3. A chemical factory spills the coast with a substance that increases the cost of catching lobsters by a group of fishermen. The chemical company produces with cost Cop = agoy + (10 2)2, where z is the quantity of spill. The fishers experience a cost of catching lobsters that is O, = bgz +4z2. Both the chemical company and the fishers sell in competitive markets. a. Characterize the externality that shows up in this problem. Why economists call this an externality? b. Write the profits and the first order conditions for the optimal decisions of the chemical company and the fishermen. Write the prices and level of pollution in competitive equilibrium. . Compute profits in competitive equilibrium. d. Calculate the Pareto Optimum production of the externality. Explain intuitively why your solution works. e. What are the Pareto Optimum profits of each activity? How is their sum compared with the sum in compatitive equilibrium? 4 A software company developing AI employs a number of engineers e to produce the same number of projects r = e. Al engineers are scarce in the market, so the cost of the firm is C,() = C.(r) = 2. A firm producing appli- cations that is located in the neighborhood benefit from the presence and ideas of the engineers (people freely socialize at lunch time). The firm produces a applications with cost C,(a,r) = a? . a What kind of externality is present among these production processes?. b Get the supply of projects and applications in competitive equilibrium with prices p, and p,. Obtain the Pareto Optimal supplies and costs. d Government wants to obtain the Pareto Optimal allocation by means of a subsidy to the company. Compute the subsidy. 5. Suppose that the inverse demand curve for Internet services p = 200 Q and private marginal cost (unregulated competitive market supply) is MC = 20+ 2Q), but Government thinks that the spread of Internet is having a marginal social benefit (cost saving) estimated in MCgsprpap = Q. a. Which is the unregulated competitive equilibrium? b. What is the social optimum? c. Compute the increase in sonsumer welfare in the equilibrium which ac- counts for the externality. d What specific subsidy (per unit of output) may induce the social optimum