factory can produce a good that it can sell at a price of 6$ per unit. The firm faces a private cost of (q^2)/2 . For every unit produced by the firm, the only landowner who lives next to the firm incurs a cost of 4$ due to pollution. a) If no well-defined property rights exist, the firm will act as if it has the right to pollute. What quantity would the firm choose to produce? What is the firm’s profit? b) What is the socially optimal quantity of the good that should be produced? What would the landowner’s surplus be in that case? c) Suppose that society

A factory can produce a good that it can sell at a price of 6$ per unit. The firm faces a private cost of (q^2)/2 . For every unit produced by the firm, the only landowner who lives next to the firm incurs a cost of 4$ due to pollution.
a) If no well-defined property rights exist, the firm will act as if it has the right to pollute. What quantity would the firm choose to produce? What is the firm’s profit?
b) What is the socially optimal quantity of the good that should be produced? What would the landowner’s surplus be in that case?
c) Suppose that society can enforce either a right to pollute or a right to fresh air. Does Coase theorem hold in this situation? Show that it does or does not.
d) Suppose that the firm can build an air filter for 7$. The filter can only be used efficiently by the firm, not by the consumers. What is the new outcome if there is a right to fresh air? How does your answer change if the air filter is only usable by consumers, and is Coase theorem still applicable?