Suppose that the (inverse) market demand for mineral water can be expressed as:

P = 3,800 - 2Q;

where Q is in thousands of bottles per year and P is in dollars per thousand bottles. Furthermore, suppose that the marginal cost of production for mineral water is MC = $200 per thousand bottles; and that fixed costs are FC = $0.

a)What are the profit-maximizing price and output levels for a monopolist in this market? What is the monopolist's profit? (3 + 1 marks)

b)Suppose that there are two firms - Firm A and Firm B - in this market, with inverse demand P = 3,800 - 2(Q_A + Q_B). Both firms have the same marginal cost MC = $200 per thousand bottles, and zero fixed costs. What level of output would be produced by each firm in a Cournot duopoly (i.e. when firms play simultaneously), and what would the price be? What would the firms' profits be? (4 + 1 marks)

c)Suppose now that as in part b) there are two firms - Firm A and Firm B - in this market, with inverse demand P = 3,800 - 2(Q_A + Q_B). What level of output would be produced by each firm in a Stackelberg duopoly (i.e. when firms play sequentially) with Firm A committing to an output choice first; and what would the price be? What would firms' profits be, and how would these compare to part b)? Briefly explain. (4 + 2 + 1 marks)