1. The inverse demand function faced by two companies competing for Cournot with homogeneous products is P=120-(q1+q2). q 1 and q 2 are the output of firm 1 and firm 2. Before innovation, the marginal cost of the two companies is the same at 60. 1) One company succeeded in a breakthrough innovation that lowered its marginal cost to 30 and is protected by a patent. If you are not licensing two firms, calculate the equilibrium output and profits of the two firms. Describe the process appropriately. 2) Let's say that company 1 charges company 2 with a certain amount of licensing (L, lump-sum). 2 Calculate how much a firm is willing to pay (L). Describe the process appropriately. 3) Let's say that Firm 1 charges Firm 2 with royalty licensing. In the first phase, firm 1 charges firm 2 with a royalty of r per unit of output. In the second stage, the marginal cost of the second firm falls from 60 to 30, but pays r royalties per unit of output. a) In the second step, draw up the profit function of the two firms and derive the output and profit of the two firms as a function of r. b) In the first stage, the optimal royalty is r * = 30. Find the output and profits of the two companies. Show R=r*xq the process appropriately. Find the amount of royalty paid by Firm 2 4) Explain which licensing company 1 prefers by comparing the fixed amount (L) in 2) above and the royalty amount (R) in 3).