Two identical firms have access to a spring. Their marginal cost of bottling wat

Question

Two identical firms have access to a spring. Their marginal cost of bottling water from the spring is a constant 10¢ per bottle. The market demand for bottled spring water is P = 25020Q, where P is the price (in cents per bottle) and Q is the quantity demanded (in hundreds of bottles).

a) Suppose the two firms form a successful cartel (i.e., they will act as a monopoly and share the resulting profits). How much bottled water will the firms produce, and what price will they charge?

b) Suppose the firms behave as in the Bertrand model of oligopoly. How much bottled water will the firms produce, and what price will they charge?

c) Suppose the firms behave as in the Cournot model of oligopoly. How much bottled water will the firms produce, and what price will they charge?

d) ) Comment on your findings – what does each model in parts (a), (b), and (c) imply and is it consistent with what we observe?

Explanation / Answer

a.)

They form a cartel and behave as a monopoly. Let them produce a total quantity q.

Profit = (250 - 20q)q - 10q

Maximizing profit with respect to q, we differentiate with respect to q

MR=MC

250 - 40q = 10

q = 6 (hundred)

P = 250 - 20*6 = 130 cents

b.) Now bertrand model. Both the firms compete on price. The firms will set a price equal to marginal cost. As there marginal cost is constant, if a firm sets price higher than MC, than the other firm can undercut it by a very small amount and service the whole. As the Marginal cost is same for both the firms, they will behave as a perfectly competitve market such that P = MC

250 - 20Q = 10

Q = 12

Each firm will produce 6 thousand and total production will be 12.

The resultant price would be 10 cents

c.) Cournot model

Let firm 1 produce q1 and firm 2 produce q2

Firm 1

Profit1 = (250 - 20(q1+q2))q1 - 10q1

Differentiating with respect to q1 to get profit maximizing condition

250 - 40q1 - 20q2 - 10 = 0 (1)

Firm 2

Profit2 = (250 - 20(q1+q2))q2 - 10q2

Differentiating with respect to q2 to get profit maximizing condition

250 - 40q2 - 20q1 - 10 = 0 (2)

q2 = 6 - q1 / 2

Subsituting q2 in (1), we get

250 - 40q1 - 20(6 - q1 / 2) - 10 = 0

120 - 40q1 + 10q1

q1 = 4

q2 = 4

Total Quantity = 8

Price = 250 - 20*8 = 90 cents

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.