An amusement park has identified its demand functions as: Q = 50 - 3P. The marginal operating cost of each unit of quantity is $5 and there are no fixed costs. The park is a monopolist and exercises significant price making power in the market. a. If the monopolist charges same price for every unit, for what price are his profits maximized? How many units will be sold at that price? What are his total profits? b. Calculate the Lerner Index at the optimal level of output. On performing a more careful market analysis it is determined by the monopolist that its customer set is made up of two sub-markets, adults (A) and children (C). The demand functions for each of these sub- markets are identified as follows: QA = 20 - PAand Qc= 30 - 2Pc c. (If the monopolist can maintain the separation between the two markets, what level of output should be produced in each market and what price will prevail? What arettotal profits in this situation? d. By comparing profit maximizing prices PAand Pc, identify the market with higher elasticity of demand. e. Compare total profits earned in part a to total profits earned in part c. Are they the same or different? Provide economic explanation underlying your answer. f. The monopolist recalls from his economics class that he can earn higher profits by charging a lump sum membership fee while setting a new ticket price. What is the profit-maximizing two-part pricing that can be employed by the monopolist