homework3answer - Department of Agricultural and Resource...

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Department of Agricultural and Resource Economics University of California Economics EEP101/ECON125, Spring 2003 Professor Zilberman Solutions to Homework Set #3 1 Public Good You find a very exciting summer internship job as an assistant to the director of a regional recreation office, and your first assignment is to give advice to the director about managing a beautiful wildlife reserve, which is called Diminishing Island. Below is the summary of information you have: The maintenance cost is MC =80 A where A is the acreage of land maintained in Diminishing Island. There are 100 citizens. But only two types of residents are attracted to Diminishing Island: 10 bird- watchers and 20 wild-flower lovers. The individual marginal benefits are given by MB b =20 2 A for each bird-watcher, and MB w =20 A for each wild-flower lover. 1. Aggregate demand and optimal level of public good (a) What is the aggregate demand for land acreage in Diminishing Island? Solution : The total marginal benefit TMB is a vertical summation of marginal benefits of 10 bird-watchers ( TMB b ) and 20 wild-flower lovers ( TMB w ) such that TMB b = MB b N b =(20 2 A ) 10 = 200 20 A, TMB w = MB w N w =(20 A ) 20 = 400 20 A, TMB = ( TMB b + TMB w if 0 A 10 TMB w if 10 <A 20 = ( 600 40 A if 0 A 10 400 20 A if 10 <A 20 . (1) Note : The aggregate demand for public good is a vertical summation of all individual marginal benefits; and the aggregate demand for private good is a horizontal summation of all individual marginal benefits (b) What is the social optimal land acreage maintained in Diminishing Island? Solution : The social optimal land acreage maintained is achieved when the total marginal benefit equals the total marginal cost. In this case, the total marginal benefit written by Equation (1) has two pieces. if TMB intercepts TC at the range of A such that 0 A 10 600 40 A =80 A A =5 , if TMB intercepts TC at the range of A such that 10 <A 20 400 20 A =80 A A =4 . conclusion: the optimal acreage of land maintained is A =5 (2) 2. Management of public good After two-week reading and talking with people, you have the four proposals on management of Diminishing Island. (a) Proposal one: the local government operates Diminishing Island using its tax revenue . How much is the optimal maintained acreage in Diminishing Island? How much is tax needed 1
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to be collected by the government? How much does each citizen need to pay in taxes for Dimin- ishing Island? How much is total consumer surplus? Solution : The optimal maintained acreage is given by A =5 . If the public good is maintained by government using tax revenue, government needs to collect tax to cover the total cost of providing the optimal level of public good. TC
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This note was uploaded on 08/01/2008 for the course ECON 101 taught by Professor Wood during the Spring '07 term at University of California, Berkeley.

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homework3answer - Department of Agricultural and Resource...

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