Before Apple introduced the iPad Pro, Apple did not offer an Apple-branded iPad keyboard. Consider the market of iPad Air and the associated keyboard sold by Logitec, and assume that Logitec is the only brand of iPad keyboard. There are two types of customers who buy iPad Air: those who intend to use the iPad only as a tablet (A-type), and those who are interested to use the iPad as a mini version of a laptop, so they are only interested in the system of an iPad together with the keyboard (type B). Suppose that the demand for the iPad Air on its own is q^A = 100, 000 100p^A (thousands of units), where p A (denominated in USD) is the price of the iPad Air on its own, and that the demand for the system of iPad Air together with the Logitec keyboard is q ^B = 50, 000 40p^B, where p ^B = p ^A + p ^L is the price of the system and p ^L is the price of the Logitec keyboard. The marginal cost of an iPad Air is c ^A = 150 and that of a Logitec keyboard is c ^L = 20.

(a)What is the profit-maximizing price p^A for any given price p ^L 1250?

(b) What is the profit-maximizing price p^L for any given price pA 1250?

(c)If Apple and Logitec choose the price of their devices independently, what is the Nash equilibrium price of each of the devices? What is the price of the system (iPad Air with the keyboard) then?

(d)Suppose that Apple makes an agreement with Logitec, that their keyboard would be sold only in Apple stores, so that Apple will dictate its price. Suppose that Apple has to pay Logitec C ^L = 30 for each keyboard it sells. What price p ^A and p ^B should Apple choose to maximize its profit? Compare your results with the answer to c).