Consider a story of Uber and Lyft in the pandemic. Beleaguered by substantial declines in revenue from their flagship rideshare services, the companies realize that the market is no longer large enough for both to remain viable (given their current cost functions). For concreteness, suppose that Lyft exits the market in Boston, leaving Uber as the effective monopolist.

a) Suppose Uber's cost function is given by C(Q)=49+ Q², and it faces a market demand given by Q = 360 4p. Find the price and quantity Uber chooses if it exercises its monopoly power.

b) Represent this equilibrium in a graph. Calculate the deadweight loss in this market, and clearly draw it on your graph.

c) A regulator wants to put a price cap on the price of rides Uber can charge. What price cap (if feasible) would they set to maximize welfare? What is Uber's profit (or loss) at this price? Conclude whether or not the strategy is feasible (assuming the regulator has enough information to accurately determine the optimal price cap).

d) Repeat your analysis from part c), this time assuming that Uber's cost function is given by C(Q) = 200 + 40Q.

e) Suppose that Lyft is able to overhaul its operations, and re-enters the market with a marginal cost of MC = 80. Assume as well that Uber has a marginal cost of MC = 40 and overall market demand is unchanged at Q = 360 4p. Calculate the Cournot equilibrium, including Uber's quantity q_U, Lyft's quantity q_L, and market price p. (Note: Fixed costs do not play a role in this analysis.)