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nakungth nakungth
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5 years ago
A paper company dumps nondegradable waste into a river that flows by the firm's plant.  The firm estimates its production function to be:
   Q = 6KW,
 where Q = annual paper production measured in pounds, K = machine hours of capital, and W = gallons of polluted water dumped into the river per year.  The marginal products of capital and labor are given as follows:
   MPK = 6W   MPW = 6K       
The firm currently faces no environmental regulation in dumping waste into the river.  Without regulation, it costs the firm $7.50 per gallon dumped.  The firm estimates a $30 per hour rental rate on capital.  The operating budget for capital and waste water is $300,000 per year.

a.   Determine the firm's optimal ratio of waste water to capital.
b.   Given the firm's $300,000 budget, how much capital and waste water should the firm employ?  How much output will the firm produce?
c.   The state environmental protection agency plans to impose a $7.50 effluent fee for each gallon that is dumped.  Assuming that the firm intends to maintain its pre-fee output, how much capital and waste water should the firm employ?  How much will the firm pay in effluent fees?  What happens to the firm's cost as a result of the effluent fee?
Textbook 

Microeconomics


Edition: 8th
Author:
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boransalboransal
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5 years ago
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a.
   MPW  = 6K
   MPK  = 6W
   MRTS =   = 

Rate of water charge to price of capital:
     =   = .25
Equating MRTS to ratio of input prices
     = 0.25,   K = 0.25W

b.
   C = PWW + PKK
   300,000 = 7.50W + 30K       
Recall K = 0.25W
   300,000 = 7.5W + 30(0.25W)
   300,000 = 7.5W + 7.5W    
      W = 20,000 gallons
   K = 0.25W
   K = 0.25(20,000)    
      K = 5000
   Q = 6(5000)(20,000)    
      Q = 600,000,000    

c.       
PW  becomes $15 (7.50 previous cost + effluent fees).       
Ratio of input price is
     =   = 0.5
   MRTS = 

Hold Q constant at 600,000,000
   Q = 6KW
   K = 0.5W
   600,000,000 = 6(0.5W)(W)
   600,000,000 = 3W2
   200,000,000 = W2
   W = 14,142.13 or W = 14,142
   K = 0.5(14,142)
   K = 7071       
Water usage falls from 20,000 to 14,142 while capital rises from 5000 to 7071.
Effluent fee is 7.5 × 7071 = $53,032.5       
Cost prior to effluent fee was $300,000 (from isocost level)       
Cost after effluent fee is
   C = PWW + PKK       
where PW  = 15 (including fee)       
   PK  = 30
   C = 15(14142) + 30(7071)
   C = 212,130 + 213,130
   C = $424,260       
Cost rises from $300,000 to $424,260.
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nakungth Author
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4 years ago
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4 weeks ago
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