Business Taxes (cont’d): In exercise 13.11, we introduced a number of possible business taxes and asked what a firm’s response would be assuming that prices w, r and p remained unchanged. Now that we have introduced the notion of equilibrium price formation, we can revisit the exercise.

A: Suppose the restaurant industry is in long run equilibrium, all restaurants use the same homothetic decreasing returns to scale technology and all have to pay a fixed annual franchise fee F.

(a) Illustrate the average cost curve for a restaurant and the related (short run) supply and demand graph for the industry.

(b) Revisit parts A(b) through A(h) of exercise 13.11 and explain whether the assumption that prices remained unchanged was warranted and, if not, why not.

B: Consider the same technology as the one used in exercise 13.11 as well as the recurring fixed cost F.

(a) Determine the long run equilibrium price p∗ and output level x^∗ as a function of A, α, β w and r. (You can use the cost function given in equation (13.45) in exercise 13.5 as well as the profit function given equation (13.48) in exercise 13.7.)

(b) In exercise 13.11, we focused on the impact of policies from A(b) through A(h) on output supply and input demand functions. Now use your result from (a) to determine the impact of each of these policies on the long run equilibrium price and firm output level.