Brand Names and Franchise Fees: Suppose you are currently operating a hamburger restaurant that is part of a competitive industry in your city.
A: Your restaurant is identical to others in its homothetic production technology which employs labor ℓ 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 recur- ring weekly fees F in order to operate. Illustrate the average weekly long run cost curve for your restaurant.
(b) On a separate graph, illustrate the weekly demand curve for hamburgers in your city as well as the short run industry supply curve assuming that the industry is in long run equilibrium. How many hamburgers do you sell each week?
(c) As you are happily producing burgers in this long run equilibrium, 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 of which the MacWendy’s parent company is happy to pay for. MacWendy’s would, however, charge you a weekly fran- chise 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 $y more per ham- burger when it carries the MacWendy’s brand name. If you accept this deal, will the market price for hamburgers in your city change?
(d) On your average cost curve graph, illustrate how many hamburgers you would produce if you accepted the MacWendy’s deal.
(e) Next, for agiven y, illustrate the largest that G could be in order for you to accept the MacWendy’s deal.
(f) If you accept the deal, will you end up hiring more or fewer workers? Will you hire more or less capital?
(g) Does your decision on how many workers and capital to hire under the MacWendy’s deal depend on the size of the franchise fee G?
(h) Suppose that you accepted the MacWendy’s deal and, because of the increased sales of ham- burgers at your restaurant, one hamburger restaurant in the city closes down. Assuming that the total number of hamburgers consumed remains the same, can you speculate whether total employment (of labor) in the hamburger industry went up or down in the city? (Think about the fact that all restaurants operate under the same decreasing returns to scale technology.)
B: Suppose all restaurants in the industry use the same technology that has a long run cost function C (w, r, x) = 0.028486(w0.5 r 0.5 x1.25) which, as a function of wage w and rental rate r , gives the weekly cost of producing x hamburgers.1
(a) Suppose that each hamburger restaurant has to pay a recurring weekly fee of $4,320 to operate in the city in which you are located and that w = 15 and r = 20. If the restaurant industry is in long run equilibrium in your city, how many hamburgers does each restaurant sell each week?
(b) At what price do hamburgers sell in your city?
(c) Suppose that the weekly demand for hamburgers in your city is x(p) = 100, 040 − 1000p. How many hamburger restaurants are there in the city?
(d) Now consider the MacWendy’s offer described in A(c) of this exercise. 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?
(e) Will you accept the MacWendy’s deal?
(f) Assuming that the total number of hamburgers sold in your city will remain roughly the same, would the number of hamburger restaurants in the city change as a result of you accepting the deal?
(g) What is the most that the MacWendy’s representative could have charged you for you to have been willing to accept the deal?
(i) How does this compare to the number of employees hired by the competing non-MacWendy’s hamburger restaurants? In light of your answer to (f), will overall employment in the ham- burger industry increase or decrease in your city as a result of you becoming a MacWendy’s restaurant?