Consider a simplied version of the Windows PC market, where the demand for a Windows Computer (Q) is given as a function of its price (PC): Q = 120 2Pc Windows Computers are the nal good, produced in a perfectly competitive market. The production process needs two intermediate inputs - a copy of Microsoft Windows and a Processor. Thus, the price of a Computer (PC) as a function of the price of a copy of Microsoft Windows (PM) and the price of a Processor (PP) is given by Note that for markets to clear, an equilibrium condition is that the total quantity in each intermediate market must equal the total quantity in the computer market. Microsoft, a monopolist in the Windows Computers market, aims to maximize prots by the choice of PM. Since Microsoft simply sells a software license, their marginal cost for a copy of Microsoft Windows is zero. Assume xed costs are ignored in Microsoft's decision. (1) Write down Microsoft's maximization problem. (2 points) (2) Derive the rst-order condition for prot-maximization. (2 points) (3) Calculate the optimal price PM as a function of Pp. (1 point) Now, consider the Processor market, where two firms, AMD and Intel, compete in Cournot fashion. Each firm respectively chooses QA and 2, to maximize profits, and sells their processors at the market price of Pp. Both AMD and Intel face a marginal cost of $10. Again, assume that neither firm considers fixed costs in their decisions. (4) Write down Intel's maximization problem. (3 points) (5) Derive the first-order condition for profit-maximization. (3 points) (6) Write down Intel's reaction function. (2 points)Derive the equilibrium price in the processor market, Pp as a function of PM. (2 points) (8) Calculate the numerical values of PM and Pp (3 points) (9) Calculate the numerical values of Pc and Q* (2 points)Further, Microsoft decides to enter the assembly space and market their own line of computers that they will sell at PCM. Their cost of producing a computer, conditional on having the processor, is the same as for other computer assemblers. (10) What is Microsoft's combined maximization problem? (HINT: Microso will choose the prices of their computers and Windows to maximize the prot from selling both computers directly and copies of Windows to the other assemblers.) (2 points) (1 1) Explain in words, what trade-off will Microsoft have to consider when raising the price of a license for Windows or lowering the price of their own machines? (3 points) (12) Apple, which is a monopolist in the production of MacOS computers, will sell Macs to students and teachers at a lower price if they have a .ea'u email address. (i) What type of price discrimination is being adopted by Apple? Why? (3 points) (ii) If Apple were to charge the same price to everyone, (2 points) (a) their prot would be Circle the correct alternative: HIGHER LOWER (b) consumer surplus would be Circle the correct alternative: HIGHER LOWER (13) Many Windows PC assemblers seek to portray their machines as different from others through branding or other methods. As such, many consumers might prefer to purchase a machine from one company over the others at a given price. (i) Which would be the right way to model competition in the Windows PC market? Circle the correct alternative: (I point) Competitive Selection Monopolistic Competition Coumot Oligopoly Bertrand Oligopoly (ii) With the new model of the PC market, which of these are present in the long-run? Circle the correct alternative: (I point) Allocative inefciency Productive inefciency Both Neither