91Ó°ÊÓ

Suppose firms \(A\) and \(B\) operate under conditions of constant average and marginal cost, but that \(M C_{A}=10, M C_{B}=8 .\) The demand for the firms' output is given by \\[Q_{D}=500-20 P.\\] a. If the firms practice Bertrand competition, what will be the market price under a Nash equilibrium? b. What will the profits be for each firm? c. Will this equilibrium be Pareto efficient?

Suppose the two firms in a duopoly pursue Cournot competition as described in Equation 19.10. Suppose each firm operates under conditions of increasing marginal cost but that firm \(A\) has a larger scale of operations than does firm \(B\) in the sense that \(M C_{A} < M C_{B}\) for any given output level. In a Nash equilibrium, will marginal cost necessarily be equalized across the two firms? Will total output be produced as cheaply as possible?

The Wave Energy Technology (WET) company has a monopoly on the production of vibratory waterbeds. Demand for these beds is relatively inelastic- at a price of \(\$ 1,000\) per bed, 25,000 will be sold, whereas at a price of \(\$ 600,30,000\) will be sold. The only costs associated with waterbed production are the initial costs of building a plant. WET has already invested in a plant capable of producing up to 25,000 beds, and this sunk cost is irrelevant to its pricing decisions. a. Suppose a would-be entrant to this industry could always be assured of half the market but would have to invest \(\$ 10\) million in a plant. Construct the payoff matrix for WET's strategies \((P=1,000 \text { or } P=600)\) against the entrant's strategies (enter, don't enter). Does this game have a Nash equilibrium? b. Suppose WET could invest \(\$ 5\) million in enlarging its existing plant to produce 40,000 beds. Would this strategy be a profitable way to deter entry by its rival?