Because of intense lobbying by the utility industry, you are asked to revise the proposed policy so that the utility industry will pay no charge if sulfur emissions are reduced by the desired 10 million tons. How can you accomplish this?
To calculate: The revised proposal of policy so that no charge must be paid by utility industry because of intense lobbying by them if sulfur emissions are reduced by the million tons from the current level of million tons and the table shows the marginal cost of reducing sulfur emissions at various level of reduction.
The table shows the marginal cost of reducing sulfur emissions at various level of reduction.
The derivative of function is;
Consider the Emission charge, .
Where k is the charges per ton of emissions.
The derivative of cost function at is because the tangent line to the curve at this point has zero slope.
Consider the original level of sulfur emissions is million tons. Evaluate q which represents the amount of reduction of emissions as;
Then evaluate the annual sulfur emissions by multiplying both sides with k,
Evaluate the total cost of emissions by adding cost of reducing emissions and total annual emission charge as;
Now, evaluate the derivative of cost function is;
Consider the function , where it is a linear function of q with slope and intercept
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