Question

Suppose subway ridership in new york city rose by 12 percent after a fare decrease of 25 cents to $2.25. Using the midpoint method, an estimate of the price elasticity of demand for subway rides is . True or false: according to your estimate, the transit authority's revenue rises when the fare decreases. True

Answer 1

Answer: The price elasticity of demand using the midpoint formula is -1.14.

b. True. A price elasticity of demand greater than -1 means that the demand for a product or service will increase greater than a given decrease in price . In such cases, the supplier stands to benefit from a reduction in prices.

We estimate the price elasticity of demand as follows:

`Price Elasticity of Demand = (percentage change in quantity)/(percentage change in price)`

From the question, we have percentage change in quantity demanded as 12%.

We estimate the percentage change in price with the midpoint formula as follows:

`percentage change in price = (P_(2)-P_(1))/(Average Price)`

where

`Average price = (P_(1) +P_(2))/(2)`

Since we have

P₂ - P₁ -0.25

and

P₂ $.2.25

from the question, we can find P₁ as follows:

`-0.25 = 2.25 - P_(1)`

`P_(1) = 2.50`

Substituting the value of P₁ in the average prices formula we get

`Average price = (2.50 +2.25)/(2)`

`Average price = 2.375`

Substituting the value of average price in the percentage change in price formula we get,

`percentage change in price = (-0.25)/(2.375)`

`percentage change in price = -0.105263158`

Substituting the value of percentage change in price in the price elasticity of demand formula we get,

`Price Elasticity of Demand = (0.12)/(-0.10526315)`

`Price Elasticity of Demand = -1.14`