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). (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?