Question

There are two polluters j∈{A,B} who produce PM2.5 (particulate matter) emissions that damage two individuals i∈{C,D}. Total emissions is given by E=eₐ +eB . The polluters generate cost savings from emissions. The marginal savings for each polluter is equal and is given by

MSₐ =20−eAMS B =20−eB The marginal damages for the two individuals is given by MDc =3EMDD =12E. The damages from emissions are non-rival. a. Plot the total marginal savings from emissions and provide the mathematical equation MST(E).

Answer 1

The total marginal savings from emissions for two polluters is defined by the equation MST(E) = 40 - E, which is a linear function. The total marginal damages for individuals C and D are given by MDT = 15E. The socially optimal level of emissions is found where the marginal savings curve intersects with the marginal damage curve.

Step-by-step explanation:

To address the student's question, first let's plot the total marginal savings (MST) from emissions for polluters A and B. The marginal savings function for each polluter is given by MSA = 20 - eA and MSB = 20 - eB.

Since both polluters have the same marginal savings function and the total emissions are E = eA + eB, we can combine these to write the total marginal savings as MST(E) = 40 - E. This linear function shows that the total marginal savings decreases as total emissions increase.

Furthermore, according to the information given, the marginal damage from emissions is 3E for individual C and 12E for individual D.

The non-rival nature of the damages from emissions implies that both individuals suffer the full impact of emissions simultaneously. Thus, the total marginal damage is MDT = MDC + MDD = 3E + 12E = 15E.

The intersection of the marginal savings curve with the marginal damage curve will indicate the socially optimal level of emissions.

This balance ensures that the marginal cost of reducing pollution is justified by the marginal benefits obtained from reduced damages to individuals C and D.