Problem 1. (Point values are from an old exam and are for reference only.) (70 points). This question (from an old midterm) asks you to evaluate how information problems complicate the efforts by private parties to negotiate solutions to externalities problems. In our running example, a firm (firm 1) produces a good x, but that production also pollutes the water of a stream where a fishery (firm 2) is located. The profits for the two firms are given by: II = rx-c(x) Il = F-e(x) (1) where r is the known market price of r; c(r) are the costs of production of good x; F are profits to firm 2 that are independent of pollution; and e(z) is the negative externality that the production of x imposes on firm 2. The exact functional forms of c(x) and e(r) are given by: c(x) = cx e(x) = ex where cand e are two positive parameters. The complication is that their exact value is only known to the relevant firm. What is commonly known is that e is equally likely to have any value in an interval [c.], and e is equally likely to have any value in an interval [e,]. If c and e were publicly known, finding the efficient level of production of good r would not be difficult. Let's begin by supposing that cand e are known. 1. (4 points). What is the efficient level of x? 2. (8 points). A central planner can impose a tax 7 per unit of r on firm I: firm 1's profits become: II = rx-cx- TI What is the value of 7 that guarantees that firm 1 will choose the efficient level of a? In all that follows, we will assume that firm 1 is granted property rights over the stream: it has the right to pollute without facing penalties, and no tax is imposed by the government. For now, we continue to suppose that c and e are publicly known.