Initial price

P1 = new price for the commodity

Qo= Initial quantity demanded at price Po

Q1 = final quantity demanded at new price P1

 

Income Elasticity:

= % ∆Q ÷ % ∆I

=    

Where:

Io = Initial Income Level

Qo = initial quantity demanded at income level Io

Q1= New quantity demanded at income level I1

I1 = New Income Level

 

Cross elasticity of demand

Where Qf and Q1 are the final and initial quantities demanded of product A, and Pf and P1 are the final and initial prices of product B.

Or also we can use this formular:

 

Examples:

Price elasticity of demand

• The price of pens today is $1, and the quantity demanded is 1 million. Next year the price rises to $1.10 and the quantity demanded falls to 950,000. Calculate the price elasticity of demand.

 

Formula =

 

Wher Po = $1,

P1= $1.10

Q0= 1 million units

Q2= 950,000 units

 

= (1,000,000- 950,000)1 / {(1-1.0) 1,000,000}

= 50,000/ (0.1 1,000,000)

= (50,000/ 100,000)

= -0.5

 

Ignore the negative sign (-) when calculating the elasticity of demand. From our calculation, the demand for pens is inelastic because it is less than 1, at 0.5. This means a change in the price of pens would lead to a less than proportionate change in the demand for pens.

 

Cross elasticity of demand

Question:

An increase in price of product A from #100 to #150 leads to an increase in quantity demanded from 1000 units to 1400 units. Calculate the cross price elasticity of demand

Possible Solution:

Where P1 =#100,

P2= #150

Q1= 1000 units

Q2= 1400 units

 

=

 

=

= 0.8333 or 83.33%.

 

Elasticity and the Pricing decision

Elasticity of demand can assist management in making pricing decisions. We are going to look at some pricing strategies management can adopt while considering the price elasticity of their products. The first one is when the product is elastic. Let’s take a look:

 

Elastic: Since an increase in price would lead to a more than proportionate decrease in quantity demanded,you do not need a wizard, harry potter in this case, to tell Ron and Hermione that an increase in prices would bring decreases in revenue, and a decrease in price would bring an increases in revenue.  If management seeks to alter the price at any time, they must ask themselves: whether the increase/decrease in costs will be less than or greater than the increases/decreases in revenue.

 

Inelastic: In a situation whereby demand is inelastic, ie an increase in price leads to a less than proportionate decrease in quantity demanded, management should increase prices because this would bring an increase in revenues and reduction in total costs; this is because the quantity that would have to be sold would reduce.

 

Perfectly Elastic: In a situation of elasticity being perfectly elastic, any increase in price would lead to a massive drop or total drop in quantity sold, whereas any decrease in price can lead to an inability of the company to break even and cover its total cost, while also inviting massive stock outs due to customers rushing its products. The only way to break free from the chains of a perfectly elastic product for a supplier is to try as much as possible to differentiate your products from others by creating a customer preference which is unrelated to price.

 

Price Inelastic Demand :In perfectly inelastic demand, a change in price has no effect on quantity. Customers are insensitive to price changes, quality, service, product mix and location are therefore more important to a firm’s pricing strategy.

 

Recommended Readings

Robert Pyndick., Daniel Rubinfield., Microeconomics (8th Edition)

Dominick Salvatore., Schaums outline of microeconomics

Paul Krugman., Robin wells., Microeconomics (4^th edition)