A city doubles the car driving fee from $8 to $16. Let\'s determine what effect

Question

A city doubles the car driving fee from $8 to $16.

Let's determine what effect this will have on revenue for the city. To be conservative, let's assume that the absolute value of the elasticity of the demand for car trips in central London is 2, which is bigger than what you calculated in the previous question. Using a higher elasticity means that if you consider a given change in the total cost, the estimated number of trips will fall by more than it would if you used the true elasticity. Using this larger elasticity is conservative because it will cause you to underestimate the revenue the city will collect at the higher fee. It predicts a bigger fall in the number of drivers, which yields less revenue. So, if you find that revenue goes up when you use an elasticity of 2 to estimate the effect of changing the fee from $8 to $20, you can be sure that it will go up with a lower value of the elasticity.

Suppose that the increase in the fee from $8 to $16 reduces travel time in the central city from 30 minutes down to 20 minutes. Which of the following values is the best estimate of the percentage change in the total cost of driving in central London?



A. 30%
B. 10%
C. 5%
D. 20%
E. 15%
F. 25%

Explanation / Answer

The car driving fee is only one of the costs of driving. We are given that the elasticity of car trips is 2. So: E = |dQ/dP * P/Q| 2 = |dQ/dP * P/Q| Remember that we're using the midpoints to calculate elasticity. So, we can break this down further to: 2 = |(Q1-Q2)/(P1-P2) * ((P1+P2)/2)/((Q1+Q2)/2)| And we are given that driving time decreased from 30 to 20. That means Q1=30 and Q2 = 20 2 = |(30-20)/(P1-P2) * ((P1+P2)/2)/((30+20)/2)| 2 = |(10)/(P1-P2) * ((P1+P2)/2)/25| (2/10)*25 = ((P1+P2)/2)/(P1-P2) 5 = ((P1+P2)/2)/(P1-P2) But notice that the expression on the right is just the formula for the percentage change in the total cost of driving in central London. So, the answer is C. The trick is to realize that the fee is only part of the cost of driving. A good follow up question would be to ask you to calculate the total cost of driving given the information you have now.

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