# A Short Example of Externalities (Coase Theorem)

Jack and May are the only residents of a small island. Jack operates a papermill, and has costs given by MPC = 10+2Q. Jack gets a price of $24 for each unit of paper he sells. May hates the pollution that the mill produces, and has damages given by MEC = Q + 2.

(a) Assume that property rights to the environment are established, and Jack has them. Further, assume that Jack and May can engage in costless bargaining. What will Jack's production level Q_ be in equilibrium?

(b) What is the minimum amount May would have to pay for Jack to produce at Q_? What is the maximum amount May would be willing to pay for Jack to produce at Q_.

(c) If May had the property rights, what is the minimum payment Jack would have to make to produce at Q_? What is the most he would be willing to pay?

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#### Solution Preview

Since the explanation contains graph and some calculations please refer to the attached file. The explanation provided below is also contained within the file:

Note that the MPC and the MEC are given, but the MSC is not. To get this, add the two functions together. That is, MSC = MPC + MEC = 12 + 3Q. Now that we have these equations, we can graph them, as in Figure.

(a) Since Jack and May can bargain at no cost, the Coase theorem ...

#### Solution Summary

This problem considers a problem of externalities and how costless bargaining can help achieve the efficient outcome (Coase Theorem). The functions used in this problem are very simple and allow following the explanations without distracting to technical issues like differentiation or integration.