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The $\textit{New York Times}$ reported (Feb. 17, 1996) that subway ridership declined after a fare increase: "There were nearly four million fewer riders in December 1995, the first full month after the price of a token increased 25 cents to \$1.50, than in the previous December, a 4.3 percent decline."a. Use these data to estimate the price elasticity of demand for subway rides.b. According to your estimate, what happens to the Transit Authority's revenue when the fare rises?c. Why might your estimate of the elasticity be unreliable?

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So for this problem, we need to calculate the elasticity. It's the percentage change in quantity divided by the percentage change in price. And fortunately, the percentage change in quantity has already been calculated for us because we were told there was a 4.3% decline in ridership. Okay, so writing 4.3 percent has a decimal yet 0.43 Now, we just need the change in price. Will. The change in price was 25 cents. And what was the price previously? Well, we know it's now a dollar 25 so just take away that 25. Excuse me. Dollar 50. Take away the 25 cents and you have a dollar 25. Okay, so we have our percentage change in quantity and then the two numbers that will give us our percentage change in price. You throw that into a calculator, what do you get? A point 215 All right now, you'll notice this is less than one. What does that tell us? Tells us it's in elastic. So for part B, we can assume that the Transit Authority's revenue is going to increase when fares rise. However, for part C. Why might this be unreliable? Because this was a one month change, right? They said this was the first full month of the fare increase. So that's the short run. What about a year from now? What about five years from now? Might people just take a cab or a bus instead of the subway, Or maybe the walk or ride a bike? Maybe they will carpool or even take their own car, so just because this happened over the course of one month doesn't give us any kind of indication of what will happen in the long run.

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