Question

Suppose a hurricane decreased the supply of oranges so that the price of oranges rose from​ $120 a ton to​ $180 a ton and quantity sold decreased from 800 tons to 240 tons. What is the absolute value of the price elasticity of​ demand? Use the midpoint formula.

Answer 1

2.69

Step-by-step explanation:

Given:

Initial price of the orange = $120

Final price of the orange = $180

Initial quantity of orange sold = 800 tons

Final quantity of orange sold = 240 tons

Now,

In midpoint formula

the percent change is given as

=
`\frac{\textup{Change in quantity}}{\textup{Average quantity}}*100%`

therefore,

The percent change in price of orange =
`\frac{\textup{Change in price}}{\textup{Average price}}*100%`

also,

Average price of orange =
`\frac{\textup{120 + 180}}{\textup{2}}` = $150

thus,

The percent change in price of orange =
`\frac{|\textup{180-120}|}{\textup{150}}*100%` = 0.4%

and,

The percent change in quantity of orange =
`\frac{\textup{Change in price}}{\textup{Average price}}*100%`

also,

Average quantity of orange sold =
`\frac{\textup{800 + 240}}{\textup{2}}` = 520

thus,

The percent change in quantity of orange sold=
`\frac{\textup{800-240}}{\textup{520}}*100%` = 1.0769

Therefore,

Absolute value of the price elasticity of​ demand

=
`\frac{\textup{percent change in quantity of orange sold}}{\textup{percent change in price of orange}}`

=
`\frac{\textup{1.0769}}{\textup{0.4}}`

= 2.69