The new york times reported 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?
Thake a shot, what do you think?
hint: elasiticty is (%change in Q)/(%change in P). And %change in P = .25/1.25 = 20% (Note: you could use the alternative mid-point method. It would slightly change the answer, but not affect the analysis)
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a.) To estimate the price elasticity of demand for subway rides, we can use the formula:
Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)
Using the information provided, we know that there were nearly four million fewer riders in December 1995 compared to the previous December. This represents a decline of 4.3 percent in subway ridership. Additionally, we know that the price of a token increased by 25 cents (from $1.25 to $1.50).
To calculate the percentage change in quantity demanded, we divide the decrease in ridership (four million) by the previous quantity (the ridership in the previous December). Multiply this result by 100 to find the percentage change.
Percentage Change in Quantity Demanded = (Change in Quantity Demanded / Previous Quantity) x 100
Since the previous quantity is not provided in the question, we cannot calculate the precise percentage change in quantity demanded. However, we can estimate it using the information given. Let's assume that the previous December ridership was 100 million (this is just an assumption for illustration purposes):
Percentage Change in Quantity Demanded = (4 million / 100 million) x 100 = 4 percent
Now we can use this estimated percentage change in quantity demanded, along with the given 25-cent increase in price, to calculate the price elasticity of demand:
Price Elasticity of Demand = (4 percent) / (25 cents / $1.25) = 0.64
Therefore, the estimated price elasticity of demand for subway rides is approximately 0.64.
b.) According to the estimate of the price elasticity of demand, when the fare rises, we can predict the impact on the Transit Authority's revenue. A price elasticity value of 0.64 suggests that the demand for subway rides is relatively inelastic, meaning that the percentage change in quantity demanded is smaller than the percentage change in price.
In this case, a fare increase led to a decrease in quantity demanded by 4.3 percent. However, the relatively inelastic demand means that the decrease in ridership is proportional to the fare increase but not to the same extent. Therefore, the increase in fare will result in a smaller percentage decrease in revenue compared to the percentage decrease in ridership.
c.) The estimate of the elasticity might be unreliable due to several reasons:
1. Assumptions: We had to assume a previous December ridership figure to estimate the percentage change in quantity demanded. If this assumption is significantly different from the actual figure, it will affect the reliability of the estimate.
2. Timeframe: The reported decline in ridership is based on only one month (December 1995) after the fare increase. It would be more accurate to consider a more extended period to capture any seasonal or cyclical effects and to account for possible delayed adjustments in demand.
3. Other Factors: The estimate assumes that the fare increase was the only factor influencing ridership. However, there may have been other factors such as changes in population, economic conditions, or alternative transportation methods that could also impact ridership.
4. Data Accuracy: The accuracy of the reported data is crucial for reliable estimates. If the ridership figures or fare increase are not accurately measured or reported, it can affect the final estimate.
5. Cross-Price Elasticity: The estimate of the price elasticity of demand assumes that there are no significant changes in the prices of substitute goods (e.g., other forms of transportation). However, if the prices of alternative modes of transportation also changed during the time period, it could influence the ridership decline and affect the estimate of the price elasticity of demand.
Considering these factors, it is important to understand the limitations of the estimate and conduct more comprehensive analysis if a more accurate estimation is required.