# Tradable Permits. Firm A and B each emit 50 units of pollution

## Question: Tradable Permits. Firms A and B each emit 50 units of pollution

- Tradable Permits. Finns A and B each emit 50 units of pollution. The federal government wants to reduce pollution levels. The total costs associated with pollution reduction at each firm are TC
_{A}=1/2 Q^{2}_{A}and TC_{B}= Q^{2}B. where Q_{A}is the quantity of pollution reduction by film A and Q_{B}is the quantity of pollution reduction by firm B. Society’s total benefit from pollution reduction is y TB = 100QT — ½ Q^{2}T where QT = QA + QB. - f) Find the equilibrium price of a permit and the number of permits bought and sold by each firm if each is given 20 permits (so that it would have to achieve 30 units of reduction if it didn’t buy or sell any permits) and the firms trade permits in a competitive market. Choose either Plan 1 or Plan 2 to find the answer. Plan 1:
- Set the marginal cost of reduction for each firm equal to the price of a permit and solve for the cost minimizing quantity of reduction for each firm as a function of price. Recognize that since reducing pollution by one allows the firm to sell a permit, the price of a. permit is also the price of “selling” reduction.
- Add the reductions of the firms to get the total reduction as a function of price. (This is horizontal summation, similar to adding up individual supply curves, qs(P), to get the market supply curve except that this equation is a. supply function for reduction. You can think of the firm as producing reduction and then selling it for the price it receives for the permit it no longer needs.)

- Find the price where the combined cost minimizing reduction equals the amount of reduction required by the government (this is the demand for reduction).

- Find the amount of reduction at each firm by using the condition that MCA = MCB = P. Then, find pollution at each firm.
- Which firm would sell permits and how many would it sell?
- g) Assuming the optimal price of a permit and the number of permits sold from part f), what is the total amount each fun spends on reduction and spends/earns from the buying/selling permits? How does it compare to its total cost of reduction from part e)? Is each firm better or worse off than in part e)? Why? Is society better or worse off than in part e)? Why?
- h) What tax on pollution would achieve the socially optimal level of pollution? How much revenue would the government raise from this tax?
- i) The government is trying to decide whether I) to use a per unit tax on pollution, II) issue a certain number of permits, or III) require a specific amount of reduction at each plant. If the marginal benefit of reduction function is known and constant (e.g. 40 dollars per unit regardless

Of the level of pollution) what are the information requirements for achieving optimal reduction under each scheme?