Question 2: Assume the marginal savings from emissions for an industry are given by MS(e) = 30 – e and that the marginal damage from emissions is given by MD(e) = e. Plot marginal damage and marginal savings from emissions for this industry. What is the efficient level of an emission tax? What is the optimal level of pollution abatement? Derive this result graphically.
Question 3: Assume and economy of two firms and two consumers. The two firms pollute. Firm one has a marginal savings function of MS1(e) = 5 - e, where e is the quantity of emissions from the firm. Firm two has a marginal savings function of MS2(e) = 8 – 2e. Each of the two consumers has marginal damage MD(e) = e, where e in this case is the total amount of emissions the consumer is exposed to.
3.1. Graph the firm-level and aggregate marginal savings functions.
3.2. Graph the aggregate marginal damage function. 3.3. [15points] What is the optimal level of pollution, the appropriate Pigovian fee, and emissions from each firm?
Question 4: An ice-cream factory produces output at C = q 2 , where q is the quantity of ice-creams produced, in tons. In addition, 2 units of emissions are produced for each ton of icecreams (e = 2q). Pollution damage is $2 for each unit of emissions, which leads the government to charge $2 per unit of emissions as a Pigovian fee. The firm's output sells competitively for $10 per ton.
4.1. How many tons of ice-creams will the factory produce? How much does it pay in emission fees?
What are its profits?
4.2. A device is invented that would reduce the firm's emissions to one unit for each town of output (e = q). How much would the firm be willing to pay for such a device?