The total operating revenues of a public transportation authority are $100 milli
ID: 1095032 • Letter: T
Question
The total operating revenues of a public transportation authority are $100 million while its total operating costs are $120 million. The price of a ride is $1, and the price elasticity of demand for public transportation has been estimated to be -0.4. By law, the public transportation authority must take steps to eliminate its operating deficit. What price per ride must the public transportation authority change to eliminate the deficit if it cannot reduce costs? Suggestion increase the price of a ride from $1 to be $1.50, a 50% increase in price. Given the price elasticity of demand of -0.4, calculate the percentage change in the ride and the total new rides (the original rides are 100 million = $100 million/$1) using equation (4-7). Then use the total new rides time the new price of $1.50 to obtain the new total revenue. The public transportation authority should increase the price by x%.
Explanation / Answer
The total operating revenues of public transportation authority are $100 million while its total operating costs are $120 million. The price of a ride is $1, and the price elasticity of demand for public transportation 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 authority adopt? (Should the transportation authority increase or decrease the price per ride based on the price elasticity of demand?)
Solution: Computation of the following
The transportation authority should increase the price to eliminate its operating deficit. Price elasticity of demand is -0.4. It means that demand is inelastic at this point. We know that total revenue increases in response to price increase for inelastic demand. So, it is advisable to increase the price per ride.
(b) What price per ride must the public transportation authority charge to eliminate the deficit if it cannot reduce costs?
Solution: Computation of the following
Operating revenues =$100 million
Price per ride=$1 per ride
Total number of rides =$100/1=100 million
Authority should increase the price per ride to eliminate the deficit. As cost reduction is not possible.
Let authority increases the price by x%.
Change in number of rides=-0.4*x=-0.4 x
Total Revenue=(1-0.4x)*(1+x)*100
Since this revenue should be equal to $120 million to eliminate the deficit.
(1-0.4x)*(1+x)*100=120
1-0.4x+x-0.4x^2-1.20=0
-0.4x^2+0.6x-0.2=0
0.4x^2-0.6x+0.2=0
4x^2-6x+2=0
2x^2-3x+1=0
2x^2-2x-x+1=0
2x*(x-1)-1(x-1)=0
x=1/2 or x=1
Price should be increased by 50% or 100%.
In case of 50% increase, New price per ride=1*(1+50%)=1.5
In case of 100% increase, New price per ride=1*(1+100%)=2
(Increase the price of a ride from $1 to be $1.50, and 50 percent increase in price. Given the price elasticity of demand of -0.4, calculate the percentage change in the ride and the total new rides with the original rides being 100 million = $100 million /$1) using equation: point price elasticity of demand = Ep=change in quantity/ change in price times price/quantity. Then use the total new rides time the new price of $1.5 to obtain the new total revenue.
Solution: Computation of the following
% change in the ride = percentage change in price*price elasticity of demand = 50*(-0.4) = -20% i.e. ride will decline by 20%.
So total new rides = 100+100*(-20%) = 80 million
New total revenue = new price *new rides = 1.5*80 = $120 million
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