If a 25 cent toll was added, what is the new volume crossing the bridge? What volume would be expected with a 50 cent increase?
A bridge has been constructed between the mainland and an island. The total cost
(excluding tolls) to travel across the bridge is expressed as C ? 50 ? 0.5V, where V is
the number of veh/hr and C is the cost/vehicle in cents. The demand for travel
across the bridge is V ? 2500 ?10C .
What will be an ideal response?
1. Add 25 cents to the original cost function.
C = 50 + 0.5V + 25
C = 75 + 0.5V
Substitute the above cost function into the demand function and solve for V.
V = 2500 – 10(75 + 0.5V)
V = 2500 – 750 – 5V
6V = 1750
V = 291.67
Therefore, the new volume crossing the bridge will now be 292 vehicles / hour with a 25 cents toll.
2. Add 50 cents to the original cost function.
C = 50 + 0.5V + 50
C = 100 + 0.5V
Substitute the above cost function into the demand function and solve for V.
V = 2500 – 10(100 + 0.5V)
V = 2500 – 1000 – 5V
6V = 1500
V = 250
With no toll, the volume would be 334 vehicles/hour; with 50 cents toll, the volume would be 250 vehicles/hour. That means that an increase of toll by 50 cents reduces traffic by 334 – 250 = 84 vehicles/hour.
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