Marginal benefit and marginal cost of abatement

Question

Please provide detailed explanations. Show all your work.

1) Externalities:

Assume that scientific studies provide you with the following information concerning the benefits and costs of sulfur dioxide emissions:

Marginal benefits of abating (reducing) emissions: MB = 400 – 10A

Marginal costs of abating emissions: MC = 100 + 20A

where A is the quantity abated in millions of tons and the benefits and costs are given in dollars per ton.

a) What is the socially efficient level of emissions abatement?

b) What are the marginal benefit and marginal cost of abatement at the socially efficient level of abatement?

c) What happens to net social benefits (benefits minus costs) if you abate one million more tons than the socially efficient level?  One million fewer?

d) Why is it socially efficient to set marginal benefits equal to marginal costs rather than abating until total benefits equals total costs?

2) Externalities:

Suppose that a honey farm is located next to an apple orchard and each acts as a competitive firm. The apple firm benefits from the bees in the honey farm because the bees help pollinate the apple trees. The apple firm pays nothing for this service, however, because the bees come to the orchard without the apple firm having to do anything. Let the amount of apples produced be measured by A and the amount of honey produced be measured by H.  The cost functions are as follows:

Honey firm:  C_H(H) = H²/100           so MC_H = H/50
Apple firm:   C_A(A) = A²/100 – H      so MC_A = A/50

The price of honey is $2 and the price of apples is $3.

a) If the firms operate independently, what will be the equilibrium amount of honey produced by the honey farm?  What will be the equilibrium amount of apples produced by the apple orchard?

b) Suppose that the honey and apple firms merged.  Now the total cost function is

C_TOTAL = H²/100 + A²/100 – H
so MC_H = H/50 – 1 and MC_A = A/50.

What would be the profit-maximizing output of honey for the combined firm?

c) What is the socially optimal amount of honey?  Why is honey production higher in part b than in part a?

d) If the firms stayed separate, how much would honey production have to be subsidized in order to induce an efficient supply?

3) Externalities:

Respond to the following statement in one paragraph, paying careful attention to your grammar, style and content. You might want to mention under what conditions the statement would be true, and under what conditions it would be false.

The price of gasoline is too low. As a result, American consumers and firms have formed the bad habit of using too much gasoline.  Increasing the per-unit tax on gasoline would actually raise social welfare.

4) Public goods:

The town of Carson is faced with a serious smog problem. The smog can be dispelled if an air treatment plant is installed at an annual cost of $3 million. There is no way to clean the air for some but not all the town’s population. Each of the town’s families acts independently, and no single family can afford to carry out the project by itself.  Why doesn’t a private firm build the air treatment plant and sell its services to the town’s families (acting individually)?  What is a possible solution to the smog problem?