A: Suppose that all firms in the fast food restaurant business face U-shaped average cost curves prior to the introduction of a recurring license fee. The only output they produce is hamburgers. Suppose throughout that hamburgers are a quasilinear good for all consumers.
(a) First, assume that all firms are identical. Illustrate the long run market equilibrium and indicate how large consumer and long run producer surplus (i.e. profit) are in this industry.
(b) Illustrate the change in the long run market equilibrium that results from the introduction of a license fee.
(c) Suppose that the license fee has not yet been introduced. In considering whether to impose the license fee, the government attempts to ascertain the cost to consumers by asking a consumer advocacy group how much consumers would have to be compensated (in cash) in order to be made no worse off. Illustrate this amount as an area in your graph.
(d) Suppose instead that the government asked the consumer group how much consumers would be willing to pay to avoid the license free. Would the answer change?
(e) Finally, suppose the government simply calculated consumer surplus before and after the license fee is imposed and subtracted the latter from the former. Would the government’s conclusion of how much the license fee costs consumers change?
(f) What in your answers changes if, instead of all firms being identical, some firms had higher costs than others (but all have U-shaped average cost curves)?
B: Suppose that each firm’s cost function is given by C (w, r, x) = 0.047287w0.5r0.5 x1.25 + F where F is a recurring fixed cost.1
(a) What is the long run equilibrium price for hamburgers x (as a function of F) assuming wage w = 20 and rental rate r = 10?
(b) Suppose that, prior to the imposition of a license fee, the firm’s recurring fixed cost F was $1,280. What is the pre-license fee equilibrium price?
(c) What happens to the long run equilibrium price for hamburgers when a $1,340 recurring license fee is introduced?
(d) Suppose that tastes for hamburgers x and a composite good y can be characterized by the utility function u(x, y) = 20x0.5 + y for all 100,000 consumers in the market, and assume that all consumers have budgeted $100 for x and other goods y. How many hamburgers are sold before and after the imposition of the license fee?
1You can check for yourself that this is the cost function that arises from the production function f (ℓ, k) = 20ℓ0.4k0.4.
(e) Derive the expenditure function for a consumer with these tastes.
(f) Use this expenditure function to answer the question in A(c).
(g) Use the expenditure function to answer the question in A(d).
(h) Take the integral of the demand function that gives you the consumer surplus before the license fee and repeat this to get the integral of the consumer surplus after the license fee is imposed.
(i) How large is the change in consumer surplus from the price increase? Compare your answer to what you calculated in parts (f) and (g).