Suppose that when the price of gasoline is $3.50 per gallon, the total amount of gasoline purchased in the United States is 6 million barrels per day. Also, suppose that when the price of gas decreases to $3 per gallon, the total amount of gasoline purchased is 8 million barrels per day. Based on these numbers and using the midpoint formula, the price elasticity of demand for gasoline is:

The price elasticity of demand is a measure used to show the responsiveness, or elasticity, of the quantity demanded of a good or service to changes in the price of that good or service.

That is, the price elasticity of demand indicates to what extent changes in price alter the demand for specific products or services.

The price elasticity of demand is calculated by dividing the percentage change in demand by the percentage change in price, resulting in the following expression:

[tex]Elasticity=\frac{percentage change in quantity demanded}{percentage change in price}[/tex]

[tex]Elasticity=\frac{\frac{deltaQ}{Q} }{\frac{deltaP}{P} }[/tex]

where:

deltaQ means the absolute change in quantities demanded.
Q represents quantity.
deltaP represents the absolute change in price.
P represents the price.

Price elasticity of demand for gasoline

Knowing that:

When the price of gasoline is $3.50 per gallon, the total amount of gasoline purchased in the United States is 6 million barrels per day.
When the price of gas decreases to $3 per gallon, the total amount of gasoline purchased is 8 million barrels per day.

First, the percentage change in quantities is calculated as follows:

The absolute change in quantities deltaQ is obtained by first subtracting the final demand from the initial demand, that is (8 million – 6 million = 2 million)
Now dividing this value by the initial demand, you obtain 2 million÷6 million=0.333, which, taken to a percentage value, finally shows that the percentage change in quantity demanded is 0.333×100%= 33.3%.

Now the percentage change in price is determined as follows:

The absolute change in the deltaP price is obtained by subtracting the final price from the initial price, that is (3 – 3.5= -0.5).
Now dividing this value by the initial price -0.5/3.5, we obtain -0.143, which, taken as a percentage value, shows that the percentage variation in the price is -0.143x100%= -14.3%.

Finally, the price elasticity of demand is calculated as:

[tex]Elasticity=\frac{33.3}{-14.3}[/tex]

Solving:

Elasticity= -2.33

In summary, the price elasticity of demand for gasoline is -2.33.

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