(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.
Question 1: Suppose you are in charge of a toll bridge that is essentially cost free....
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