Question

Suppose you are the administrator in charge of setting the toll for crossing a toll bridge across a river. The current toll is $1 per trip and at that toll 1000 trips per hour are taken across the bridge. (a) If the price elasticity of demand for trips is 2.0, what will happen to the number of trips taken per hour if you raise the toll by 10 percent? How would this affect the total revenue collected per hour? (b) If the price elasticity of demand for trips is 0.5, what will happen to the number of trips taken per hour if you raise the toll by 10 percent? How would this affect the total revenue collected per hour? (c) Other things equal, at the current toll of $1, what do you think will happen to the elasticity of demand for trips, if the average incomes of people who use the bridge rise? Explain why. (d) Other things equal, at the current toll of $1, what do you think will happen to the elasticity of demand for trips if a non-toll bridge is built a few miles up the river? Explain why. Please provide formula for each problem and how each number/calculation was found for clarity. Thank you

Answer 1

Initial revenue = $1 x 1,000 = $1,000

(a) Price elasticity is 2, so if price (toll) increases by 1%, number of trips decreases by 2%.

If toll increases by 10%, number of trips decrease by (2 x 10) = 20%.

New number of trips = 1,000 x 80% = 800

New revenue = P x Q = $1 x 1.1 x 800 = $880

Revenue has decreased by $(1,000 - 880) = $120

(b) Price elasticity is 0.5, so if price (toll) increases by 1%, number of trips decreases by 0.5%.

If toll increases by 10%, number of trips decrease by (0.5 x 10) = 5%.

New number of trips = 1,000 x 95% = 950

New revenue = P x Q = $1 x 1.1 x 950 = $1,045

Revenue increased by $(1,045 - 1,000) = $45

(c) If average income increases, assuming the bridge is a normal good, percent of income spent on the bridge will increase. Higher usage will make usage of the bridge more price-sensitive, so demand will be more elastic.

(d) The non-toll bridge will allow users to switch from the toll bridge to the non-toll bridge (assuming they ignore the transportation cost), and demand for the toll bridge will fall. Demand will become more price-sensitive, and more elastic.

Answer 2

Now using basic definition & formula for price elasticity of demand.

Answer 3

1. Thetotal revenue test of price elasticity of demand I Imagine that you run the toll authority for a city bridge. You must charge all of your customers the exact same toll. Initially, you have set the price at 56 per trip. The blue line on the following graph shows the weekly demand curve for trips across the city bridge. On the following graph, use the purple rectangle (diamond symbols) to shade the area representing the total weekly revenue when the toll is $ 6 on the graph. Note: Select and drag shaded regions from the palette to the graph. To resize the shaded region, select one of the points and move to the desired position. To see the area of ​​the rectangle, select the shaded region. 10 Demand 0 0 00 10 20 30 40 50 60 70 80 QUANTITY (Thousands of vehicles per week) 100 When the toll is $ 6, total revenue is TR at $ 6 TR at 58 An advisor has suggested that if you raise the toll to 58, the toll authority would bring in more revenue. To analyze this, use the green rectangle (triangle symbols) to shade the area representing the total weekly revenue when the toll is $ 8 on the previous graph. (?) incorrect per week, but when the toll is $ 8, total revenue is Based on your analysis, you can conclude that your advisor is suggesting that total revenue would rise if you increase the toll from $ 6 to $ 8, because the demand for trips across the bridge for prices between $ 6 and $ 8 is Inelastic correct per week. elastic