Oldtronics and Newtronics are two producers of lie detectors. After many years of R&D (research and development), Newtronics developed Nolies, a new machine that makes no mistakes in uncovering lies. To protect its innovation, Newtronics has patented the new lie detector. Suppose that the direct demand for Nolies is QD = 60-P, Newtronics' total cost for Nolies is represented by TC = 500 + Q2, and Newtronics' marginal cost for Nolies is represented by MC = 2Q. a) If Newtronics is the sole producer of Nolies, how many lie detectors will it sell? What will the price of the new lie detectors be? What are Newtronics' profits? Newtronics could grant Oldtronics a license that allows Oldtronics to produce and sell Nolies. Suppose, for now, that the two firms face the same costs and that Newtronics is forced by the government to provide the license free of charge. Assume, for simplicity, that if Oldtronics decides to produce and sell Nolies, each firm in the resulting duopoly will produce either 10 or 12 units. b) Complete the game given below, where the payoffs for the two players are the profits from the resulting strategies. Find the Nash equilibrium of this game. Is there a dominant strategy? Are some strategies dominated? Explain. Note that because the two firms face the same costs, the game is symmetric. Oldtronics Newtronics Q = 10 Q = 12 Q = 10 Q = 12 $200 *** *** ..., $220 c) How does the monopolist's profit derived in part a) compare to the profits of the two duopolists when they collude and produce the monopolist's optimal quantity? Explain. d) What is the maximum amount of money that Newtronics is willing to pay Oldtronics to stay out of the business? What is the minimum amount of money that Oldtronics is willing to accept to keep out of this business? Is there room for negotiation between the two parties? e) If there was no government coercion, what is the minimum royalty that Newtronics would be willing to accept from Oldtronics in exchange for the license?* What is the maximum royalty that Oldtronics is willing to pay to Newtronics in order to sell Nolies? Is there room for negotiation between the two parties?