Citizens of Zephyronia consume only two goods and do not trade with the outside world. There is a fixed supply of labor in Zephyronia, which can be applied to production of either good. Good 1 is produced at constant returns to scale, using one unit of labor for each unit of output. Good 1 generates no externalities. Good 2 is also produced at constant returns to scale, with one unit of labor needed for each unit of output, but every unit of Good 2 that is produced also generates one unit of pollution. Both industries are perfectly competitive. Zephyronia has 1,000 citizens, and each citizen of this economy supplies 10 units of labor and each has a quasi linear utility function

Where x1 and x2 are her consumptions of goods 1 and 2, and where s is the total amount of pollution generated by the production of good 2. The currency of Zephyronia is known as the Puff. We will treat labor as the numeraire so that each consumer has an income of 10 Puffs.
(a) If there are no controls on pollution, then in competitive equilibrium, the price of each good must be equal to the marginal cost of producing the good. The marginal cost of good 1 is ______and the marginal cost of good 2 is ______. Suppose that individuals assume that the effect of their own purchases on pollution levels is negligible. Then each citizen chooses x1 and x2 to maximize utility subject to the budget constraint x1 + x2 = ______. Each citizen will choose to consume 3 units of x2. Total production of good 2 in Zephyronia will be ______units, and the total amount of pollution generated will be ______units. Total utility of each citizen of Zephyronia will be ______.
(b) Suppose that the government imposes a pollution tax of 1 Puff for each unit of pollution produced by any firm and divides the revenue collected from the tax equally among all citizens. Then the marginal cost of producing a unit of good 2 will rise to ______ and since the industry is competitive, the price of good 2 will be ______. Suppose that individuals ignore the tiny effect of their own purchases on the level of pollution and on the amount of their own rebate. Then each citizen will choose to consume 2 units of good 2 and the total amount of pollution will be ______. The total revenue of the government from the pollution tax will be ______. Each citizen will therefore receive a rebate of ______and hence will have a total income of ______ including wages and rebate. Therefore each consumer will consume ______ units of good 1, 2 units of good 2, and will experience ______units of pollution. The utility of each consumer will now be ______
(c) If you did the previous section correctly, you will have found that with a pollution tax of 1 Puff per unit of pollution produced, the total level of pollution produced will be 2,000 units. Suppose that instead of taxing pollution, the government required that firms must have a pollution permit for each unit of pollution produced and the government issued exactly 2,000 pollution permits. Suppose that these permits are purchased and used by producers of good 2. How many units of good 2 will be produced? ______At what price will the total demand for good 2 equal 2,000? 2 (Each individual€™s demand for good 2 is given by the equation x1 = 4ˆ’p2. Market demand is the total demand of 1,000 individuals like this, so market demand is D (p2) = 4, 000ˆ’1, 000p2. In equilibrium, the total amount of good 2 demanded must equal the supply.)
(d) (Extra Credit) Show that a tax of t = 1 Puffs per unit of pollution is the tax rate that results in the highest total utility for consumers.

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