Question

The cab fare in Horseville is regulated. Recently, the government decided to raise it from $2.00 to $2.50 per ride. After this rise in fare, cab ridership decreased by 10 percent.

a) what was the percentage change in price?

b) what is the price elasticity of demand Ed =

c) Would the cab company realize an increase in total revenue? Why?

Answer 1

(a)

To calculate the percentage change in price, we need to use the mid point theorem.

change in Price = (P₂ - P₁) / {(P₁ + P₂) / 2}

Here, P₂ = New Price = $2.50

P₁ = Old Price = $2.00

So,

change in Price = ($2.50 - $2.00) / {($2.00 + $2.50) / 2}

change in Price = $0.50 / $2.25

change in Price = 0.2222

So, the percentage change in Price is 22.22%.

(b).

Now, from theory we knew that,

The price elasticity of demand (E_d) = (% change in quantity demanded / % change in Price)

The price elasticity of demand (E_d) = 10% / 22.22% = 0.45.

So, the price elasticity of demand E_d is 0.45.

(c)

As the price elasticity of demand for the cab company in inelastic, That means, when the value of E_d is less than 1, the price elasticity of demand is inelastic. so an increase in price leads to an increase in total revenue.

This is because, when the price elasticity of demand is inelastic, changes in quantity demanded is less than changes in price.

So, the cab company would realize an increase in total revenue.