Question

Question 1: Suppose you are in charge of a toll bridge that is essentially cost free. The inverse demand for bridge crossings Q is given by P 20 , where P designates the potential toll fee. a How many people would cross the bridge if there was no fee? b What is the loss of consumer surplus associated with the charge of a bridge toll of $5? c As the toll bridge operator you're debating raising the toll to $6. At this higher price, would the toll revenues increase or decrease? What does your answer tell you about the elasticity of demand?

Answer 1

(a)

If there is no fee, P = 0.

0 = 20 - (Q/3)

Q/3 = 20

Q = 60

(b)

When P = $5,

5 = 20 - (Q/3)

Q/3 = 15

Q = 45

Consumer surplus (CS) = Area between demand curve and price charged.

When Q = 0, P = $20 (Vertical intercept of demand curve)

When P = 0, CS = (1/2) x $(20 - 0) x 60 = 30 x $20 = $600

When P = $5, CS = (1/2) x $(20 - 5) x 45 = 22.5 x $15 = $337.5

Loss in CS = $600 - $337.5 = $262.5

(c)

When P = $5, Revenue = P x Q = $5 x 45 = $225

When P = $6,

6 = 20 - (Q/3)

Q/3 = 14

Q = 42

When P = $6, Revenue = P x Q = $6 x 42 = $252

At higher price, toll revenue will increase. Since a rise in price increases revenue, demand is inelastic and absolute value of elasticity of demand is less than 1.