Identify a marginal social abatement cost curve and a

Question

SCENARIO

Now we have two pollution sources,factory A and factory B, both of which produce 160 ton of pollutants respectively every year. A total of 320 ton of the emitted pollutants causes the health damage of residents in city 1 and city 2.There are currently 100 residents in the two cities. The regulatory authority now knows that marginal abatement cost in $ (MAC) is a function of annual amount of emission of the pollutantsin ton (M) and that of two factories A and B are defined as follows, respectively.

MAC_A = 8 - 1/20 M
MAC_B = 4 - 1/40 M

PROBLEM 1

When the pollutants are uniformly mixed over two neighboring cities, the spatially homogeneous ambient concentration of the pollutants is defined as:

A = 1/20000 M²

Furthermore, the damage function is defined as:

D = 1/20000 M²·POP

where, POP denotes total affected residents.

QUESTION 1: Identify a marginal social abatement cost curve and a marginal social damage curve and draw them inone graph takingM as horizontal axis for the rage between 0 ton and 320 ton.

QUESTION 2: What is socially optimal level of the annual emission M*?Answer in ton.

QUESTION 3: To achieve the social optimum, how much of the emissions should be abated for the factory A and factory B, respectively? Answer in ton.

QUESTION 4: To achieve the social optimum via market-based instruments such as tax or subsidy, how much economic incentives are given for factory A and factoryB, respectively? Answer in $.

QUESTION 5: To achieve the social optimum through subsidy program, how much subsidy does factory A and factory Breceive, respectively? Answer in $.

PROBLEM 2

When the pollution has spatially heterogeneous effects where the mixing of pollutants is not uniform, the ambient concentrations of the city 1 denoted by A₁ and the city 2 denoted by A₂ can be differentand are defined as follows:
A₁ = 2/20000.MA² + 2/20000.MB²
A₂ = 6/20000.MA² + 4/20000.MB²

Furthermore, the damage functions in each city can be written:

D₁ = A₁·POP₁
D₂ = A₂·POP₂

QUESTION 6: When POP₁ =75 and POP₂ =25, what are the socially optimal levels of emissions M_A*and M_B*? Answer in ton.

QUESTION 7: At the optimal levels of emissions, what are the marginal abatement costs for factory A and factory B, respectively? Answer in $.

QUESTION8: At the optimal levels of emissions, what are the ambient concentrations of city 1 and city 2, namely A₁* and A₂*? Answer in $ per person.

QUESTION 9: At the optimal levels of emissions, what are the total damage of city 1 and city 2, namely D₁* and D₂*? Answer in $.