Q1: The government has decided to introduce a marketable permit system to address a pollution problem. Currently there are three firms releasing 15 units each of emissions (denoted as E) into the environment for a total of 45 units. Each firm's Abatement costs are as follows Firm 1: TAC = 3A² Firm 2: TAC = A2 Firm 3: TAC = 1.5A² Where A is a unit of abatement such that E 15 - A would be the level of emissions with abatement. The regulator has estimated the aggregate benefit of abatement as B = 90A - A² 1. Find the MAC for each firm and aggregate to get the total MAC for the industry (aggregate horizontally: A1 + A2 + A3 = A). Draw a graph with A on the horizontal axis and carefully graph the MAC 2. Find the marginal benefit of abatement, MB, and add it to your graph from (a) 3. What is the optimal level of Abatement? What would be the permit price for this level of abatement? What would be the aggregate amount of emissions still being produced? If we write the marginal benefit of abatement in term of emission, we get the marginal damage function. 1. If the current emissions (total) are 45 - A = E, then find a simplified expression for the marginal damage function MD = f(E) 2. Similarly, each firm's marginal savings function is found by replacing A₁ = 15 - E; Write out each firm's MAC as a function of E. 3. Aggregate each firm's MAC to get the aggregate MAC function. With E on the horizontal axis, graph the MD and MAC functions. What is the equilibrium value of E? 4. Now suppose the government gives each firm five permits (E = 5) which they can use or trade amongst themselves. Calculate the outcome of the trading market. What will be 1. The permit price? 2. Each firm's E and abatement (A). 3. Who will be net sellers and net buyers of the permits?

13. The 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? What would be the total cost of abatement in this latter case?

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No hand written solution Afirm has an industrial plant that emits pollutants into a town’s lake. The plant’s marginal abatement function is MAC= 200 – 0.5E and damages caused by its emissions are given by MD = 2E where emissions are in kg. per day. What is the socially efficient level of emissions from this plant? Illustrate this in a graph.   As an incentive to reduce emissions to the socially efficient level, government offers to pay the firm for each kg. of emissions it abates per day from this plant.   What subsidy per kg. should the government offer? If the plant abates to the socially efficient level of emissions, what total subsidy payment would the firm receive? Identify the area in your graph. How much better or worse off would the firm be compared to if it did no abating? Identify the area in your graph. What would be the net benefit to society if we pay the firm to reduce the plant’s emissions to the socially efficient level? Identify this area in your graph.