Martin's Movies is a movie theater in the small rural town of Hamilton. As such, it acts as a monopolist in the market for the movies. Martin faces a downward-sloping demand curve of QD = 200 - 3P. Martin's cost function is TC(Q) = 200, which gives his MC = 20. a.) Rearrange the demand curve to get P as a function of Q: the inverse demand curve. What is the slope of the demand curve? b.) If MR = 200/3 - 2/3, use the condition MR = MC to solve for Martin's optimal level of output, Qm*, the price in the market, Pm*, and Martin's profit at this optimal level of output, AM* Hamilton is a college town, and Martin notices students seem to have different demand for the movies than the local residents. Therefore, Martin would like to price discriminate, and charge two groups of consumers ('students' and everyone else in town') two different prices. The cost of production is the same for Martin in either market: TC(Q) = 200. However, now Martin faces two separate demand curves: QD,TOWN = 100 - P. and QD.STUDENTS = 100 - 2P2. PL is the price Martin charges to the town, while P2 is the price he charges to the students. c.) Which market has more elastic demand? Explain your answer by graphing the demand functions in each market. d.) Martin will choose the optimal quantity in each market by setting MC = MR in each market. Since MRTOWN = 100 - 2Qrown and MRSTUD =50 - Qstud, use this to solve for both Qp,Town* and QD STUDENTS*. e.) Find P.* and P2*, and the total profit Martin makes when price discriminating. Compare with your answer from b. Does price discrimination help Martin increase his profit? f.) Relate your answer from e. to the question of elasticity. How does the pricing pattern relate to the different demand characteristics