(4) (30 marks) Let us get back to a daily situation, i.e. short run situation. Suppose the daily market demand for hot dogs is Q = 5,000-1,000P, in which P denotes the price per hot dog and O denotes the total number of hot dogs demanded a day at price P. Each vendor's marginal cost is the same as before. Suppose also that, due to its new environmental law, the city has decided to regulate the hot dog market by issuing the business permit only to 20 vendors. And, as a response, 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 to maximize the joint profit.) Suppose also that each of the 20 vendors agreed to sell an equal number of hot dogs at the same price, thus each taking an equal amount of one-twentieth of the cartel's profit. Answer the following questions, quantifying and supporting through a diagram. (1) What price would the vendors agree on? (11) How many hot dogs would each vendor sell a day? (ifi) How much of profit would each vendor make a day? (iv) How much of deadweight loss a day would the cartel cause to the market? (Hint: The cartel's MC curve will be horizontal summation of all vendors' MC curves.)