Fast Food Restaurants and Grease (cont’d): In exercise 12.8, you investigated the impact of hybrid vehicles that can run partially on grease from hamburger production on the number of hamburgers produced by a fast food restaurant. You did so, however, in the absence of considering the equilibrium impact on prices — assuming instead that prices for hamburgers are unaffected by the change in demand for grease.
A: Suppose again that you use a decreasing returns to scale production process for producing ham- burgers using only labor and that you produce 1 ounce of grease for every hamburger. In addition, suppose that you are part of a competitive industry and that each firm also incurs a recurring fixed cost F every week.
(a) Suppose that the cost of hauling away grease is q > 0 per ounce. Illustrate the shape of your marginal and average cost curve (given that you also face a recurring fixed cost.)
(b) Assuming all restaurants are identical, illustrate the number of hamburgers you produce in long run equilibrium.
(c) Now suppose that, as a result of the increased use of hybrid vehicles, the company you previously hired to haul away your grease is now willing to pay for the grease it hauls away. How do your cost curves change?
(g) In exercise 12.8, you concluded that the cholesterol level in hamburgers will increase as a result of these hybrid vehicles if restaurants can choose more or less fatty meat. Does your conclusion still hold?
(f) Would your answers change if you instead assumed that restaurants used both labor and capital in the production of hamburgers?
(e) How does your answer change in the long run?
(d) Describe the impact this will have on the equilibrium price of hamburgers and the number of hamburgers you produce in the short run.
B: Suppose, as in exercise 12.8, that your production function is given by f (ℓ) = Aℓα (with 0 < α < 1) and that the cost of hauling away grease is q. In addition, suppose now that each restaurant incurs a recurring fixed cost of F.
(a) Derive the cost function for your restaurant.
(b) Derive the marginal and average cost functions.
(c) How many hamburgers will you produce in the long run?
(d) What is the long run equilibrium price of hamburgers?
(e) From your results, determine how the long run equilibrium price and output level of each restaurant changes as q changes.