HW4,Sp2000sols

HW4,Sp2000sols - EEP101/ECON 125 Spring 00 Prof D Zilberman...

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Unformatted text preview: EEP101/ECON 125 Spring 00 Prof D. Zilberman GSI’s: Malick/McGregor/St-Pierre Suggested Solutions to Problem Set 4 Stock of deer = S Harvest or deer that are killed = X Growth of the Stock = 2 ) ( bS aS S g- = , where 00002 . , 8 . = = b a Marginal Benefit (or price) per deer = P Total Cost per deer = S KX S X C = ) , ( , where 000 , 80 = K A) A steady state, defined by ) ( S g X = , implies a sustainable harvest level and a constant stock level. The maximum sustainable yield occurs at ) ( ' = S g . The environmental carrying capacity occurs at ) ( = S g . Carrying Capacity: 000 , 40 00002 . 8 . ) ( 2 = = = =- =- = b a Scc bS a bS aS S g Maximum Sustainable Yield 000 , 8 ) 000 , 20 ( 00002 . ) 000 , 20 ( 8 . ) ( ) ( ) ( 000 , 20 00004 . 8 . 2 2 ) ( ' 2 2 =- =- = = = = = =- = MSY MSY MSY MSY S b S a S g MSY b a S bS a S g g(S) X = g(S) S MSY = 20,000 S CC = 40,000 MSY = 8,000 g(S) X = g(S) S MSY = 20,000 S CC = 40,000 MSY = 8,000 B) The government charges a hunting fee equal to 5 = l , and allows anyone who wants to hunt to do so. Therefore, there is an open access situation in which profits are ultimately driven down to zero. If a steady state equilibrium is to be found, then the following conditions must hold: i 1. Total Revenues = Total Costs (Zero Profits) 2. ) ( S g X = (Sustainability or steady state) At steady state, Total Revenues = ) )( ( ) ( ) ( ) ( 2 bS aS l p S g l p X l p TR-- =- =- = Total Costs = bKS aK S S Kg S KX TC- = = = ) ( Open access equilibrium is found by setting TR =TC K S l p bKS aK bS aS l p TC TR =-- =-- = ) ( ) )( ( 2 000 , 16 5 10 000 , 80 =- =- = l P K S oa Since ) ( S g X = , then the open access level of hunting is 680 , 7 ) ( = = oa oa S g X . The government revenues are 400 , 38 ) 680 , 7 ( 5 = = oa lX Total Revenues= (p-l) g(S) $ S MSY = 20,000 S CC = 40,000 40,000 38,400 S OA = 16,000 64,000 Total Costs = aK - bKS Open Access Solution Total Revenues= (p-l) g(S) $ S MSY = 20,000 S CC = 40,000 40,000 38,400...
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HW4,Sp2000sols - EEP101/ECON 125 Spring 00 Prof D Zilberman...

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