Assume that the market for rubber bike tires in the town of

Assume that the market for rubber bike tires in the town of “Cycle City” is a competitive market and the demand for rubber tires is given by the inverse demand function P_D = 100 – 4Q_D. Furthermore the Supply for tires is given by P_s= 10 +2Q_s.   While the citizens of Cycle City enjoy riding their bikes everywhere they have noticed that the smog from the bike tire factories in town is getting worse and worse. While the smog makes the view of the surrounding mountains unpleasant, many citizens have also complained of challenges with breathing; and a group of environmentalists has stated that the wildlife in the forest on the border of town is suffering from the excess air pollution from the bike tire factories.

Clean Air Corp has hired a team of economists to estimate the damages caused by the pollution. They have estimated that the pollution from the multiple bike tire factories in the city add an additional cost of $12 per bike tire produced on the citizens of the city.

a. If the bike tire market is allowed to operate without intervention, what amount of bike tires will be produced and at what price?

b. What is the dead weight loss placed on the city if production continues at this amount? What is the Total Social Welfare for the city if this production amount continues?

c. What is the socially optimal amount of bike tires that should be produced?

d. Tell me two policies that could ensure this optimal quantity is achieved.

e. For each of the two ways you suggested in part f, use a supply and demand graph to sketch the related scenario and label the areas that represent the consumer surplus and producer surplus after the policy is implemented. Also tell me what the amount of the producer surplus, consumer surplus, and total social welfare is in each case.

Solution

(a) In free market equilibrium, PD = PS

100 - 4Q = 10 + 2Q

6Q = 90

Q = 15

P = 10 + (2 x 15) = 10 + 30 = 40

(b)

To get answer to this question, you need to specify: Deadweight loss compared to which situation? Is it vis-a-vis a perfectly competitive scenario (where Price, a horizontal curve, equals MC), or if the market were a monopoly? In the 1st case, either Price or MC data should be provided, and in 2nd case, MC data should be provided. The question has insufficient information.

(c)

Additional $12 will increase PS by $12:

New PS = 10 + 2Q + 12 = 2Q + 22

Equating new PS with unchanged PD,

2Q + 22 = 100 - 4Q

6Q = 78

Q = 13

P = 100 - (4 x 13) = 100 - 52 = 48

(d)

Two policies that can be used to ensure optimal quantity is achieved is a pollution (emission) tax as the question states, and a tradable or non-tradable pollution permit.

NOTE: First 4 sub-questions have been answered (or clarified).