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You have been hired as a managing director for Tesla Motors, a small electric vehicle maker in Palo
Alto, California. Tesla is currently the only producer worldwide for luxury electric vehicles. They
currently make two models: the Roadster; their flagship sports-car, and the Model S; a luxury sedan.
Sales of the Model S are given by the demand formula QS=40,000 – 0.5PS + 0.1PR + 0.001A.
Tesla Motors currently has an advertising budget of $10 million, and has been selling Roadsters at PR =
$100,000 per unit at a rate of 1000 units per year since 2008. The list price for the Model S is $80,000,
but Elon Musk, the CEO of Tesla Motors, is considering lowering the price of the sedan to $72,000.
Currently, the Roadster and the Model S are built in two separate facilities in Southern California. The
cost function for the Roadster is TCR = $3,000,000 + 50,000QR and for the Model S the cost is
TCS=$2,000,000 + $45,000QS. The firm is considering moving production of the Model S into the
Roadster plant, but they are concerned because of the extra costs that would be incurred by merging
production as the joint costs would become TC=$3,000,000 + 50,000 QR + 45,000 QS + 0.11*QR*QS
a. Advise Elon regarding his decision to lower the price of the Model S
b. Advise the Tesla production team on their decision to merge the production facilities.
c. Determine if the marketing team chose the optimal markup (price) for the Model S
The Tesla Roadster was originally designed as a prototype for Tesla Motors, and in an interview last
month, Musk claimed that “[Tesla] would halt North American sales of the Roadster this year”.
Following this news came a press release from GM motors, who have developed an electric sedan, the
Edison, that is set to compete directly with the Model S.
The Edison and the Model S will compete directly with each other, but due to the large barriers to entry,
it is unlikely that any other firm will enter the market. The market researchers hired by Tesla Motors
have determined that the market demand for luxury electric vehicles is given by the formula P =
135,000 – 3Q, and your corporate spies have informed you that the marginal cost faced by GM is
identical to your own.
Your research and development (R&D) team assure you that they can reduce the marginal cost of
production by $30,000, if you can invest $35 million in purchasing new technology from Bloom
Energy, a local green-energy supplier. Meanwhile, the Chief Financial Officer (CFO), Deepak Ahuja
believes that you can buy off GM’s EV division, and halt production of the Edison for an annual
payment of $370 million, which will allow Tesla to receive monopoly profits once more.
d. Advise the board of their best option (compete with GM, invest in the new technology, or buy
Lastly, assume that annual sales of the Model S and the Edison will not change, and further that the two
companies will be competing (as the only two suppliers) for sales for many years to come (read
infinitely). Using a normal form game, where the players options are to compete, (and receive Cournot
profits) or collude (and receive joint monopoly profits if the other colludes, or play a Stackelberg game
if the leader decides to compete), show whether it is possible for the two firms to collude, or is there an
incentive to cheat in this market. If the incentive exists, determine the maximum interest rate that
would be needed for a trigger strategy to be credible.
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