Question: In 2007, Mid West Autoparts (MWA) invests exist6M to produce hood latches for GM. The unit cost of production for MWA is constant at exist5 per latch, and it expects to sell 1M hood latches at exist12 per piece. In 2008 the economy enters recession, and GM asks to renegotiate the price of a hood latch. If the renegotiation fails, GM produces latches in-house at the cost of exist13 per unit with no investment needed, and MWA receives a compensation of exist3M from GM, with no additional revenue.
(a) What is the minimal price that MWA will accept in the renegotiation process? What is the maximal price that GM will pay?
(b) How does your answer to (a) change if the compensation that GM pays to MWA when renegotiations fail is CM, where C is a constant and CM is the total compensation in million dollar terms.
(c) Suppose the bargaining process is now sequential, i.e. one player offers a price, and then the other player chooses to accept or reject the offer. Consider first the case where both compensation constant C and renegotiated price p are integer numbers between the minimal and maximal price you found in (b). Does it matter who plays first? Discuss both cases, and find the subgame perfect Nash equilibria in each case.
(d) Now suppose p can be any real number in the price range you found in question (b), how will your answer to question (c) change?