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Wize AP Microeconomics Textbook > Elasticity

Point Price Elasticity of Demand

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Price Elasticity of Demand

Inelastic
  • Means you are insensitive to the price
  • If price rises, the quantity demanded will fall by only a little bit. Example: Medicine
Elastic
  • Means you are sensitive to the price
  • If price rises, the quantity demanded will fall by a lot. Example: Pepsi

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Point Price Elasticity of Demand

Point Price Elasticity of Demand= %ΔQ%ΔP  =  ΔQΔP ⋅ PQ\boxed{\text{Point\ Price\ Elasticity\ of\ Demand} =\ \frac{\%ΔQ}{\%ΔP}\ \ =\ \ \frac{ΔQ}{ΔP}\ \cdot\ \frac{P}{Q}}

  • For products that have inelastic demand, the absolute value of Price Elasticity of Demand (Ed) will be
    less
    than 1 Example: If the price of medicine increases by 50% and the quantity demanded falls by 10% (notice percentage change in quantity is smaller than percentage change in price), then what would be the price elasticity of demand?
Elasticity of demand = -10% / 50% = -0.2

The absolute value of -0.2 is 0.2 which is less than 1 (meaning inelastic).
  • For products that have elastic demand, the absolute value of Ed will be
    greater
    than 1 Example: If the price of Pepsi increases by 5% and the quantity demanded falls by 50% (notice percentage change in quantity is larger than percentage change in price), then what would be the price elasticity of demand?
Elasticity of demand = -50% / 5% = -10

The absolute value of -10 is 10 which is greater than 1 (meaning elastic).
  • For products that have unit elastic demand, the absolute value of Ed will be
    equal
    to 1 Example: If the price of oranges increases by 5% and the quantity demanded falls by 5% (notice percentage change in quantity is equal to percentage change in price), then what would be the price elasticity of demand?
Elasticity of demand = -5% / 5% = -1

The absolute value of -1 is 1 which is unit elastic (in the real world there's no example of products with unit elastic demand, it's just a concept.

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For products with different types of demand, the absolute value of the Price Elasticity of Demand will have different values:
Type of DemandAbsolute Value of the Price Elasticity of DemandInelasticLess than 1ElasticGreat than 1Unit ElasticEqual to 1\begin{array}{|c|c|} \hline\\ \bold{\text{Type of Demand}} & \bold{\text{Absolute Value of the Price Elasticity of Demand}}\\ \\ \hline\\ \text{Inelastic} & \text{Less than 1}\\ \\ \hline\\ \text{Elastic} & \text{Great than 1}\\ \\ \hline\\ \text{Unit Elastic} & \text{Equal to 1}\\ \\ \hline \end{array}

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Percentage Change

In the examples above the percentage changes were given. If they give you just a change (without percentages) you can use the following formula to convert to percentages:
Percentage Change= (New − Old)Old⋅100\boxed{\text{Percentage\ Change} =\ \frac{\left(New\ -\ Old\right)}{Old}\cdot100}


Example: If the quantity changes from 40 to 50 units what is the percentage change?

Percentage change = (50 - 40) / 40 * 100 = 25%


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Example: Point Elasticity with Numbers and Equations

a) Suppose the price of textbooks increase from $20 to $30 and the quantity demanded drops from 100 units to 90 units. What is the point price elasticity of demand at a Price of $20? Is the demand elastic or inelastic at this price?


Point price elasticity of demand (point Ed) = %Change in Q%Change in P\frac{\%Change\ in\ Q}{\%Change\ in\ P}

% Change in P = (30−20)20⋅100 = 50%\frac{\left(30-20\right)}{20}\cdot100\ =\ 50\%
% Change in Q = (90−100)100⋅100=−10%\frac{\left(90-100\right)}{100}\cdot100=-10\%

Point Ed = −10%50%\frac{-10\%}{50\%}

Point Ed = -0.2 which is inelastic (absolute value is less than 1)




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b) If the demand equation is P = 70 – 2Q, what is the price elasticity of demand at a price of $40?

First lets plug in price of 40 in the demand equation to get the quantity:

40 = 70 - 2Q
2Q = 30
Q = 15

Since they only gave you one price, you can just make up any number for a second price and plug in to the demand so that you can get the corresponding quantities (you can always do this). For example let's plug the second price as $50:

50 = 70 - 2Q
2Q = 20
Q = 10

Now we have 2 prices and 2 quantities so we can find the percentage changes:
% Change in P = (50−40)40⋅100 =25%\frac{\left(50-40\right)}{40}\cdot100\ =25\%
% Change in Q = (10 − 15)15⋅100 = −33.33%\frac{\left(10\ -\ 15\right)}{15}\cdot100\ =\ -33.33\%


Point price elasticity of demand (point Ed) = %Change in Q%Change in P\frac{\%Change\ in\ Q}{\%Change\ in\ P}


Point Ed = −33.33%25%\frac{-33.33\%}{25\%}

Point Ed = -1.33 which is elastic (absolute value is greater than 1)