Take the example of the vertical relationship of in-line skate and wheel production given in the chapter. Every skate requires four wheels, and the marginal cost of producing the skates itself is zero. The marginal cost of producing a set of four wheels is c. The inverse demand for skates is given by P(Q) = a - bQ.

This implies that the marginal revenue from skates sale is a - 2bQ.

(a) Suppose both skate and wheel production are integrated and operated by a monopolist. What would the integrated monopoly price of skates be? What is the profit of the integrated mo- nopolist?

(b) Now assume that the two production processes are not integrated and each industry is mo- nopolized. Let the price of a set of wheels be w. What is the derived demand for wheels faced by the wheel monopolist?

Write down an expression (in terms of w) for the wheel monopolist's profit. Show that for any w> 0, the total profits of the skate and wheel monopolists is lower than the integrated monopolist's profit.

(c) The game we have just considered is one where the wheel monopolist acts as a Stackelberg leader in setting the price of wheels. That is, it chooses w to maximize its profit, taking into account how the skate monopolist will respond. The skate monopolist, on the other hand, is a follower and chooses P without considering the effect of its actions on the wheel monopolist. Now, suppose the two monopolist played Nash strategies and picked their actions simultaneously. What is the Nash equilibrium of this game?