Imagine that Gillette has a monopoly in the market for razor blades in Mexico. The market demand curve for blades in Mexico isP= 968 - 20Q, wherePis the price of blades in cents andQis 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. LettingQ₁andMC₁denote the output and marginal cost at the L.A. plant, we haveMC₁(Q₁) = 8. The Mexican plant has a marginal cost function given byMC₂(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?