Suppose we have a small inhabited island with three residents and a volcano that generates air pollution. Two people live upwind of the volcano and one person lives downwind. For $21,000 we can clean up the volcano with a patented ”smoke guzzler.” The three upwind people wold pay $1,000 each to get rid of the smoke whereas the downwind person would be willing to pay $15,000. Consider two plans to finance the ”smoke guzzler.” Plan A calls for a head-tax of $5,000. Plan B calls for the affected party (the downwind person) to pay $21,000 and everyone else nothing. Compare each plan to the status quo and indicate society’s choice using (a) the Pareto criterion (b) majority rule, and (c) potential Pareto improvement.

2. In this question we will combine a very simplified model of an externality that has long-lasting impacts with the model of discounted utility that we learned in our game theory topic. Consider a hypothetical environmental externality: produced as the byproduct of industrial activity, each unit of emission of a pollutant that is emitted once, today, causes $10 of external harm to society each and every year, starting immediately, forever. Let's say that policymakers apply a discount factor of 8 € (0, 1) to future gains and losses, in an analog of the discounted utility model except for cash payoffs rather than utilities. What would the socially efficient Pigouvian tax on the emission of this pollutant be if we applied a discount factor of (i) 8 = 0.5, (ii) 6 = 0.9, and (iii) 8 = 0.99? Give an intuitive explanation of how to interpret the parameter & in this context, and explain precisely but in simple terms what the goal and effect of the Pigouvian tax would be.

9. Assume that the city government of Pollutersville taxes the production of electricity in an effort to make the market internalize the external cost imposed on society in the form of air pollution that is created when coal is burned to produce electricity. a. Draw a supply and demand diagram for electricity in Pollutersville. Be sure to label your axes, curves, and intercepts, as well as MSC, MSB, MPC, MSB curves and the amount of the tax. b. If the government imposes a tax equal to the amount of the marginal external cost generated by each kwh of electricity, is there any deadweight loss in the market? Explain in one sentence of less. C. Discuss the changes in welfare for consumers, producers, society, and those individuals affected by the pollution once the tax is imposed. 4

3. The effect of negative externalities on the optimal quantity of consumption Consider the market for steel. Suppose that a steel manufacturing plant dumps toxic waste into a nearby river, creating a negative externality for those living downstream from the plant. Producing an additional ton of steel imposes a constant marginal external cost (MEC) of $165 per ton. The following graph shows the demand (marginal private benefits, or MPB) curve and the supply (marginal private costs, or MPC) curve for steel. Use the purple points (diamond symbol) to plot the marginal social costs (MSC) curve when the marginal external cost is $165 per ton. PRICE (Dollars per ton of steel) 1100 990 880 770 660 550 440 330 220 110 0 0 + 1 O ☐ O 2 0 H 3 ▬ The market equilibrium quantity is O 4 5 QUANTITY (Tons of steel) ☐ ☐ 6 Supply (MPC) Demand (MPB) 7 MSC ? tons of steel, but the socially optimal quantity of steel production is To create an incentive for the firm to produce the socially optimal quantity…