You are the Southeastern Michigan regional manager at Coca-Cola, responsible for production and pricing in the Metro Detroit area. Your primary competitor is Pepsi. The market research team at Coca-Cola is thinking about launching a new product, Orange Vanilla Coke, to boost the brand. The cost function to produce a 12-pack of 12 fl. oz. cans of Orange Vanilla Coke is C(qcoke) = 0.25qcoke and the market research team has estimated inverse market demand for a 12-pack of this new "pop" in Southeastern Michigan to be P = 10.25 - 0.00025Q.

a. Assuming Pepsi decides not to produce a similar product, allowing Coca-Cola to maintain monopoly power in the market for orange vanilla cola, what price and quantity will you choose to maximize profit? How much profit does Coca-Cola earn?

b. What price and quantity you would choose to maximize profit if Pepsi spies discover your product before launch, allowing Pepsi to produce and launch an identical product at the same time. For your answer, assume the cost function to produce a 12-pack of 12 fl. oz. cans of Orange Vanilla Pepsi is C(qpepsi) = 0.25qpepsi and Michiganders view Pepsi's product as identical to Coke's. How much profit does Coca-Cola earn?

c. If you can make an unrecoverable fixed investment of $20,000 to bring your product to Michigan's market before Pepsi can finalize their Orange Vanilla Pepsi production plans (e.g., perhaps this "investment" represents the cost to bribe Pepsi spies to delay sharing information Pepsi), should you make this investment? Provide a thorough explanation (hint: explicitly show how your decision affects profits for Coca-Cola).

d. What will be the Cournot equilibrium price and quantity if a third company (e.g., Faygo) enters the orange vanilla cola market?