Question

There are two coal-fired power plants located in the vicinity of a major metropolitan area. These power plants emit sulphur dioxide, which causes respiratory issues for the metro population as well as resulting in acidic rainfall. The EPA has determined that the amount of sulphur dioxide emitted needs to be reduced by 169 tons. The marginal abatement cost function for the first power plant is given by MC(x) = 4x and the marginal abatement cost function for the second power plant is given by MC(y) = 9y, where x is the amount of emissions reduction done by the first power plant, and y is the amount of emissions reduction done by the second power plant. In order to ensure that the target level of emissions reduction is achieved in the most cost-effective way, what should x be? Please round your answer to 2 decimal places

Answer 1

Determined that the amount of sulphur dioxide emitted needs to be reduced by 169 tons.

Aslo given that it would be done in such a way so that emissions reduction is achieved in the most cost-effective way .

And given that the marginal abatement cost function for the first power plant is given by MC(x) = 4x and the marginal abatement cost function for the second power plant is given by MC(y) = 9y,.

So here we can see that X and Y are the amount of emission reduced by both the plants

respectively.

But the marginal cost given here is 4X and 9Y

By which we can see that cost incurred due to 2nd plant will be higher so we try to reduce emissions in such a way that plant 1 will more than 2nd or if possible then whole reducetion can be done by 1st.

Here there is no such conditions like how much emmission will be reduced by respective plants.

So we use plant 1st only for reducetion for emission so cost will be minimise.

X=169 tons.

N total cost is =4*169=676