20.6 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 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?