What is the socially optimal level of automobile tire

Question

Assignment 1-

Question 1

Suppose the production of a good X damages the environment (i.e. there is a negative externality). Using a diagram, show the dollar amount of inefficiency generated by the free market. Briefly explain how a corrective tax or subsidy policy could help reduce the inefficiency in the market.

Question 2

Suppose the consumption of a good M benefits not only the people who consume it but also the people who don't consume it (i.e. there is a positive externality). Using a diagram, show the dollar amount of inefficiency generated by the free market. Briefly explain how a corrective tax or subsidy policy could help reduce the inefficiency in the market.

Question 3

Suppose that the consumption of canned beverages imposes an external cost on society of $1 per each can consumed. The market for canned beverages is competitive and the marginal cost of production is constant at $0.75 per can. A typical individual's demand for this product is given as q = 500 - 40p.

a) How many canned beverages would a typical individual consume?

b) What is the socially optimal level of consumption for a typical individual?

c) If there are a million people with the same demand for canned beverages what is the total net cost imposed on society from the overconsumption of canned beverages?

d) Draw a detailed supply and demand diagram for the canned beverage market in part (c) above, and show the dollar amount of inefficiency generated by the free market.

Question 4

Suppose the market supply curve for automobile tires in the U.S. is Q_S = 2p - 20, and the market demand curve is Q_D = 220 - 4p. However, in producing tires the firms emit pollution that causes health damage to the local community, and the external cost on society is estimated to be $9 per automobile tire.

a) What is the equilibrium level of automobile tire production?

b) For the 60th automobile tire, what is the marginal benefit (MB) to consumers?

c) For the 60th automobile tire, what is the marginal private cost of production (MPC)?

d) For the 60th automobile tire, what is the marginal social cost (MSC)?

e) For the 60th automobile tire, what is the marginal net loss to society?

f) What is the socially optimal level of automobile tire production?

g) What is the total net loss to society from the production of tires 49 through 60?

Question 5

Suppose firm A and firm B are solely responsible for all pollution in society. Pollution emissions are currently unregulated; however, the government would like to implement a policy that reduces total pollution emissions by 50 tons per year. Economists estimate the marginal abatement cost (MAC) for each firm as, MAC_A = 45, 000 - 600e_A and MAC_B = 15, 000-200e_B , where"e" measures the total amount of each firm's annual pollution emissions in tons.

a) What is the least expensive policy the government can implement to reduce total pollution emissions by 50 tons per year?

b) How much would the policy in part (a) above cost each of the firms?

c) Under the policy in part (a), how much would society spend to reduce total pollution emissions by 50 tons per year?

d) Suppose that lobbyists for Firm B argue that the policy in part (a) is unfair because, in equilibrium, Firm B spends more money on reducing its pollution emissions relative to Firm A. Do you agree that the policy is unfair? Explain why or why not.

e) Suppose that lobbyists for Firm B convince the government to change its policy and require each firm to reduce pollution emissions by an equal 25 tons. Under this new policy, how much would society spend to reduce total pollution emissions by 50 tons per year?

f) What is the underlying economic intuition for the difference in your answers for part (c) and part (e) above?

Question 6

Suppose there are three families on an island and the ratio of their marginal benefits from a defensive wall around the island MB_A : MB_B : MB_C is 5:2:1 at any thickness. For example, at a thickness of 0 feet, MB_A = $1, 000, MB_B = $400, MB_C = $200, and at a thickness of 5 feet, MB_A = $500, MB_B = $200, MB_C = $100. The marginal cost (MC) of building an additional foot of thickness is $800.

a) Draw the diagram, label the curves (lines), and show numbers.

b) Would it be socially optimal to increase the wall thickness above 0 feet? Explain why or why not.

c) What wall thickness is socially optimal?

Question 7

Suppose there are 4 families in society. Each have different preferences for a public good, and their demand curves are expressed as q₁ = 3 - (1/5) p, q₂ = 30 -p, q₃ = 15 - ½ p, and q₄ = 5 - (1/9) p.

The marginal cost of producing the good is a constant $86.

a) What is the equilibrium quantity in this market?

b) What is the socially optimal quantity?

c) What is the underlying economic intuition for the difference in your answers for part (a) and part (b) above?

Question 8

Suppose the following voting preferences shown in the table below. Each family (H, M, L, and D) votes between two choices (such as thick and thin) and then between two other choices.

Choice	H	M	L	D
First	Thick	Intermediate	Thin	Thin
Second	Intermediate	Thin	Intermediate	Thick
Third	Thin	Thick	Thick	Intermediate

a) With H, M, and L voting, but not D, what happens? Why?

b) With H, M, and D voting, but not L, what happens? Why?

Question 9

Suppose a factory would be built in one year (year 0) and last only a year (year 1). The construction cost in year 0 would be $100,000 financed by borrowing and the profit in year 1 would be $120,000.

a) Should the firm build the factory? Explain why or why not.

b) Suppose the factory lasts two years instead of one, and the profit is $60,000 in year 1 and $72,000 in year 2. Should it be built? Explain.

Question 10

Suppose a city has 20,000 residents who ride the subway 200 times per year at a cost of $1.50 per trip. The only alternative is a bus that takes 10 minutes longer and costs $0.50 per trip. The city is considering renovations of the subway system that would reduce the trip time by 5 minutes, but fares would increase by $1.00 per trip to cover the renovation costs. Assume that the fare increase and reduced travel time both take effect next year and last forever, and that the interest rate is constant at 8%.

a) Should the city renovate the subway? Explain why or why not.

b) To justify the $1.00 increase in subway fares based on cost-benefit analysis, the renovations would need to reduce the subway trip time by how many minutes?