“Economic Rent” and Profiting from Entrepreneural Skill: Suppose, as in exercise 14.4, that you are operating a hamburger restaurant that is part of a competitive industry. Now you are also the owner, and suppose throughout that the owner of a restaurant is also one of the workers in the restaurant and collects the same wage as other workers for the time he/she puts into the business each week. (In addition, of course, the owner keeps any weekly profits.)
A: Again, assume that all the restaurants are using the same homothetic decreasing returns to scale technology, but now the inputs include the level of entrepreneural capital c in addition to weekly labor ℓ and capital k. As in exercise 14.4, assume also that all restaurants are required to pay a recurring weekly fixed cost F.
(a) First assume that all restaurant owners possess the same level of entrepreneural skill c. Draw the long run AC curve (for weekly hamburger production) for a restaurant and indicate how many weekly hamburgers the restaurant will sell and at what price assuming that the industry is in long run equilibrium.
(b) Suppose next that you are special and possess more entrepreneural and management skill than all those other restaurant owners. As a result of your higher level of c, the marginal product of labor and capital is 20% greater for any bundle of ℓ and k than it is for any of your competitors. Will the long run equilibrium price be any different as a result?
(c) If your entrepreneuralskill causes the marginal product of capital and labor to be 20% greater for any combination of ℓ and k than for your competitors, how does your isoquant map differ from theirs? For a given wage and rental rate, will you employ the same labor to capital ratio as your competitors?
(d) Will you produce more or less than your competitors? Illustrate this on your graph by deter- mining where the long run MC and AC curves for your restaurant will lie relative to the AC curve of your competitors.
(e) Illustrate in your graph how much weekly profit you will earn from your unusually high entrepreneural skill.
(f) Suppose the owner of MacroSoft, a new computer firm, is interested in hiring you as the man- ager of one of its branches. How high a weekly salary would it have to offer you in order for you to quit the restaurant business assuming you would work for 36 hours per week in either case and assuming the wage rate in the restaurant business is $15 per hour.
(g) The benefit that an entrepreneur receives from his skill is sometimes referred to as the economic rent of that skill — because the entrepreneur could be renting his skill out (to someone like MacroSoft) instead of using it in his own business. Suppose MacroSoft is willing to hire you at the rate you determined in part (f). If the economic rent of entrepreneural skill is included as a cost to the restaurant business you run, how much profit are you making in the restaurant business?
(h) Would counting this economic rent on your skill as a cost in the restaurant business affect how many hamburgers you produce? How would it change the AC curve in your graph?
B: Suppose that all restaurants are employing the production function f (ℓ, k, c) = 30ℓ0.4k0.4c where ℓ stands for weekly labor hours, k stands for weekly hours of rented capital and c stands for the entrepreneural skill of the owner. Note that, with the exception of the c term, this is the same production technology used in exercise 14.4. The weekly demand for hamburgers in your city is, again as in exercise 14.4, x(p) = 100, 040 − 1, 000p.
(a) First, suppose that c = 1 for all restaurant owners, that w = 15 and r = 20, that there is a fixed weekly cost $4,320 of operating a restaurant, and the industry is in long run equilibrium. Determine the weekly number of hamburgers sold in each restaurant, the price at which ham- burgers sell, and the number of restaurants that are operating. (If you have done exercise 14.4, you should be able to use your results from there.)
(b) Next, suppose that you are the only restaurant owner that is different from all the others in that you are a better manager and entrepreneur and that this is reflected in c = 1.24573 for
you. Determine your long run AC and MC functions. (Be careful not to use the cost function
given in exercise 14.4 since c is no longer equal to 1. You can instead rely on the cost function derived for Cobb-Douglas technologies given in equation (13.45) in exercise 13.5 (and remember to add the fixed cost).)
(c) How many hamburgers will you produce in long run equilibrium?
(d) How many restaurants will there be in long run equilibrium given your higher level of c?
(e) How many workers (including yourself) and units of capital are you hiring in your business compared to those hired by your competitors? (Recall that the average worker is assumed to work 36 hours per week.)
(f) How does your restaurant’s weekly long run profit differ from that of the other restaurants?
(g) Suppose Macrosoft is interested in hiring you as described in part A(f). How high a weekly salary would MacroSoft have to offer you in order for you to quit the restaurant business and accept the MacroSoft offer?
(h) If you decide to accept the MacroSoft offer and you exit the restaurant business, will total employment in the restaurant business go up or down?