I am completely lost in working this problem.
1.
The total operating avenues of a public transportation authority are$100 million while its operating costs are $120 million. The price of a ride is $1, and the price of elasticity of demand has been estimated to be -0.4. By law, the public transportation authority must take steps to eliminate its operating deficit.(a) What pricing policy should the transportation adopt? (b) What price per ride must the public transportation authority charge to eliminate the deficit if it cannot reduce cost?
Note:P7(b) Suggestion- increase the price of a ride from $1 to be $1.50, a 50% increase in price. Given the elasticity of demand of -0.4, calculate the percentage change in the rides (the original rides are 100 million=$100 million/$1). Then use the total new rides time the new price of $1.50 to obtain the new total revenue.
To determine the pricing policy and the price per ride that the public transportation authority should adopt, we can follow the steps below:
Step 1: Calculate the original number of rides:
Divide the total operating revenues by the price per ride.
Original rides = Total operating revenues / Price per ride
Original rides = $100 million / $1
Original rides = 100 million rides
Step 2: Calculate the new price per ride:
Increase the price per ride by 50%.
New price per ride = $1 + ($1 * 50%)
New price per ride = $1 + $0.50
New price per ride = $1.50
Step 3: Calculate the percentage change in rides:
Multiply the original rides by the price elasticity of demand.
Percentage change in rides = Original rides * Price elasticity of demand
Percentage change in rides = 100 million rides * -0.4
Percentage change in rides = -40 million rides
Step 4: Calculate the new number of rides:
Add the percentage change in rides to the original number of rides.
New rides = Original rides + Percentage change in rides
New rides = 100 million rides + (-40 million rides)
New rides = 60 million rides
Step 5: Calculate the new total revenue:
Multiply the new number of rides by the new price per ride.
New total revenue = New rides * New price per ride
New total revenue = 60 million rides * $1.50
New total revenue = $90 million
Since the public transportation authority's operating costs are $120 million and the new total revenue is $90 million, there is still a deficit of $30 million. Therefore, the transportation authority must further adjust its pricing or reduce costs to eliminate the deficit.
To solve this problem, we need to follow the steps outlined in the note provided.
(a) To determine the pricing policy, we can use the price elasticity of demand. The elasticity of demand measures the responsiveness of quantity demanded to changes in price. In this case, the estimated elasticity of demand is -0.4.
According to the note, one suggestion is to increase the price of a ride from $1 to $1.50, a 50% increase in price. To find out how this change in price will affect the total rides, we can calculate the percentage change in rides using the elasticity formula:
Percentage change in quantity = Elasticity of demand * Percentage change in price
Given that the elasticity of demand is -0.4 and the percentage change in price is 50%, we can substitute these values into the formula:
Percentage change in quantity = -0.4 * 50% = -20%
This means that a 50% increase in price would result in a 20% decrease in the number of rides.
(b) To determine the new price per ride that the public transportation authority must charge to eliminate the deficit, we need to calculate the new total revenue based on the suggested price change.
The original total revenue can be calculated by multiplying the original number of rides (100 million) by the original price ($1):
Original total revenue = 100 million * $1 = $100 million
Now, since the number of rides is expected to decrease by 20% due to the suggested price increase, we need to calculate the new total number of rides:
New total rides = Original total rides - (Original total rides * 20%) = 100 million - (100 million * 20%) = 100 million - 20 million = 80 million
The new total revenue can be calculated by multiplying the new number of rides (80 million) by the new price ($1.50):
New total revenue = 80 million * $1.50 = $120 million
To eliminate the operating deficit, which is $20 million, the public transportation authority needs to generate sufficient revenue to cover this deficit. This means that the new total revenue of $120 million should exceed the operating costs of $120 million.
Therefore, based on these calculations, the public transportation authority should increase the price per ride to $1.50 and generate new total revenue of $120 million to eliminate the operating deficit if it cannot reduce costs.