Asked by Marco-Amar Drummond on Jun 28, 2024
Verified
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, of capital, and 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?
Nondegradable Waste
Waste materials that cannot be broken down or decomposed by natural processes, leading to long-term environmental pollution.
Environmental Regulation
Rules and standards set by governments to control activities that cause environmental harm, aiming to protect the environment and public health.
Production Function
A mathematical relationship expressing the amount of output produced as a function of the quantities of various inputs.
- Calculate and interpret the effects of environmental regulations on firm costs and production decisions.
Verified Answer
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.
Learning Objectives
- Calculate and interpret the effects of environmental regulations on firm costs and production decisions.
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