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Elasticity

Practice Problems for Elasticity

Elasticity

Elasticity in the Real World

Problem : Yesterday, the price of envelopes was $3 a box, and Julie was willing to buy 10 boxes. Today, the price has gone up to $3.75 a box, and Julie is now willing to buy 8 boxes. Is Julie's demand for envelopes elastic or inelastic? What is Julie's elasticity of demand?

To find Julie's elasticity of demand, we need to divide the percent change in quantity by the percent change in price.

% Change in Quantity = (8 - 10)/(10) = -0.20 = -20%
% Change in Price = (3.75 - 3.00)/(3.00) = 0.25 = 25%
Elasticity = |(-20%)/(25%)| = |-0.8| = 0.8

Her elasticity of demand is the absolute value of -0.8, or 0.8. Julie's elasticity of demand is inelastic, since it is less than 1.

Problem : If Neil's elasticity of demand for hot dogs is constantly 0.9, and he buys 4 hot dogs when the price is $1.50 per hot dog, how many will he buy when the price is $1.00 per hot dog?

This time, we are using elasticity to find quantity, instead of the other way around. We will use the same formula, plug in what we know, and solve from there.

Elasticity =
And, in the case of John, %Change in Quantity = (X – 4)/4
Therefore :
Elasticity = 0.9 = |((X – 4)/4)/(% Change in Price)|
% Change in Price = (1.00 - 1.50)/(1.50) = -33%
0.9 = |(X – 4)/4)/(-33%)|
|((X - 4)/4)| = 0.3
0.3 = (X - 4)/4
X = 5.2

Since Neil probably can't buy fractions of hot dogs, it looks like he will buy 5 hot dogs when the price drops to $1.00 per hot dog.

Problem : Which of the following goods are likely to have elastic demand, and which are likely to have inelastic demand?

Home heating oil
Pepsi
Chocolate
Water
Heart medication
Oriental rugs

Elastic demand: Pepsi, chocolate, and Oriental rugs
Inelastic demand: Home heating oil, water, and heart medication

Problem : If supply is unit elastic and demand is inelastic, a shift in which curve would affect quantity more? Price more?

Shifting the demand curve would affect quantity more, and shifting the supply curve would affect price more.

Problem : Katherine advertises to sell cookies for $4 a dozen. She sells 50 dozen, and decides that she can charge more. She raises the price to $6 a dozen and sells 40 dozen. What is the elasticity of demand? Assuming that the elasticity of demand is constant, how many would she sell if the price were $10 a box?

To find the elasticity of demand, we need to divide the percent change in quantity by the percent change in price.

% Change in Quantity = (40 - 50)/(50) = -0.20 = -20%
% Change in Price = (6.00 - 4.00)/(4.00) = 0.50 = 50%
Elasticity = |(-20%)/(50%)| = |-0.4| = 0.4

The elasticity of demand is 0.4 (elastic).

To find the quantity when the price is $10 a box, we use the same formula:

Elasticity = 0.4 = |(% Change in Quantity)/(% Change in Price)|
% Change in Price = (10.00 - 4.00)/(4.00) = 1.5 = 150%

Remember that before taking the absolute value, elasticity was -0.4, so use -0.4 to calculate the changes in quantity, or you will end up with a big increase in consumption, instead of a decrease!

-0.4 = |(% Change in Quantity)/(150%)|
|(%Change in Quantity)| = -60% = -0.6
-0.6 = (X - 50)/50
X = 20

The new demand at $10 a dozen will be 20 dozen cookies.

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