4 (25 pts). A software company developing AI employs a number of engineers e to produce the same number of projects r = e. AI engineers are scarce in the market, so the cost of the firm is Cr(e) = Cr(r) = >r2. A firm producing applications 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 Ca(a, r) = za2 - 2r. a (5 pts). What kind of externality is present among these production pro- cesses?. b (7 pts). Get the supply of projects and applications in competitive equi- librium with prices pr and Pa c (7 pts). Obtain the Pareto Optimal supplies and costs. d (6 pts). Government wants to obtain the Pareto Optimal allocation by means of a subsidy to the company. Compute the subsidy