Consider the business partnership between the chip manufacturer AMD and the EV manufacturer Tesla. Suppose AMD sells chips exclusively to Tesla, and Tesla buys chips exclusively from AMD. Assume each Tesla EV is equipped with one AMD chip. AMD produces the chip at a constant marginal cost CA = 4 and sells it to Tesla at PA (the price per chip): AMD does not incur other costs. Tesla's EV production cost solely comes from the purchase cost of AMD chips. Tesla faces the following inverse demand for its EV: PT = 100-QT where PT is the price of Tesla EV and QT is the demand of Tesla EV.

(a) Suppose PA = 10: Determine Tesla's optimal pricing strategy and profit. Next consider the sequential-move game between AMD and Tesla. In stage one, AMD chooses its pricing strategy PA: In stage 2, after observing the price PA set by AMD, Tesla chooses its pricing strategy PT :

(b)Following the notion of SPNE, determine Tesla's optimal pricing strategy PT in the second stage for any given PA in the first stage.

(c) Following the notion of SPNE, determine AMD's optimal pricing strategy PA in the first stage.

(d) Based on your answers in (b) and (c), calculate each firm's profit at the SPNE of the game.

(e) Suppose Tesla is considering to acquire AMD to bring the chip production in house. Determine Tesla's optimal pricing strategy PT and profit if the acquisition is successful.

(f)Compare the combined profit of Tesla and AMD in (d) with Tesla's profit after acquisition in (e). How much is Tesla willing to pay to acquire AMD?