Econ 381/ES312 Midterm 2: Sample Questions

Transcription

1 Econ 381/ES312 Midterm 2: Sample Questions 1. Suppose there are two polluting firms with marginal abatement costs given by: MCA1 = - (1/40)E1; and MCA2 = 5 - (1/80)E2. These marginal abatement cost curves are illustrated below. MC A 1 W 5 MC A 2 Y X 3 p E Firm 1 buys 180 Z 400 E Firm 2 sells 180 Suppose the government decides to reduce aggregate emissions to 440 using a cap and trade program. Firm 1 is given 0 permits and Firm 2 is given 340 permits. (a) Illustrate the equilibrium in the permit market on the diagram above. Make sure your diagram clearly identifies (i) the equilibrium price of permits; (ii) the equilibrium quantity demanded; (iii) the equilibrium quantity supplied; and (iv) the emissions levels for each firm in equilibrium. At the initial allocation of permits, MC A 1 > MC A 2. So firm 1 will buy and firm 2 will sell. Equilibrium is where MC A 1 = MC A 2, given that E1 + E2 = 440. This is where E1 = 280 and E2 = 160. Thus 180 permits are traded at a price of 3/permit.!1

2 Now suppose we learn that the marginal damages from emissions are given by: MD = (1/80)(E1 + E2) (b) In order to maximize the social surplus from abatement, should aggregate emissions be greater than 440, less than 440, or equal to 440? Explain your reasoning. Note: math alone is not an explanation. Given E1 + E2 = 440, MD = MD > MC A ( =3 at the equilibrium), so the marginal benefit of abatement (reduced MD) is greater than MC A, so SS max entails more abatements and lower emissions. (c) Now calculate the emissions levels for each firm that maximize the social surplus from abatement. Show each step. Set MC A 1 = MC A 2: - (1/40)E1 = 5 - (1/80)E2, (1/40)E1 = 5 + (1/80)E2, E1 = (1/2)E2. (1) Set MC A 1 = MD: - (1/40)E1 = (1/80)(E1 + E2) (3/80)E1 = - (1/80)E2, E1 = (800/3) - (1/3)E2. (2) Set E1 from (1) equal to E1 from (2): (1/2)E2 = (800/3) - (1/3)E2, (5/6)E2 = 200/3, E2 = 1200/15, * E2 = 80. From (1): E1 = (1/2)E2. (1) * So E1 = 240. Check answer: MCA1 = - (1/40) 240 = 4. MCA2 = 5 - (1/80) 80 = 4. MD = (1/80) ( ) = 4.!2

3 2. Suppose there are two polluting firms with marginal abatement costs illustrated below. 20 MC A 2 12 MC A 1 4 t J L K M E A1 = 20 A2 = 20 The government introduces an emissions tax of 4 per unit of emissions. (a) How much will firm 1 emit after the tax is implemented? How much will firm 2 emit after the tax is implemented? E1 = 80 & E2 = 40. (b) How much will firm 1 abate after the tax is implemented? How much will firm 2 abate after the tax is implemented? A1 = A2 = 20. Each firm undertakes exactly the same level of abatement. (c) Explain the relationship between abatement for each firm. (For example, if one firm abates more than the other firm, explain why. Each firm has different baseline (unregulated) emissions (60 for firm 1 and 0 for firm 2), but they have identical marginal abatement costs as they reduce emissions from that baseline. This will be true whenever two MC A s have the same slope. Because they have the same marginal costs, it is optimal for them to undertake the same level of abatement. (d) Illustrate the firms compliance costs on the diagram above.!3

4 CC1 = TCA1 + (t E1) = K + J on diagram. CC2 = TCA2 + (t E2) = M + (L + K + J) on diagram. (e) Explain the relationship between compliance costs for each firm. (For example, if one firm pays more in compliance costs that the other firm, explain why.) Note that the TC A components costs are identical (area M = area K), because each firm undertake the same level of abatement and has the same MC A. Because Firm 2 has higher baseline emissions, however, it ends up emitting more than Firm 1 after the tax is implemented. This means that the tax cost component of CC is higher for Firm 2 that for Firm Are the following statements true or false? (You must offer an explanation to receive any credit for your answer.) (a) Compliance costs under cap and trade will generally be higher than compliance costs under a carbon tax. False. Compliance costs under a carbon tax will generally be higher than compliance costs under cap and trade. Under a carbon tax, firms must pay the tax for all units emitted. They are not permitted to emit anything for free. Under cap and trade, as long as each firm is given at least some permits, the firm is given the right to emit at least some pollution for free. This means CC will generally be lower under cap and trade. (b) Carbon taxes and cap and trade are similar in that they both ensure that aggregate abatement costs are minimized. However, a carbon tax allows the policy-maker to choose the aggregate abatement target while cap and trade doe not. False. While both ensure least cost abatement, only under cap and trade can the government select the abatement tax (through selection of the cap on emissions). Under a carbon tax, the government chooses the tax rate (the price of emissions) and market participants are free to choose their response to this tax. That is, market participants choose the levels of abatement. Under cap and trade, the government chooses the level of abatement and the decisions of market participants collectively determine the price of emissions. That is, the cap (aggregate abatement) is exogenous (chosen by the policy maker) under cap and trade while the price of emissions is exogenous under a carbon tax.!4

5 4. Suppose we have 15 units of a good to distribute between two consumers, with marginal benefits as follows: MBA = 20 - QA; and MBB =. (a) Draw one neat and appropriately labeled diagram illustrating both marginal benefit curves. 20 MBB MBA 5 20 Q (b) Solve for the efficient distribution of the 15 units between the two consumers. Illustrate this distribution on your diagram. Note from the diagram that MBA > MBB for any Q <. For any Q >, MBB > MBA. Thus we should give units to A and 5 units to B. Now suppose we only have 5 units of the good to distribute between the two consumers. (c) Explain why it is efficient for person A to receive all five units of the good. Since MBA > MBB for any Q <, if we have less than units in total we should give them all to person A, the high MB consumer.!5

6 5. The market demand curve for a good is illustrated below. The market supply curve is given by D MSC pc S(MPC) p1 ps Q S = 3P. The production of the good results in a negative externality with MEC = 2. (a) Draw the supply and marginal social cost curves on the diagram. On the diagram, indicate the equilibrium quantity and the quantity that maximizes social surplus (I want numbers here, and also make clear which quantity is which). Equilibrium quantity is. SS max quantity is 8. (b) On the diagram, illustrate the equilibrium effects of a per unit output tax that corrects the market failure. Make sure your diagram clearly identifies consumer and producer prices after the tax is implemented. Taxed equilibrium Q is 8. Consumer price rises to PC. Producer/seller price falls to PS. (c) Does social surplus increase or decrease as a result of the tax from part (b)? On the diagram above, identify the area that represents the change in social surplus resulting from the tax. SS increases by blue shaded area Q 5. Suppose there is one polluting firm with marginal abatement costs given by MC A = 0-2E. Marginal damages from this firm s emissions are given by MD = + E. (a) Solve for the emissions level that maximizes the social surplus from abatement. 0-2E = + E so 3E = 90 and E = 30.!6

7 (b) Draw a diagram illustrating your answer. 0 MC A MD x 30 y z 50 E (c) On your diagram, label the area that represents the social benefit of abatement. When E = 50 (abatement = 0), damages from emissions equal area x + y + z. When E = 30, damages from emissions equal are reduced to area x. So the SB of abatement = reduction in damages = y + z. (d) On your diagram, label the area that represents the social cost of abatement. SC = TC A = area y when emissions are reduced from 50 to 30. (e) Use your answers to (c) and (d) to identify the area on the diagram that represents the social surplus from abatement. SS = SB - SC = area z.!7