# Berkeley ENVECON C101 - Midterm Solutions (7 pages)

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## Midterm Solutions

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- School:
- University of California, Berkeley
- Course:
- Envecon C101 - Environmental Economics

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Department of Agricultural and Resource Economics University of California Economics EEP101 ECON125 Spring 2004 Professor Zilberman Midterm Solutions 1 Question 1 30 points The inverse demand facing a farm sector is denoted by p 20 x where x is output and p is output price The sector s activities also generate positive externalities and the marginal externality benefits is M EB 10 0 5x The marginal cost of production is M C 2 x a How much output will be produced and at what consumer price if the industry operates as a monopoly in the output market 4 points Solution Monopoly will achieve its optimal quantity when the marginal revenue M R equals the marginal cost M C p 20 x M R 20 2x MC 2 x M R M C 20 2x 2 x Xm 6 and Pm 20 Xm 14 b What will be the welfare loss in this case relative to the socially optimal outcome 8 points At the socially optimality the marginal social benefit M SB equals the marginal social cost M SC In this case the marginal social benefit includes the marginal private benefit M P B and the marginal externality benefit M EB M SB M P B M EB 20 x 10 0 5 30 1 5x M SC 2 x M SB M SC 30 1 5x 2 x Xs 11 2 and Ps 20 11 2 8 8 30 F M SB G 20 A MPB Pm Ps MC B H I C MR E O Xm 10 Xs 20 X Figure 1 Welfare Comparison between Monopolistic and Socially Optimal Outcomes As shown by Figure 1 we can identify the area for the deadweight loss in a comparison between the monopolistic and socially optimal outcomes 1 The net social welfare under the social optimality is given by SWs total benefits total costs F HXs O EHxs O F HE The net social welfare under monopolistic outcome is given by SWm consumer surplus producer surplus externality benefits ABPm Pm BCE F GBA F GCE Therefore the welfare loss relative tot he socially optimal outcome is given by SWm SWs F GCE F HE GHC 1 M SB Xm M C Xm Xs Xm 2 1 30 1 5Xm 2 Xm Xs Xm 2 1 30 1 5 6 2 6 11 2 6 2 33 8 c What policies can be used to attain the social optimum How will the welfare of various groups affected by these policies 10 points There are several policies can be used to attain the social optimum such as subsidies and quota Subsidies The optimal subsidies are given by Soptimal M C Xs M R Xs 2 Xs 20 2Xs 2 11 2 20 2 11 2 15 6 As shown by Figure 1 Table 1 demonstrates the welfare analysis Table 1 Welfare analysis for monopoly with and without subsidies Without any regulation With subsidies Change Consumer surplus ABPm 18 ARPs 62 72 Pm BRPs 34 72 Producer surplus Pm BCE 54 Ps N E N HR JHST 94 56 50 56 AF GB 51 GHRA 80 64 GHRB 29 64 0 JHST 81 12 81 12 F GCE 123 156 80 GHC 33 8 Externality benefit government net gain social welfare Therefore consumers producers and the environment all gain from subsidies while government loses Notes 1 Producer surplus has three elements including Ps N E is the surplus of producing units at which the marginal benefit is at least as great as the marginal cost 2 N HR is the loss due to the fact that this monopoly produces additional xs xm units where the marginal cost exceeds the marginal benefit if selling at ps JHST is the gain from subsidies 2 The net welfare gain from subsidies is exactly represented by the area GHC if you carefully work out the area for producer surplus 30 F M SB 20 A G MPB I J L Ps K M H Q N C E O MC B Pm Xm R MR Xs 10 20 X S T Figure 2 Welfare Comparison between Monopolistic and Socially Optimal Outcomes quota The government sets up production quota to the monopolistic producers such that they should produce the socially optimal level 11 2 If the government has no supplementary policy producer surplus is represented by Ps N E N HR 3 52 0 which implies that this monopolistic firm will still stay in business Following the same principle we obtain the following welfare analysis in Table 2 Therefore consumers and the environment gain from quota and producers lose This direct control has no effect on governmental welfare d How much will be produced under competition and at what price 4 points At the competitive outcome without any regulation the marginal private benefit M P B equals the marginal cost M P C M P B M P C 20 x 2 x Xc 9 and Pc 20 9 11 3 1 Table 2 Welfare analysis for monopoly with and without quota Without any regulation With quota Change Consumer surplus ABPm 18 ARPs 62 72 Pm BRPs 34 72 Producer surplus Pm BCE 54 Ps N E N HR 13 44 50 48 AF GB 51 GHRA 80 64 GHRB 29 64 0 0 0 F GCE 123 156 80 GHC 33 8 Externality benefit government net gain social welfare e What policies are needed to move from the competitive outcome to the optimal outcome Who will be the gainers and losers 4 points Solution Both subsidies and quota can move the competitive to the socially optimal outcome If subsidies are chosen consumers producers and the environment are gainers and government incurs cost of subsidies If quota is chosen consumers and the environment gain but producers lose 2 Question 2 36 points A community has n members The marginal benefit of each person from clean air is M Bx 10 0 4x a Is it a public good Why 4 points Solution Clean air is a public good An individual cannot prevent others from using clean air non excludibility and the use of clean air by one person will not reduce the benefit to others non rivalry b What is the socially optimal quality for a community of n 5 individuals if the marginal cost of improving x is M C 10 2x 2 points What is the net social welfare per member of the community if they share the cost of clean up equally 4 points Solution To get the aggregate marginal benefit of public goods we need vertically sum all individual marginal benefits together M B5 5M Bx 5 10 0 4x 50 2x M B5 M C 50 2x 10 2x x5 10 2 M C 10 2x Thus the net welfare for each member of the community is given by 10 10 0 10 2x dx 10 0 4x dx 5 0 individual benef it shared cost of an invidual 4 40 3 c What is the socially optimal quality for n 10 and n 6 points Solution M B10 10 10 0 4x 100 4x n 10 M C 10 2x M B10 M C …

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