Unformatted text preview: Economics 101 Microeconomics Problem Set 10 March 25 & 26 University of Michigan Winter 2010 Econ 101.400 Winter 2010 Question One Two producers sell their goods in completely different markets. They share one thing in common: their production processes release the same toxic byproduct into the atmosphere. Left to their own devices, each producer releases 500 units of this toxin into the atmosphere every month. The government decrees that 1000 units of the toxin is too much to be released into the atmosphere, and promotes new legislation that will limit the total quantity of this toxin released to 400 units each month. This means that 600 units of pollution must be abated each month. The marginal abatement cost (MAC) for each of the two firms is shown in the diagram below. MAC1 MAC2 600 MAC1 = Q1 MAC2 = 2Q2 400 300 400 Q1: 0 600 300 300 400 200 600 0 :Q2 Q1 and Q2 are the quantities of pollution abated by the two firms. The horizontal dimension of the diagram shows the total abatement required is 600 units. Measuring quantity Q1 from the origin on the left, the MAC1 curve shows the marginal abatement cost for firm 1. The marginal abatement cost increases as firm 1 abates more pollution. Similarly, measuring Q2 from the right hand origin, the MAC2 curve shows firm 2’s marginal abatement cost increasing as Q2 increases. Econ 101.400 Winter 2010 Any point along the horizontal axis represents a particular division of the 600 units of abatement between firms 1 and 2. The distance to the left origin is the quantity abated by firm 1. The distance to the right origin is the quantity abated by firm 2. By design, these two quantities will sum to 600. (a) If 600 units of pollution are to be abated efficiently, firm 1 should abate 400 units and firm 2 should abate 200 units. Explain why. (b) If the government wishes to encourage the firms to abate in the manner described in (a), could they achieve this by taxing pollution? If so, how high would the tax have to be, per unit of pollution? Suppose instead that the government issued 400 pollution permits, 200 to each firm. In order to emit one unit of pollution, a firm will need to hold one permit. Under the initial allocation of permits, each firm is allowed to emit 200 units of pollution. As we know that each firm wishes to emit 500 units of pollution, this means that each firm must abate 300 units of pollution if there is no trade in permits. Importantly, the permits are tradable. If a firm sells a permit, then it will be required to abate an additional unit of pollution. This means that the cost of selling the marginal permit is simply the seller’s marginal abatement cost. Similarly, if a firm buys a permit, that firm is entitled to reduce abatement. This leads to a saving in abatement costs. The value of the marginal permit to the buyer, then, is the buyer’s marginal abatement cost. (c) Given that 200 permits are allocated to each firm, what value does Firm 1 place on its marginal permit? What value does Firm 2 place on its marginal permit? Are there mutual gains available from trading the marginal permit? If so, in what direction should they trade? At what range of prices might the trade take place? (d) Suppose the two firms are able successfully to trade a permit whenever there are gains from trade available. How many permits will be traded? If all permits trade at the same price, what will that price be? (e) Compare the outcomes under the taxation scheme described in part (b) and the permit trading scheme in part (d). Which is more efficient? What are the advantages and disadvantages of each scheme? Econ 101.400 Winter 2010 Question Two Consider this famous fable that emerged from the 1952 article by Meade: The Fable of the Bees. An orchardist cultivates fruit trees of many varieties on his land, concerning himself only with the private benefits and costs of doing so. It is of little concern to him that his neighbor, the apiarist, derives significant benefits from his trees: the nectar from the trees feeds his bees. The fruit trees provide a positive externality by helping to nourish the bee colony. This suggests that the orchardist is likely to under‐provide fruit trees on his property, as the external benefits they provide are ignored. Simultaneously, the apiarist unwittingly provides external benefits for the orchardist, as the bees that gorge themselves on the fruit trees’ nectar also pollinate those trees. This positive externality would suggest that the apiarist’s bee population is also likely to be inefficiently small. (a) If the fruit trees provide a ready supply of cheap food for the bees, how do you think this tends to affect the size of the colony the apiarist wishes to keep? (b) If the bees assist in the propagation of the fruit trees by assisting with pollination, what effect is the bee colony likely to have on the number of trees growing in the orchard? (c) Is there an externality “problem” here? Do you think that the bee population is smaller or larger than is efficient? Do you think that the orchard will have more or fewer trees than is efficient? Should the beekeeper receive a subsidy? Or should he be taxed for keeping so many bees? Should the orchardist receive a subsidy, or should he be taxed for cultivating too many fruit trees? (d) Can you propose a private solution that is bound to internalize all the externalities in this situation? Econ 101.400 Winter 2010 Question Three The cap‐and‐trade scheme is becoming an increasingly popular approach to the regulation of pollution. However, it is not clear that such schemes will ever generate efficient levels of pollution. Instead, these schemes seem effective in finding the lowest cost distribution of a pre‐determined quantity of pollution amongst producers. Given that pollution permits are freely tradable, there is nothing to prevent those affected by pollution purchasing the pollution rights and retiring them. Why do we not see a great deal of this activity? Can you relate this to our theory of public goods provision? ...
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