Problem 1 Duopoly: Oldtrom'cs and Newtmm'cs are two producers of lie detectors. After many years of R.&D (research and development), Newtmnics developed Nolz'es, 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 Nolz'es is Q D : 607 %P, Newtrom'cs' total cost for N olies is represented by TC : )00 + Q2, and Nemtmm'csl marginal cost for Nolz'es is represented by 11-10 : 2Q. a) If Newtronics is the sole producer of N alias, how many lie detectors will it sell? \\V hat will the price of the new lie detectors be? What are Newtrom'cs' prots? Newtrom'cs could grant Oldtrom'cs a license that allows Oldtrom'cs to produce and sell Nolz'es. Suppose, for now, that the two rms face the same costs and that Newtrom'cs is forced by the government to provide the license free of charge. Assume, for simplicity, that if Oldtrom'cs decides to produce and sell Nolz'es, each rm 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 prots 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 rms face the same costs, the game is symmetric. Oldtronics m (210 6212 Q: 10 ,$200 Q :12 , .3320 c) How does the monopolist's prot derived in part a) compare to the prots of the two duopolists when they collude and produce the monopolist's optimal quantity? Explain. d) What is the maximum amount of money that Newtrom'cs is willing to pay Oldtrom'cs to stay out of the business? W" hat is the minimum amount of money that Oldtmnics 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 Newtrom'cs would be willing to accept from Oldtmm'cs in exchange for the license?* What is the maximum royalty that Oldtronics is willing to pay to Newtrom'cs in order to sell Nolz'es? Is there room for negotiation between the two parties