Wilfrid LAURIER UNIVERSITY
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Student Number: _________________ Student Name:___________________ Section:_________________________
Wilfrid LAURIER UNIVERSITY Department of Economics EC238 – Environmental Economics Suggested Solutions to Midterm Examination October 27, 2011 Instructor:
Sharif F. Khan
Time Limit: 1 Hour 10 Minutes Instructions: Important! Read the instructions carefully before you start your exam. Write your answers for Part A and Part B in the booklet provided. Please record your name, student number and class section on the answer booklet and on the exam question paper. Hand in the exam question paper inside the answer booklet.
Marking Scheme: Part A [15 marks] THREE short questions Part B [30 marks] TWO problem solving questions
Calculators: Non-programmable calculators are permitted
Page 1 of 8 Pages
Part A
[15 marks]
Answer the following three questions in the answer booklet. Each question is worth 5 marks. A1. [5 marks] Suppose you are part of an economic analysis team charged with recommending a policy response to pesticide risks. Your team decides to use risk-benefit analysis as its risk management strategy. On the risk side of the analysis, your team reviews the following data from the risk assessment process. Interpret each of these quantitative findings about pesticide risk, by stating precisely what numerical value(s) mean or imply in each case. Be specific. (i)
Pesticide W: Reference Dose (RfD) = 0.005
[1 mark]
(ii)
Pesticide X: threshold level of 0 for infants and children
[1 mark]
(iii)
Pesticide Y: carcionogenic risk of 0.0075 percent
[1 mark]
(iv)
Pesticide Z: a dose (D)-response (R) function modeled as R= 0 for all D < [2 marks] 0.6, R = -0.3 + 0.5D for all D ≥ 0.6.
See the solutions to Practice Problems and Essay Questions # 1(a) of Chapter 3 of the study guide – Resources and Learning Tools in Environmental Economics & Management (1st or 2nd ed.).
Page 2 of 8 Pages
Instructions for Question A2 and A3: Explain why the following statements are True, False, or Uncertain according to economic principles. Use diagrams and/or numerical examples where appropriate. Unsupported answers will receive no marks. It is the explanation that is important. A2. [5 marks] According to the Coase Theorem, an efficient outcome can be achieved even if the polluter controls the property rights. [Diagrams Required] True The Coase Theorem argues that under certain conditions the assignment of property rights will lead to bargaining between the parties such that an efficient solution can be achieved, no matter which part holds the property rights. See Page 69-72 and Figure 3.6 of the textbook (5th ed.) for an explanation. Or, See Page 62-63 and Figure 3.6 of the textbook (4th ed.) for an explanation.
A3. [5 marks] An emission charge creates static incentives that encourage a single polluter to choose the least-cost option. [Diagrams Required] True See Page 101-102 and Figure 5.2 of the textbook (5th ed.) for an explanation. Or, See Page 89-90 and Figure 5.2 of the textbook (4th ed.) for an explanation.
Page 3 of 8 Pages
Part B
Problem Solving Questions
[30 marks]
Answer the following questions in the answer booklet. Read each part of the question very carefully. Show all the steps of your calculations to get full marks. B1. [10 Marks] Consider a model of a hypothetical competitive market for abatement equipment, such as scrubbers, with the following functions: MPB = 350 − 0.9Q
MSC = 70 + 0.5Q
MEB = 56 − 0.2Q
MEC = 0
where Q is the number of scrubber systems produced in a year, and MSC, MPB, MEB, and MEC are denominated in millions of dollars. a) Find the competitive equilibrium, QC and PC , and the efficient equilibrium, QE and PE . Illustrate your results on a diagram. [Notes/Hints: Show all steps of your calculations to get full marks. Clearly label each axis of the diagram and clearly identify the intercepts and the equilibrium.] [4.5 marks] Competitive equilibrium is found where: MPB MPB 350 – 0.9Q 1.4Q QC
= = = = =
MPC MSC - MEC 70 + 0.5Q 280 200
PC = 350 – 0.9(200) or 70 + 0.5(200) = $170 million Efficient equilibrium is found where: MSB = MSC MPB +MEB = MSC 350 – 0.9Q + 56 - 0.2Q = 70 + 0.5Q 406 – 1.1Q = 70 + 0.5Q 1.6Q = 336 QE = 210 PE = 406 – 1.1(210) or 70 + 0.5(210) = $175 million Figure B1 illustrates the results.
Page 4 of 8 Pages
b) Is the market for scrubbers failing to achieve an efficient outcome? If yes, explain why. If no, explain why not. [1.5 marks] Yes, the market for scrubbers failing to achieve an efficient outcome. In an unregulated competitive market, too few scrubbers are exchanged at too low a price because the external benefits of a cleaner environment are not recognized by the market participants.
c) In case of the market failure, should the government impose a Pigouvian tax or provide a Pigouvian subsidy to achieve the efficient equilibrium in this hypothetical market for scrubbers? Determine the dollar value of a Pigouvian tax or subsidy that the government should impose or provide to achieve the efficient equilibrium. Explain the effects of this Pigouvian tax or subsidy on the competitive equilibrium in that case. Illustrate the amount of Pigouvian tax or subsidy and its effects on the diagram which you drew for part (a). [Notes/Hints: Show all steps of your calculations to get full marks. Clearly label each axis of the diagram and clearly identify the intercepts and the equilibrium.] [4 marks] The should government provide a Pigouvian subsidy to achieve the efficient equilibrium in this hypothetical market for scrubbers. The dollar value of Pigouvian subsidy is equal to the MEB at QE. At QE, MEB = 56 - 0.2(210) = $14 million, which would be the dollar value of Pigouvian subsidy that would generate an efficient equilibrium. Figure B1 illustrates the effects of this Pigouvian subsidy. By setting a Pigouvian subsidy equal to $14 million, shown as the distance KL, the MPB curve shifts up to MPBs. Thus, this Pigouvian subsidy is inducing purchasers to internalize the positive externality by taking account of the MEB in their purchase decisions. The competitive equilibrium output is then determined by the intersection of MPBs and MPC, which is the efficient production level, QE.
Page 5 of 8 Pages
B2. [20 Marks] Assume that there are two firms, each emitting 15 units of pollutants into the environment, for a total of 30 units in their region. The government sets an aggregate abatement standard ( AST ) of 10 units. The polluters’ total abatement cost functions are as follows, where the dollar values are in thousands: Polluter 1:
TAC1 = 20 + 1.5( A1 )
2
Polluter 2: TAC 2 = 15 + ( A2 )
2
where A1 and A2 represent the units of pollution abatements achieved by firm 1 and 2, respectively, and TAC1 and TAC2 represent total abatement costs for firm 1 and 2, respectively. a)
Suppose the government allocates the abatement responsibility uniformly. Calculate the total abatement cost (TAC) and marginal abatement cost (MAC) under this uniform abatement standard. Does this allocation policy achieve a cost-effective solution? Explain. [Notes/Hints: Show all steps of your calculations to get full marks.] [7 marks]
MAC1 ≡
∂TAC1 2 −1 = 1.5 * 2( A1 ) = 3 A1 ∂A1
MAC 2 ≡
∂TAC 2 2 −1 = 2( A2 ) = 2 A2 ∂A2
Based on a uniform standard, A1 = A2 = 5. Therefore, MAC1 = 3(5) = $15 thousand, TAC1 = 20+ 1.5(5)2 = $57.5 thousand, MAC2 = 2(5) = $10 thousand, and TAC2 = 15+(5)2 = $40 thousand. With a uniform abatement standard, the MACs are unequal, which means that the abatement allocation is NOT cost-effective.
Page 6 of 8 Pages
b)
Find the cost-effective solution and illustrate graphically, labeling all curves, intercepts, and relevant intersections. Compare the total abatement costs of this allocation to the total abatement costs of using the uniform standard described in part (a) and quantify the cost savings associated with this allocation. Clearly identify the area of the cost savings on the graph. [Notes/Hints: Show all steps of your calculations to get full marks. Clearly label each axis of the diagram. Clearly identify the intercepts, the cost effective solution, and the area of the cost savings.] [7 marks]
First, find the cost-effective solution as follows: Cost-effectiveness requires:
3A1 = 2A2
(1)
Abatement standard requires:
A1 + A2 = 10
(2)
Solving equations (1) and (2) simultaneously: Therefore:
3(10 – A2) = 2A2 30 – 3A2 = 2A2, so A2 = 6, and A1 = 10 – A2 = 4
Second, calculate each firm’s total abatement costs based on the cost-effective allocation: TAC1 = 20 + 1.5 (4)2 = $44 thousand
TAC2 = 15 + (6)2 = $51 thousand
Finally, determine the cost savings by comparing the sum of these TAC values to the sum under a uniform standard. Combined TACs under a uniform standard = $57.5 + $40 =97.5 Combined TACs under the cost-effective solution = $44 + $51 = $95 thousand Cost savings = $97.5 – $95 thousand = $2.5 thousand The results and the area of the cost savings re illustrated on Figure B2.
Page 7 of 8 Pages
c)
Now assume that the government implements a pollution permit trading system to achieve a cost-effective solution. How many one-unit permits should the government issue to achieve its aggregate abatement standard of 10 units? Explain the mechanism through which this pollution permit trading system would achieve a cost-effective allocation of the targeted abatement. [4 marks]
Under a pollution permit trading system, the government issues (or sells) an aggregate number of permits equal to the level of pollution deemed acceptable by the objective. In this case, 10 units of abatement are required to reduce the existing 30 levels of pollution down to 20. Hence, the government will issue 20 one-permits to the two polluters, who may then exchange these with one another in an open market. The two polluters will buy and sell permits as long as there are gains from trading. The high-cost abater would be willing to purchase permits as long as the selling price is lower than its MAC. The lowcost abater would be willing to sell a permit as long as it receives a price higher than its MAC. Trading will continue until the price reaches the point where neither firm has anything further to gain from an exchange. This occurs when both polluters are abating at the point where their MACs are equal (i.e., where the condition of a cost-effective allocation is satisfied). This is how this pollution permit trading system would achieve a cost-effective allocation of the targeted abatement.
d)
Calculate the pollution permit price which would achieve a cost-effective allocation of the targeted abatement under a pollution permit trading system. [2 marks]
At the cost-effective abatement levels (A1 = 4 and A2 = 6), MAC1 = 3(4) = $12 thousand and
MAC2 = 2(6) = $12 thousand.
To achieve a cost-effective solution, the pollution permit price (P) must be equal to the MAC of the two firms: P = MAC1= MAC2 = $12 thousand So, a permit price of $12 thousand yields a cost-effective solution.
Page 8 of 8 Pages
Student Number: _________________ Student Name:___________________ Section:_________________________
Wilfrid LAURIER UNIVERSITY Department of Economics EC238 – Environmental Economics Suggested Solutions to Midterm Examination October 27, 2011 Instructor:
Sharif F. Khan
Time Limit: 1 Hour 10 Minutes Instructions: Important! Read the instructions carefully before you start your exam. Write your answers for Part A and Part B in the booklet provided. Please record your name, student number and class section on the answer booklet and on the exam question paper. Hand in the exam question paper inside the answer booklet.
Marking Scheme: Part A [15 marks] THREE short questions Part B [30 marks] TWO problem solving questions
Calculators: Non-programmable calculators are permitted
Page 1 of 8 Pages
Part A
[15 marks]
Answer the following three questions in the answer booklet. Each question is worth 5 marks. A1. [5 marks] Suppose you are part of an economic analysis team charged with recommending a policy response to pesticide risks. Your team decides to use risk-benefit analysis as its risk management strategy. On the risk side of the analysis, your team reviews the following data from the risk assessment process. Interpret each of these quantitative findings about pesticide risk, by stating precisely what numerical value(s) mean or imply in each case. Be specific. (i)
Pesticide W: Reference Dose (RfD) = 0.005
[1 mark]
(ii)
Pesticide X: threshold level of 0 for infants and children
[1 mark]
(iii)
Pesticide Y: carcionogenic risk of 0.0075 percent
[1 mark]
(iv)
Pesticide Z: a dose (D)-response (R) function modeled as R= 0 for all D < [2 marks] 0.6, R = -0.3 + 0.5D for all D ≥ 0.6.
See the solutions to Practice Problems and Essay Questions # 1(a) of Chapter 3 of the study guide – Resources and Learning Tools in Environmental Economics & Management (1st or 2nd ed.).
Page 2 of 8 Pages
Instructions for Question A2 and A3: Explain why the following statements are True, False, or Uncertain according to economic principles. Use diagrams and/or numerical examples where appropriate. Unsupported answers will receive no marks. It is the explanation that is important. A2. [5 marks] According to the Coase Theorem, an efficient outcome can be achieved even if the polluter controls the property rights. [Diagrams Required] True The Coase Theorem argues that under certain conditions the assignment of property rights will lead to bargaining between the parties such that an efficient solution can be achieved, no matter which part holds the property rights. See Page 69-72 and Figure 3.6 of the textbook (5th ed.) for an explanation. Or, See Page 62-63 and Figure 3.6 of the textbook (4th ed.) for an explanation.
A3. [5 marks] An emission charge creates static incentives that encourage a single polluter to choose the least-cost option. [Diagrams Required] True See Page 101-102 and Figure 5.2 of the textbook (5th ed.) for an explanation. Or, See Page 89-90 and Figure 5.2 of the textbook (4th ed.) for an explanation.
Page 3 of 8 Pages
Part B
Problem Solving Questions
[30 marks]
Answer the following questions in the answer booklet. Read each part of the question very carefully. Show all the steps of your calculations to get full marks. B1. [10 Marks] Consider a model of a hypothetical competitive market for abatement equipment, such as scrubbers, with the following functions: MPB = 350 − 0.9Q
MSC = 70 + 0.5Q
MEB = 56 − 0.2Q
MEC = 0
where Q is the number of scrubber systems produced in a year, and MSC, MPB, MEB, and MEC are denominated in millions of dollars. a) Find the competitive equilibrium, QC and PC , and the efficient equilibrium, QE and PE . Illustrate your results on a diagram. [Notes/Hints: Show all steps of your calculations to get full marks. Clearly label each axis of the diagram and clearly identify the intercepts and the equilibrium.] [4.5 marks] Competitive equilibrium is found where: MPB MPB 350 – 0.9Q 1.4Q QC
= = = = =
MPC MSC - MEC 70 + 0.5Q 280 200
PC = 350 – 0.9(200) or 70 + 0.5(200) = $170 million Efficient equilibrium is found where: MSB = MSC MPB +MEB = MSC 350 – 0.9Q + 56 - 0.2Q = 70 + 0.5Q 406 – 1.1Q = 70 + 0.5Q 1.6Q = 336 QE = 210 PE = 406 – 1.1(210) or 70 + 0.5(210) = $175 million Figure B1 illustrates the results.
Page 4 of 8 Pages
b) Is the market for scrubbers failing to achieve an efficient outcome? If yes, explain why. If no, explain why not. [1.5 marks] Yes, the market for scrubbers failing to achieve an efficient outcome. In an unregulated competitive market, too few scrubbers are exchanged at too low a price because the external benefits of a cleaner environment are not recognized by the market participants.
c) In case of the market failure, should the government impose a Pigouvian tax or provide a Pigouvian subsidy to achieve the efficient equilibrium in this hypothetical market for scrubbers? Determine the dollar value of a Pigouvian tax or subsidy that the government should impose or provide to achieve the efficient equilibrium. Explain the effects of this Pigouvian tax or subsidy on the competitive equilibrium in that case. Illustrate the amount of Pigouvian tax or subsidy and its effects on the diagram which you drew for part (a). [Notes/Hints: Show all steps of your calculations to get full marks. Clearly label each axis of the diagram and clearly identify the intercepts and the equilibrium.] [4 marks] The should government provide a Pigouvian subsidy to achieve the efficient equilibrium in this hypothetical market for scrubbers. The dollar value of Pigouvian subsidy is equal to the MEB at QE. At QE, MEB = 56 - 0.2(210) = $14 million, which would be the dollar value of Pigouvian subsidy that would generate an efficient equilibrium. Figure B1 illustrates the effects of this Pigouvian subsidy. By setting a Pigouvian subsidy equal to $14 million, shown as the distance KL, the MPB curve shifts up to MPBs. Thus, this Pigouvian subsidy is inducing purchasers to internalize the positive externality by taking account of the MEB in their purchase decisions. The competitive equilibrium output is then determined by the intersection of MPBs and MPC, which is the efficient production level, QE.
Page 5 of 8 Pages
B2. [20 Marks] Assume that there are two firms, each emitting 15 units of pollutants into the environment, for a total of 30 units in their region. The government sets an aggregate abatement standard ( AST ) of 10 units. The polluters’ total abatement cost functions are as follows, where the dollar values are in thousands: Polluter 1:
TAC1 = 20 + 1.5( A1 )
2
Polluter 2: TAC 2 = 15 + ( A2 )
2
where A1 and A2 represent the units of pollution abatements achieved by firm 1 and 2, respectively, and TAC1 and TAC2 represent total abatement costs for firm 1 and 2, respectively. a)
Suppose the government allocates the abatement responsibility uniformly. Calculate the total abatement cost (TAC) and marginal abatement cost (MAC) under this uniform abatement standard. Does this allocation policy achieve a cost-effective solution? Explain. [Notes/Hints: Show all steps of your calculations to get full marks.] [7 marks]
MAC1 ≡
∂TAC1 2 −1 = 1.5 * 2( A1 ) = 3 A1 ∂A1
MAC 2 ≡
∂TAC 2 2 −1 = 2( A2 ) = 2 A2 ∂A2
Based on a uniform standard, A1 = A2 = 5. Therefore, MAC1 = 3(5) = $15 thousand, TAC1 = 20+ 1.5(5)2 = $57.5 thousand, MAC2 = 2(5) = $10 thousand, and TAC2 = 15+(5)2 = $40 thousand. With a uniform abatement standard, the MACs are unequal, which means that the abatement allocation is NOT cost-effective.
Page 6 of 8 Pages
b)
Find the cost-effective solution and illustrate graphically, labeling all curves, intercepts, and relevant intersections. Compare the total abatement costs of this allocation to the total abatement costs of using the uniform standard described in part (a) and quantify the cost savings associated with this allocation. Clearly identify the area of the cost savings on the graph. [Notes/Hints: Show all steps of your calculations to get full marks. Clearly label each axis of the diagram. Clearly identify the intercepts, the cost effective solution, and the area of the cost savings.] [7 marks]
First, find the cost-effective solution as follows: Cost-effectiveness requires:
3A1 = 2A2
(1)
Abatement standard requires:
A1 + A2 = 10
(2)
Solving equations (1) and (2) simultaneously: Therefore:
3(10 – A2) = 2A2 30 – 3A2 = 2A2, so A2 = 6, and A1 = 10 – A2 = 4
Second, calculate each firm’s total abatement costs based on the cost-effective allocation: TAC1 = 20 + 1.5 (4)2 = $44 thousand
TAC2 = 15 + (6)2 = $51 thousand
Finally, determine the cost savings by comparing the sum of these TAC values to the sum under a uniform standard. Combined TACs under a uniform standard = $57.5 + $40 =97.5 Combined TACs under the cost-effective solution = $44 + $51 = $95 thousand Cost savings = $97.5 – $95 thousand = $2.5 thousand The results and the area of the cost savings re illustrated on Figure B2.
Page 7 of 8 Pages
c)
Now assume that the government implements a pollution permit trading system to achieve a cost-effective solution. How many one-unit permits should the government issue to achieve its aggregate abatement standard of 10 units? Explain the mechanism through which this pollution permit trading system would achieve a cost-effective allocation of the targeted abatement. [4 marks]
Under a pollution permit trading system, the government issues (or sells) an aggregate number of permits equal to the level of pollution deemed acceptable by the objective. In this case, 10 units of abatement are required to reduce the existing 30 levels of pollution down to 20. Hence, the government will issue 20 one-permits to the two polluters, who may then exchange these with one another in an open market. The two polluters will buy and sell permits as long as there are gains from trading. The high-cost abater would be willing to purchase permits as long as the selling price is lower than its MAC. The lowcost abater would be willing to sell a permit as long as it receives a price higher than its MAC. Trading will continue until the price reaches the point where neither firm has anything further to gain from an exchange. This occurs when both polluters are abating at the point where their MACs are equal (i.e., where the condition of a cost-effective allocation is satisfied). This is how this pollution permit trading system would achieve a cost-effective allocation of the targeted abatement.
d)
Calculate the pollution permit price which would achieve a cost-effective allocation of the targeted abatement under a pollution permit trading system. [2 marks]
At the cost-effective abatement levels (A1 = 4 and A2 = 6), MAC1 = 3(4) = $12 thousand and
MAC2 = 2(6) = $12 thousand.
To achieve a cost-effective solution, the pollution permit price (P) must be equal to the MAC of the two firms: P = MAC1= MAC2 = $12 thousand So, a permit price of $12 thousand yields a cost-effective solution.
Page 8 of 8 Pages
