Microeconomics assignment

4. (I20 points; 25 minutes) Your company monopolizes the production of an automated trash sorting system for upscale kitchens. Your system has certain type of servo- mechanism as a key part; there is one servo per system. Q denotes the number of servos in thousands, or equivalently the number of sorting systems in thousands. Demand for the sorting system is given as P=1120-Q where P is in dollars per system. Given the servo, there are additional costs of $900 to assemble the sorting system. Your rm has three fabrication plants for servos; their marginal cost structures are given as MCI = 2001 MC; = 10Q2 MC; = 5Q: 4:) Show that net marginal revenue for servos is given as NMR = 220 2 Q That is, show your derivation of net marginal revenue for servos from the production of sorting systems. 3. (120 points: 25 minutes) The Museum of Black Velvet Paintings has hired you to set its admission prices. There are two types of people who live in the museum's area: Black Velvet Connoisseurs (BVCs), who love black velvet paintings. and Black Velvet Philistines (BVPs), who are less enchanted with black velvet paintings. The demand of each BVC is estimated as Q,=2o- 2P where Q is number of visits per year and P is in dollars per visit. The demand of each BVP is estimated as 9510 P There are 1.000 BVCs and 10.000 BVPs in the local population. Also, the Museum faces a marginal cost of zero per visit. 3a) Suppose that the Museum has a single admission price for all patrons. Assuming that the Museum has no competitors, what price would maximize its prots. and what would prots be? 3b) Some of the more elitist Museum trustees argue that the Museum should only serve BVCs, and that the Museum should consider charging an annual membership fee and/or an admission fee per visit. Namely, to visit the Museum one must pay an annual membership fee and the per-visit admission fee. What admission fee andfor annual membership fee should the Museum charge to maximize prots 'om BVCs (while not attracting BVPs)? What are prots here