11.21. Imagine that Gillette has a monopoly in the market for razor blades in Mexico. The market demand curve for blades in Mexico is P ! 968 # 20Q, where P is the price of blades in cents and Q is annual demand for blades expressed in millions. Gillette has two plants in which it can produce blades for the Mexican market: one in Los Angeles and one in Mexico City. In its L.A. plant, Gillette can produce any quantity of blades it wants at a marginal cost of 8 cents per blade. Letting Q1 and MC1 denote the output and marginal cost at the L.A. plant, we have MC1(Q1) ! 8. The Mexican plant has a marginal cost function given by MC2(Q2) ! 1 " 0.5Q2.

a) Find Gillette’s profit-maximizing price and quantity of output for the Mexican market overall. How will Gillette allocate production between its Mexican plant and its U.S. plant?

b) Suppose Gillette’s L.A. plant had a marginal cost of 10 cents rather than 8 cents per blade. How would your answer to part

(a) change?