# Marginal External Benefit

HW 4 © Prof John Gasper / Carnegie Mellon University Page 1 of 9
Homework Assignment 4
Due: Friday, November 6, 2020 at 11:59 p.m. (23:59) Eastern
General Submission Instructions:
• Submit this assignment as one .pdf file via Gradescope. Do not forget to select the page(s) that contain the solution to each of the assigned problems. For more information, see the “Gradescope submitting hw guide.pdf” on Canvas.
General Instructions:
• Write neatly; illegible work will not be given any points.
• Be certain to label graphs, equilibria, intersections (where appropriate).
• Show all of your work / reasoning. Writing the correct number with no derivation will not be given full credit. I need to know you understand the reasoning process.
First Name:
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HW 4 © Prof John Gasper / Carnegie Mellon University Page 2 of 9
1. We’ve been discussing the effect of taxes. Let’s now consider the effect of subsidies, which also generate deadweight loss. A subsidy creates a gap between the price received by sellers and the price paid by buyers.
Figure 1: Subsidies
(a) (4 points) Complete the table using the letters from Figure 1. The government “revenue” is negative, because a subsidy requires a payment by the government. (Recall that society consists of producers, consumer and the government)
Grading key: 16.6% for each correct cell
No Subsidy
With Subsidy
Consumer Surplus
Producer Surplus
Government “Revenue”
Social (Total) surplus
HW 4 © Prof John Gasper / Carnegie Mellon University Page 3 of 9
(b) (1 point) Based on this table, what is the deadweight loss of the subsidy? (Hint: this is the difference in social surplus between the two columns.)
(c) (1 point) Describe why a subsidy creates deadweight loss. Try to use your answer to (b) as a guide.
HW 4 © Prof John Gasper / Carnegie Mellon University Page 4 of 9
2. (5 points) Suppose demand is QD = 20 – P, supply is QS = P. There is a constant positive externality of \$6 per unit (Marginal External Benefit, MEB = \$6). Find the maximum possible social surplus.
• Explanation/Calculation shown – 80%
• The maximum possible social surplus is correct – 20%
HW 4 © Prof John Gasper / Carnegie Mellon University Page 5 of 9
3. Many cities tax or ban plastic grocery bags. The rationale for these taxes and bans is an externalities argument: plastic bags are an eyesore, take up space in landfills, and damage fish, birds, and other wildlife.
(a) (2 points) In the diagram below, show the efficient number of plastic bags and the equilibrium number of plastic bags in the absence of any government policies.
• The graph is correct, including
– All relevant curves/lines and areas are labeled.
– The efficient number of plastic bags is labeled.
– The equilibrium number of plastic bags is labeled.
(b) (1 point) Show the efficiency loss from plastic bags in your diagram.
(c) (1 point) Show the tax on plastic bags that would lead to the efficient outcome.
HW 4 © Prof John Gasper / Carnegie Mellon University Page 6 of 9
4. Table 1 gives information about three industrial steel producing firms in Pittsburgh. The government wants to reduce total pollution to 120 units, and so it gives 40 tradable pollution permits to each firm. Each permit entitles a firm to pollute by one unit.
Firm
Initial Pollution Level
Cost of Reducing Pollution by One Unit
A B
C
80 units
200 units
20 units
\$10
\$5
\$20
Table 1
(a) (4 points) Graph the market demand and the supply for pollution permits.
Grading key: The graph is correct, including
– Axes are labeled and all relevant curves are labeled.
HW 4 © Prof John Gasper / Carnegie Mellon University Page 7 of 9
(b) (2 points) For each firm, indicate if they buy or sell permits and how many.
• Grading key: 33% for each correct value
(c) (2 points) By how much does each firm reduce pollution?
• Grading key: 33% for each correct value
Principles of Microeconomics (73-102) – Fall 2020
HW 4 © Prof John Gasper / Carnegie Mellon University Page 8 of 9
(d) (1 point) What is the total cost of pollution reduction in this situation? Show your work to receive full credit.
– Explanation/Calculation – 70%
– Total cost of pollution reduction is correct – 30%
Principles of Microeconomics (73-102) – Fall 2020
HW 4 © Prof John Gasper / Carnegie Mellon University Page 9 of 9
(e) (1 point) What would the total cost of pollution reduction be if the permits could not be traded? Show your work to receive full credit.
– Explanation/Calculation – 70%
– Total cost of pollution reduction is correct – 30%

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