Suppose you are currently operating a hamburger restaurant that is part of a competitive industry in your city. Your restaurant is identical to others in its production technology which employs labor 8 and capital k and has decreasing returns to scale. (a) In addition to paying for labor and capital each week, each restaurant also has to pay recurring weekly fees F in order to operate. Illustrate the average weekly long run cost curve for your restaurant. Suppose all restaurants in the industry use the same technology that has along run cost function C(w, r,x) = 0.028486lw0'5r \"'5x1'25) which, as a function of wage w and rental rate r, gives the weekly cost of producing x hamburgers. (b) Suppose that each hamburger restaurant has to pay a recurring weekly fee of $4,220 to operate in the city in which you are located and that w = 18 and r = 25. If the restaurant industry is in long run equilibrium in your city, how many hamburgers does each restaurant sell each week? (c) At what price do hamburgers sell in your city? (cl) Suppose that the weekly demand for hamburgers in your city is x(p) =1000401000p. How many hamburger restaurants are there in the city (round if need be)? (e) A representative from the national MacWendy's chain comes to your restaurant and asks you to convert your restaurant to a MacWendy's. It turns out, this would require no effort on your part you would simply have to allow the MacWendy's company to install a MacWendy's sign, change some of the furniture and provide your employees with new uniforms all ofwhich the MacWendy's parent company is happy to pay for. MacWendy's would, however, charge you a weekly franchise fee of G for the privilege of being the only MacWendy's restaurant in town. When you wonder why you would agree to this, the MacWendy's representative pulls out his marketing research that convincingly documents that consumers are willing to pay 5y more per hamburger when it carries the MacWendy's brand name. In particular, suppose that the franchise fee required by MacWendy's is G = 5,000 and that consumers are willing to pay 94 cents more per hamburger when it carries the MacWendy's brand name. How many hamburgers would you end up producing if you accept MacWendy's deal? On your average cost curve graph, illustrate how many hamburgers you would produce if you accepted the MacWendy's deal. (f) Will you accept the MacWendy's deal