4. Assume that the inverse demand function is given by P = 240 Q. The discount factor is [1.9. Mlarginal production costs are initially 120. (a) (b) (d) (9) Calculate the market equilibrium price. output. and prots on the assumption that the market is currently: (i) monopolized. and (ii) a Bertrand duopoly with homogeneous products. Note that in the duopoly case with identical marginal costs. if rms charge the same price, they share the market equally. [10 marks] Suppose that a research institute develops and obtains a patent for a new technology that reduces the marginal costs to 60. Calculate the new market equilibrium price, output. and prots for (i) the monopolist, and [ii] each duopolist. Note that in the duopoly case, the innovation is made available to only one rm, and if both rms charge the same price, consumers always buy from the most efcient rm. [10 marks] How much will the monopolist and duopolist be willing to pay for the patent on this innovation if the patent lasts forever? [10 marks] Now assume that there is a potential entrant in the monopolized case and that the research institute is considering oering the patent to this rm as well as to the monopolist. Only one rm is able to purchase the patent. [fthe entrant purchases the patent, it will enter the market as a Bertrand competitor. if the incumbent purchases the patent, entry does not occur, and the incumbent remains a monopolist. How does this affect the amount the incumbent monopolist will be willing to pay for the innovation? [10 marks] What are the \"Shumpetarian hypotheses". Are your answers to parts (c) and (d) consistent with these hypotheses. [10 marks]