Consider a city that has a number of hot dog vendors operating in the downtown area. Suppose that each vendor has an identical constant marginal cost of $1.00 up to 150 hot dogs per day but it surges to a constant level of $5.00 for the units after 150 hot dogs a day. (In case you wonder, this surge in marginal costs is due to the facility capacity and manpower issues in running the vendor business.) A vendor's fixed cost - mainly for the vending cart - is all sunk and thus negligible. The vendors of course are profit-maximizers. Assume that the market is perfectly competitive for question (1), (2) and (3) below. This assumption is to be relaxed for (4) and (5). (These assumptions may not sound realistic but let us assume so for analytical purpose.) Answer the following questions. Show your work with graphical support. (1) (10 marks) Derive each vendor's supply curve and the market supply (in the downtown area of the city) for hot dogs in short run. (For market supply, assume there are n vendors in the market for now) (2) (5 marks) Suppose that the market price of a hot dog is $2. How many hot dogs would each vendor currently want to sell in the short run? What will be each firm's daily short run profit at this price? (3) (5 marks) Will the price remain at $2 for a hot dog in the long run? If not, what will the price be in the long run equilibrium? (4) (15 marks) Suppose the daily market demand for hot dogs is Q = 5,000 - 1,000P, in which Q denotes the total number of hot dogs demanded a day at price P and P denotes the price per hot dog. The vendors' marginal costs are the same as before. Suppose also that, due to its new environmental law, the city has decided to regulate hot dog vendors by issuing the business permit only to 20 vendors. The number of being small enough now, the 20 vendors with permits managed to form a cartel to coordinate their pricing and improve their profits. (This means the cartel would behave as if it were a monopolist in the market,) Suppose also that each of the 20 vendors agreed to sell an equal number of hot dogs at the same price. Answer the following questions, supporting through a diagram. (Hint: The cartel's MC curve will be horizontal summation of all vendors' MC curves.) (i) What price would the vendors agree on? (ii) How many hot dogs would each vendor sell? (iii) How much of profit would each vendor make? (5) (15 marks) Concerned about the deadweight loss the above cartel causes, the city government now has decided to further regulate the market through a price ceiling. (i) To fully restore the market efficiency, what level of price ceiling should the government impose? (ii) How many hot dogs would each vendor sell a day after the price regulation? How much of profit would each vendor make? (iii) Quantify the deadweight loss the city would get to avoid through this price regulation.