Amy and Soma discover a stream that flows wine. Amy and Soma decide to bottle th

Question

Amy and Soma discover a stream that flows wine. Amy and Soma decide to bottle the wine and sell it. The marginal cost and the fixed cost to bottle wine are $4 and zero respectively. The market demand for bottled wine is given by: P = 100 - 0.5Q, where Q is the total quantity of bottled wine produced and P 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?

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?

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

Explanation / Answer

a. In case perfect competition,

Equilibrium is attained, When P = MC

100 - 0.5Q = 4

Q = 96/0.5 = 192

P = 100 - 0.5*192 = 4

Profit = 0

b. In case they collude , then they will act like a monopoly , and produce till MR = MC

TR = P*Q = (100 - 0.5Q)Q

MR = dTR/dQ = 100 - Q

Putting , MR = MC

100 - Q = 4

Q = 96

Price = 100 - 0.5*96 = 52

Quantity of Amy = Quantity of Soma = Q/2 = 96/2 = 48

Profit of Amy = profit of soma = 52*48 - 4*48 = 2304

C. In case Cournot

QA + QS = Q where QA and Qs are quantity produced by Amy and soma.

Profit function for Amy

PA = TR - TC = (100 - 0.5(QA + QS))QA - 4QA

dPA/dQA = 100 - QA - 0.5QS - 4

Putting dPA/dQA = 0

QA = 96 - 0.5QS (reaction function of Amy)

Similarly reaction function of soma

QS = 96 - 0.5QA

Solving these equation for QA and QS

QA = 48*4/3 = 64

QS = 64

Q = QA + QS = 128

P = 100 - 0.5Q = 100 - 0.5*128 = 36

Profit of AMy = 36*64 - 4*64 = 2048

Profit of Soma = 36*64 - 4*64 = 2048

If you don't understand anything then comment, I'ill revert back on the same. :)

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