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?

Given the information that 25,000 beds will be sold at a price of \(\$1,000\) and 30,000 will be sold at a price of \(\$600\), we can find the linear demand function using the point-slope form: Price = m (Quantity) + b Plug in price and quantity for the two points: \(\$1,000\) = m\((25,000)\) + b (1) \(\$600\) = m\((30,000)\) + b (2) Subtracting equation (1) from equation (2): \(-\$400\) = m\((5,000)\)

Solving for b: b = \(\$3,000\) Now we have our demand function: Price (P) = -0.08 (Quantity) + \(\$3,000\)

Using the demand function, we can find the quantity demanded at prices \(\$1,000\) and \(\$600\): At P = \(\$1,000\) -> Q1 = 25,000 (given) At P = \(\$600\) -> Q2 = 30,000 (given) Calculate WET's revenue for each scenario: R1 = Q1 * P1 = 25,000 * \(\$1,000\) = \(\$25,000,000\) R2 = Q2 * P2 = 30,000 * \(\$600\) = \(\$18,000,000\)

We need to construct a 2x2 matrix (WET's strategies x Entrant's strategies). Payoffs will be represented as [WET, Entrant]: Entrant ------------ | Enter | Don't Enter | WET |-----------------| P1 | [25M, 10M] | [25M, 0] | |-----------------| P2 | [18M, 10M] | [18M, 0] | --------------- Analyzing the matrix, Entrant prefers to enter if WET charges P1, as 10M>0 and not to enter if WET charges P2, as 0>10M causing a loss. There is no Nash Equilibrium because, if one company chooses a strategy, the other can change its strategy accordingly and get better payoffs.

WET considers investing \(\$5\) million to enlarge the plant, assuming they'll be able to produce 40,000 beds in total. If WET enlarges the plant, they can supply the whole market demand if the Entrant decides to enter. So the payoffs change in that case. New payoff matrix: Entrant ------------ | Enter | Don't Enter | WET |-----------------| P1 | [25M-5M, 10M] | [25M-5M, 0]| |-----------------| P2 | [18M-5M, 10M] | [18M-5M, 0]| --------------- If WET enlarges the plant, their profit is reduced to 20M and 13M, respectively. The Entrant wouldn't enter the market in any of the scenarios, so there would be no additional competition for WET. However, it is important to notice that it would be better if WET kept charging P1 without investing in enlargement (25M > 20M or 13M). Taking into account the payoff matrix and considering the potential entrant's actions, it would not be profitable for WET to invest in enlarging its plant to deter entry in this situation.