Suppose the governor of California has proposed increasing toll rates on California's toll roads, and has presented two possible scenarios to implement these increases. Following are projected data for the two scenarios for the California toll roads:
Scenario 1: Toll rate in 2015: $10.00. Toll rate in 2019: $22.50
For every 100 cars using the toll roads in 2015, only 81.6 cars will use the toll roads in 2019.
Scenario 2: Toll rate in 2015: $10.00. Toll rate in 2019: $17.50
For every 100 cars using the toll roads in 2015, only 96.2 cars will use the toll roads in 2019.
a. Using the midpoint formula, calculate the price elasticity of demand for Scenario 1 and Scenario 2.
b. Assume 10,000 cars use California toll roads every day in 2015. What would be the daily total revenue received for each scenario in 2015 and in 2019?
c. Is demand under Scenario 1 and under Scenario 2 price elastic, inelastic, or unit elastic. Briefly explain.
(For above questions, assume that nothing other than the toll change occurs during the time frame listed that would affect consumer demand.)
What will be an ideal response?
a.
For Scenario 1:
Percentage change in quantity demanded = [(81.6 - 100 ) / 90.8] × 100 = -20.3%
Percentage change in price = [($22.50 - $10.00 ) / $16.25] × 100 = 76.9%
Price elasticity of demand = -20.3% / 76.9% = -0.26.
For Scenario 2:
Percentage change in quantity demanded = [(96.2 - 100 ) / 98.1] × 100 = -3.9%
Percentage change in price = [($17.50 - $10.00 ) / $13.75] × 100 = 54.5%
Price elasticity of demand = -3.9% / 54.5% = -0.07.
b. The daily total revenue in 2015 under both scenarios is (10,000 cars × $10.00 ) = $100,000.
The daily total revenue in 2019 under Scenario 1 is (8,160 cars × $22.50 ) = $183,600.
The daily total revenue in 2019 under Scenario 2 is (9,620 cars × $17.50 ) = $168,320.
c. For both scenarios, total revenue increases when the toll increases, because the demand under both scenarios is price inelastic.
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