he marginal benefit of being able to emit a ton of sulfur dioxide emissions for two firms are given by: MBX = 1000 – ( Ex / 2 ) MBY = 600 – ( Ey / 3 ) Note that these marginal benefit figures can be interpreted as marginal cost of abating emission down to levels Ex and Ey. Government regulators want to reduce total sulfur dioxide emissions to a total of 1800 tons. a) If the government imposes the same standard of 900 tons maximum emissions on both firms what would be the total cost of abatement (calculated as the aggregated marginal benefits forgone)? b) If the government distributed 900 tradable pollution permits (one ton each) to each firm what would be the final allocation of these permits after the firms trade them? c) What would be the total cost of abatement in this latter case?

Hand written solutions not allowed

Suppose there are three polluting sources with MAC1 = 100 - 4E, MAC2 = 80 - 2E and MAC3 = 60 - 0.5E. When MAC equals $10, the aggregate level of abatement for these sources would be _______.

Exton and Shill are 2 firms that can control emissions at the following marginal costs: MC1 = 400q1, MC2 = 200q2, where q1 and q2 are the amount of emissions reduced by Exton and Shill, respectively. Assume that with no control at all, each firm would be emitting 25 units of emissions. Estimate the cost-effective allocation of emissions control needed if a total reduction of 30 units of emissions is necessary.

Suppose there are two industries with the estimated MAC functions as follows: MACA = 900-3Ea and MACB=600-2EB And suppose their estimated damages could be MD = 2E (the same for both industries). What would be the optimal emission standards for each industry and what would be the abatement costs for each polluter? Show your calculations.

Gerard.inc. is one of the leading producers of dairy exports. The company has 2 variants of superior milk, namely mocha and green tea. Based on historical data, the R&D team has found that the advantage per liter for each milk variant follows the following equation: πmocha = $45 - 0.9x and πgreen-tea = $65 - 1.7y Where x is the number of liters of mocha milk produced and y is the number of liters of green tea milk produced. It takes 2 hours to produce 1 liter of mocha milk and 5 hours to produce 1 liter of green tea milk. With the current number of workers, companies have a total of 40 hours of work in a day, and everything should be used to make both variants. The company wants to know the optimal amount of milk to be produced. a. How many liters of mocha milk and green tea should the company produce? b. What is the optimal objective function value based on your calculations? c. What is the lagrange multiplier value and what does it mean?

Imagine a firm with a marginal abatement cost (MAC) function equal to: MAC = 27-3E. The government introduces a per-unit tax on emissions equal to $6. For a profit-maximizing firm, total compliance costs (total abatement costs plus tax payment) are $ Answer:

Consider an industry with two firms that emit a uniformly mixed air pollutant (e.g., carbon dioxide). The marginal abatement cost functions for Firm 1 and Firm 2 are: MAC1 = 100 - e1 MAC2 = 100 - 4e2 Aggregate emissions for the industry are denoted as E = e1 + e2. 1. In an unregulated environment how many units of emissions does each firm emit?             Firm 1’s unregulated level of emissions ____________             Firm 2’s unregulated level of emissions ____________             Total unregulated level of emissions ______________ Suppose a regulator has a goal of reducing the total level of emissions from the amount from the amount you answered in [1] to 25 units. The regulator would like to achieve the goal of 25 units of total emissions in a cost-effective way. To do so it issues 25 permits, 10 are given to Firm 1 and 15 are given to Firm 2. A firm can only emit a unit of pollution if they have a permit for that unit, otherwise they must abate. After the permits are allocated,…

Under what circumstances might an equal allocation of abatement responsibility across all firms in an industry do a pretty good job of achieving a desired overall level of abatement at the lowest overall cost, without the need to resort to market-based methods such as pollution taxes or cap-and-trade?

Suppose a power generating plant emits particulates that damage crops and affect human health. The relationship between emissions and environmental damage is represented by the marginal damage function, MD=9e where e represents tons of emissions per month. The cost to the firm (and society) of eliminating emissions is represented the marginal abatement cost function, MAC=108.5 - 6.5e Both MD and MAC are dollar costs per month. If the power generating firm were allowed to ignore the social cost of its emissions, what would be the firm’s monthly emission level? Calculate the socially efficient level of pollution. If the emissions calculated in part B is a level found to shorten some people’s lives, could it still be considered socially efficient? Suppose the EPA set an emission standard at the socially efficient level calculated in part B.  Calculate the cost to the firm of achieving this standard. Suppose that instead of a standard, the EPA charged an emissions tax. The tax is set at…