A firm’s total costs c are

c = 4 q^ 2

where q is the level of output. It can sell any number of units of output at a price of 64. However, production inflicts damage on the firm’s neighbours. The total damage D inflicted depends on the firm’s output:

D = 4 q + q^ 2

a) Assume that the firm has the property rights. In the absence of an agreement with its neighbours, what would its level of output be? Suppose that the neighbours negotiate with the firm. To what level of output would the negotiations lead? What is the minimum payment that the neighbours must make to the firm to achieve this change in output? What is the maximum payment?

b) Assumethattheneighbourshavethepropertyrights.Intheabsenceofanagreement between the firm and its neighbours, what would the level of output be? If an agreement between the firm and its neighbours is negotiated, what are the smallest and largest payments that the firm would have to pay?

c) Assume that the firm has the property rights. If the government wishes to control the externality by imposing a tax, what should the tax be? How much revenue does it collect?