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- Q42Firms in a polluting industry can be classified in two groups: newer firms with a cleaner technology that can abate pollution at a lower marginal cost MCLA = (1/2)aL and older firms with dirtier MCHA = aH, where ai is the level of abatement undertaken by firms of type i = L, H. The social marginal benefit of abating pollution from this particular industry is MBA= 120 - A, where A is the aggregate level of abatement in that industry. To design an efficient emissions standard, the government needs to determine which is the efficient abatement allocation (aL, aH). In order to do this, obtain a cost effective abatement allocation (aL, aH)that provides an aggregate abatement level A = aL + aH, and then proceed to determine the efficient level A (Hint: You should obtain that MCA = A=3)5B. Two textile mills, located across a river from each other, are polluting the river. The marginal costs of pollution reduction for each firm are MCE₁ = 4E₁ + 4 MCE2 = 4/3E2 + 4/3, where E is the reduction in pollution from unregulated levels. The associated marginal social benefit is estimated to be MSB = 10-E, where E = E₁ + E₂. a. What is the socially optimal level of water-pollution reduction? c. If instead the government imposed a standard requiring each firm to equally reduce the level of pollution to achieve the socially optimal solution in part (i), what are the costs for each firm?
- Firms in a polluting industry can be classified in two groups: newer firms with a cleaner technology that can abate pollution at a lower marginal cost MCLA = (1/2)aL and older firms with dirtier MCHA = aH, where ai is the level of abatement undertaken by firms of type i = L, H. The social marginal benefit of abating pollution from this particular industry is MBA= 120 - A, where A is the aggregate level of abatement in that industry. Suppose that in order to avoid the costly obtention of disaggregate information about individual firms' costs, the government just implements a uniform standard aui = A* / 2. Is this allocation efficient? If not, what is the deadweight loss?Consider two firms with the following marginal abatement costs (MAC) as a function of emissions (E): MAC_1 = 12-.5E_1 MAC_2 = 12-E_2, and assume marginal external damages (MED) from the aggregate emissions of both firms (E_Agg = E_1 + E_2) is: MED = (1/3)E_Agg. To achieve the socially efficient level of aggregate emissions (E*_Agg), the government institutes a per unit tax on emissions. The per- unit tax on emissions is $ Answer:A profit-maximizing firm operating two factories currently emits 10 tons of pollution. Marginal private benefit of each ton emitted at each factory is listed in the table below. If it must reduce pollution by 6 tons, how many tons would it continue to emit from Factory B? Marginal Private Benefit Factory B $14 $12 $9 Factory A $20 Ton $18 $15 $11 $7 3 4 $6 $3
- PRICE (Dollars per ton) 70 63 56 49 42 35 28 + 21 T 14 7 0 Demand +++ 0 40 80 120 160 200 240 280 320 360 400 QUANTITY (Millions of tons) Graph Input Tool Daily Demand for Pollution Rights Price (Dollars per ton) Quantity Demanded (Millions of tons) 7 360 Suppose the government has determined that the socially optimal quantity of particulate matter is 120 million tons per day. One way governments can charge firms for pollution rights is by imposing a per-unit tax on emissions. A tax (or price in this case) of $ of particulate matter emitted will achieve the desired level of pollution. ? per ton Now suppose the U.S. government does not know the demand curve for pollution and, therefore, cannot determine the optimal tax to achieve the desired level of pollution. Instead, it auctions off tradable pollution permits. Each permit entitles its owner to emit one ton of particulate matter per day. To achieve the socially optimal quantity of pollution, the government auctions off 120 million…In a market for chemicals, the demand function is P = 200 – Q. The private marginal cost for the chemicals produ cers is MCP = 50 + Q. Pollution generated during the production process causes external marginal cost for the society equal to MCE = 3Q. 4. (a) What specific tax would resultin a competitive market producing the socially optimal quantity of chemicals? Instead of taxation, whatelse can the government do to make sure that the market will work itself out to achieve the socially optimal output? (b)Suppose there are only two polluting firms, called A and B, with the following marginal abatement costs: MACA=160 2- e and MACB=100-es, where e represents firm A's emissions in tons and ea represents firm B's emissions in tons. Suppose the government wishes to ensure that the two firms together emit 60 tons of the pollutant and uses a Tradable Emission Permit (TEP) policy. Assume that each TEP allows its holder to emit 1 ton, and that the market for permits is perfectly competitive. a. Suppose the government initially distributes the total number of TEPs it issues equally between the two firms. The permits are distributed free of charge. Once trade in permits takes place, what will be the equilibrium in the market for TEPS (i.e. which firm will buy how many TEPs from the other, and at what price)? b. Briefly describe three problems of setting up a TEP market.
- Firms in a polluting industry can be classified in two groups: newer firms with a cleaner technology that can abate pollution at a lower marginal cost MCLA = (1/2)aL and older firms with dirtier MCHA = aH, where ai is the level of abatement undertaken by firms of type i = L, H. The social marginal benefit of abating pollution from this particular industry is MBA= 120 - A, where A is the aggregate level of abatement in that industry. What Pigouvian tax t will implement the efficient allocation (aL, aH)? Is the resulting allocation an efficient allocation? What is the government's tax revenue?There are two towns, A and B, each with a plant emitting pollution. The emission from plant Ais uniformly distributed across both town A and B. The emissions from plant B are local to town B. Despite the difference in affected area, the marginal benefit to either town of abating one unit of pollution from either source is the same, MB(Qi) = 17 − Qi per person, where Qi is total emissions abated from town i’s air. The marginal cost of abatement at plants A and B are MCA(qA) = 200qA and MCB(qB) = 100qB, respectively. If town A has 300 citizens and town B has 200, what is the efficient tax to set at each plant?An emissions tax equal to _____ induces polluters to internalize the externality and leads to the socially optimal quantity of pollution. OA) the marginal social benefit at zero pollution B) the marginal social cost of pollution at the market-determined level of pollution C) the marginal social cost of pollution at the socially optimal quantity of pollution D) the marginal social benefit of pollution at the market-determined level of pollution
