Stanford Energy (SE) and Tree Power (TP) are duopoly firms, each with constant (horizontal) marginal cost of $20 per unit; the total market demand for their product is given by P=200-Q. Note that Q=q_S+q_T, where q_S is the quantity produced by SE and q_T is the quantity produced by TP. Assume (at least initially) that both firms have zero fixed costs.

a. What would be the competitive equilibrium price in this market? If these two firms split the market evenly (each providing half of the demanded output), how much will they each produce? How much will they each earn in profits?

b. What price will these firms charge if they act as a profit-maximizing cartel? How much will they each produce (again assuming that they split the market evenly)? How much will they each earn in profits? Show your work, using what you know about marginal revenue for a single-price monopolist; summarize your answers to parts a & b with a diagram showing the (joint) monopoly and competitive outcomes.

c. Suppose each of these firms can choose to produce 45, 60, or 90 units of output.Construct a payoff matrix similar to those ones shown in class and in the textbook, depicting Stanford Energy's choices in the rows and Tree Power's in the columns; in each cell, include numerical values for SE's profits (first) and TP's profits (second). To ensure partial credit, include evidence of your calculations. Identify and describe the [Cournot] Nash equilibrium, assuming that SE and TP make decisions separately and simultaneously. Is there an outcome in your matrix that is better for both firms?If so, briefly explain why this "better for both" outcome is not a Nash equilibrium.

d. Suppose SE and TP have each been choosing to produce 60 units of output, so that P=80 (since Q=q_S+q_T=120) but they now realize that they are each able to announce a price separately to prospective customers.Since their products are identical, consumers will only buy from whichever firm offers the lower price (so that that firm captures the entire market); if both firms offer the same price, they will split the market equally. If Stanford Energy continues to charge P_S=80, what price would be optimal for Tree Power? [Assume that only integer prices are feasible.] Briefly explain.

e. Following from your reasoning in part d), what is the Nash Equilibrium in the (Bertrand) game in which firms choose prices, not quantities? Briefly explain.

f. Finally, return to the case where firms choose quantities, not prices. Assume again that marginal costs are each a constant $20, but now assume that each firm also has a fixed cost of $4000. SE executives arrange a meeting with regulators in which they argue that in order to avoid duplicative fixed costs it would be efficient for them to supply the entire market themselves (i.e., without competition from TP). Is there merit to their argument? Should Stanford Energy be granted monopoly power in this market, with or without price regulation?