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 = 250 - 20Q, where P is the price (in cents per bottle) and Q is the quantity demanded (in hundreds of bottles).

(i) Suppose the two firms form a successful cartel. How much bottled water will the firms produce, and what price will they charge?
(ii) 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?
(iii) 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?

(i) When demand is linear, marginal revenue has the same vertical intercept and double the slope, so the formula for marginal revenue is MR = 250 - 40Q. Solving the equation MR = MC shows that Q = 6. Substituting this value into the demand formula shows P = 130. Thus each firm produces 300 bottles, and the cartel charges a price of $1.30 per bottle.
(ii) The result of a Bertrand oligopoly is the same as the competitive equilibrium. Solving the equation P = MC shows that Q = 12 and P = 10. Thus each firm produces 600 bottles and charges a price of 10¢ per bottle.
(iii) When there are two firms, the Cournot equilibrium quantity is two-thirds of the competitive quantity, so Q = 8 and P = 90. Thus each firm produces 400 bottles and charges a price of 90¢ per bottle.