# Find the equilibrium price and quantity and compute the equilibrium profits.

1. Assume that there are six modes of transportation from Tufts to downtown Boston for people who do not own a car. They have the following market shares: Mode of Transport Market Share MBTA 35% Walk 1% Bike 4% Lyft 20% Uber 30% Taxi 10%a) Lyft and Uber are proposing a merger. Explain how you would go about defining the relevant market for their services?b) Calculate the HHI index for the case in which the relevant market includes Lyft, Uber, Taxis and the MBTA. [Hint: You have to recalculate market shares to be based on the relevant market only.]c) Calculate the HHI index for the case in which the relevant market includes Lyft, Uber and Taxis.d) Compare your results from parts (b) and (c) of this question. Which market is more concentrated and why?2. The large turbine generator industry is a duopoly. The two firms, GE and Westinghouse, compete according to the Cournot model of quantity competition. The demand curve for the industry is P = 200-Q, where P is the price (in $millions) and Q is the total quantity produced by GE and Westinghouse. Currently, each firm has marginal cost of $40 and no fixed costs. Find the equilibrium price and quantity and compute the equilibrium profits.3. The dancing machine industry is a duopoly. The two firms, Chuckie B Corp. and Gene Dancing Machines, compete through Cournot quantity-setting competition. The demand curve for the industry is P = 100 – Q, where Q is the total quantity produced. Chuckie B’s cost function is C1(q1) = (q1) 2 Gene’s cost function is C2(q2) = 20q2a. Derive the best response function for each firm. (Hint: The best response function will show the firm’s optimal quantity as a function of the other firm’s quantity.)b. Use the best response functions from part (a) to calculate each firm’s production quantity in Nash Equilibrium.c. Calculate the market price. d. Calculate each firm’s profit. 4. Consider a market with two horizontally differentiated firms, X and Y. Each has a constant marginal cost of $40. The demand functions are: Qx = 120 – 2Px + 1Py Qy = 120 – 2Py + 1Pxa. Derive the best response function for each firm.b. Use the best response functions from part (a) to calculate each firm’s price in Nash Equilibrium.c. Calculate each firm’s production quantity.d. Calculate each firm’s profit

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