Amy and Soma discover a stream that flows with wine. They decide to bottle the wine and sell it. The marginal cost and the fixed cost to bottle wine are 54 and zero, respectively. The market demand for bottled wine is given by: [tex] P = 904 - Q [/tex], where [tex] Q [/tex] is the total quantity of bottled wine produced and [tex] P [/tex] is the market price of bottled wine. Answer the following questions:

a. What are the economically efficient (in other words, perfectly competitive) price and quantity of bottled wine? Show your work. How much will be the profit? (6 points)

b. If Amy and Soma were to collude with one another and produce the profit-maximizing monopoly quantity of bottled wine and share the profit equally, how much bottled wine will each one of them produce? Show your work. At what price? How much profit will each one of them earn? (8 points)

c. Suppose that Amy and Soma act as Cournot duopolists. How much bottled wine will each one of them produce? Show your work. At what price? How much profit will each one of them earn? (14 points)

d. Suppose Soma is a naive Cournot duopolist, allowing Amy to act as a Stackelberg leader. What level of output will each one of them produce? Show your work. What will be the price of wine? How much profit will each one of them earn? (16 points)