Question

The demand for hourly landings at the Richmond airport is: Qd=30-(1/3)P The airport is willing to provide landings Qs= (1/4)P-1.5. Unfortunately, landings are noisy and disturb Richmond residents.  The damage is estimated to be TD=3Q+Q².  (Q is hourly landings)

The BC government has proposed three solutions to our problem:

Solution A: An optimal Pigou tax on airport landings

Solution B: The airport is ordered to stop producing noise until they get permission to do so from Richmond residents.

Solution C: Residents are informed that they choose to live next to the airport and will have to bargain with the airport if they want noise reduction.

e. What is the optimal Pigou tax and how much revenue will this tax earn for the government?

f. Under Solution B, what is the maximum payment the airport is willing to make to Richmond residents to allow noise to operate?  What is the minimum payment residents will demand from the airport in order them to operate at the optimal level?

g. Under Solution C, what is the maximum payment residents are willing to pay to get the airport to reduce production?  What is the minimum payment the airport must receive to reduce production?

Complete this table showing the effects of each of these solutions:

                 Landings   Total gains to airport customers (CS + PS)     Noise Damage  Total Social Gains

Solution A

Solution B

Solution C

Answer 1

a).

Qd = 30 - (P/3), so 3Qd = 90 - P, and P = 90 - 3Qd

Qs = (P/4) - 1.5, so 4Qs = P - 6, and P = 6 + 4Qs

Setting Qd = Qs = Q,

90 - 3Q = 6 + 4Q

7Q = 84 $\Rightarrow$ Q = 12

P = 90 - 3 x 12 = 90 - 36 = 54

b).

When Qd = 0, P = 90

Consumer surplus (CS) = (1/2) x (90 - 54) x 12 = 6 x 36 = 216

When Qs = 0, P = 6

Producer surplus (PS) = (1/2) x (54 - 6) x 12 = 6 x 48 = 288

Total private surplus (TS) = CS + PS = 216 + 288 = 504

c).

When Q = 12,

TD = 3 x 12 + 12 x 12 = 36 + 144 = 180

TS (including damage) = TS (excluding damange) - TD = 504 - 180 = 324

d).

MD = dTD/dQ = 3 + 2Q

In social optimal, Demand = Supply + MD

90 - 3Q = 6 + 4Q + 3 + 2Q

9Q = 81 $\Rightarrow$ Q = 9

P = 90 - 3 x 9 = 90 - 27 = 63

CS = (1/2) x (90 - 63) x 9 = 4.5 x 27 = 121.5

When Q = 9, from supply function, P = 6 + 4 x 9 = 6 + 36 = 42

PS = (1/2) x (42 - 6) x 9 = 4.5 x 36 = 162

TS = 121.5 + 162 = 283.5