Question

Suppose the price of a DVD rose from​ $15 to​ $17 and the quantity demanded decreased from​ 1,000 per month to 900 per month. Using the midpoint​ formula, the​ ________ percent change in price lead to a​ ________ percent change in the quantity demanded.

Answer 1

Using the midpoint​ formula, the​ 12.5 percent change in price lead to a​ 10.5 percent change in the quantity demanded.

Explanation:

This problem is related to the price elasticity of demand.

The price elasticity of demand is defined as the percent change in quantity demanded divided by the percent change in price.

Using the midpoint formula:

The formula for percent change in quantity demanded is:

Percent change in quantity demanded
`=(Q_(2)-Q_(1))/(((Q_(1)+Q_(2)))/(2)) * 100`

The formula for percent change in price is:

Percent change in price
`=(P_(2)-P_(1))/(((P_(1)+P_(2)))/(2)) * 100`

Given:

`Q_(1) = 1000\\Q_(2)=900\\P_(1)=\$15\\P_(2)=\$17`

Percent change in quantity demanded =

`=(900-1000)/(((900+1000))/(2)) * 100\\=-10.53\%`

Percent change in price =

`=(17-15)/(((17+15))/(2)) * 100\\=12.5\%`

The complete statement is:

Using the midpoint​ formula, the​ 12.5 percent change in price lead to a​ 10.5 percent change in the quantity demanded.