A firm's total cost C is given by the function:

C = 4X2

Where X is the level of output and C is the cost. The firm 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 = 4X + X2

(a) Assume that the firm has the property rights:

(i) In the absence of an agreement with its neighbours, what would its level of output be?

(ii) Suppose that the neighbours negotiate with the firm. To what level of output would the negotiations lead?

(iii) What is the minimum payment that the neighbours must make to the firm to achieve this change in output?

(iv) What is the maximum payment that the neighbours must make to the firm to achieve this change in output?

(b) Assume that the neighbours have the property rights:

(i) In the absence of an agreement between the firm and its neighbours, what would the level of output be?

(ii) If an agreement between the firm and its neighbours is negotiated, what are the smallest and largest payments that the firm would have to make?