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:

$Price Elasticity of Demand = \frac{percentage change in quantity}{percentage change in price}$

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:

$percentage change in price = \frac{P_{2}-P_{1}}{Average Price}$

where

$Average price = \frac{P_{1} +P_{2}}{2}$

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

$Average price = \frac{2.50 +2.25}{2}$

$Average price = 2.375$

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

$percentage change in price = \frac{-0.25}{2.375}$

$percentage change in price = -0.105263158$

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

$Price Elasticity of Demand = \frac{0.12}{-0.10526315}$

$Price Elasticity of Demand = -1.14$