tutorial 12 - wednesday - july 16, 2014 - 4pm - 5pm
TUTORIAL 12 - WEDNESDAY - JULY 16, 2014 - 4PM - 5PM
QUESTION 12.2 – pp. 445 – 446 Suppose demand is Q = 10,000 – 1,000P and marginal cost is constant at MC = 6. From the given demand curve, one can compute the following marginal revenue curve: MR = 10 - 500/Q (a) Graph the demand, marginal cost, and marginal revenue curves. (b) Calculate the price and quantity associated with point C, the perfectly competitive outcome. Compute industry profit, consumer surplus, and social welfare. (c) Calculate the price and quantity associated with point M, the monopoly or perfect cartel outcome. Compute industry profit, consumer surplus, social welfare and deadweight loss. (d) Calculate the price and quantity associated with point A, a hypothetical imperfectly competitive outcome, assuming that it lies at a price halfway between C and M. Compute industry profit, consumer surplus, social welfare and deadweight loss. QUESTION 12.4 – p. 446 Consider the model of Bertrand competition with differentiated products. Let the demand curves for firms A and B be given by qA = (1/2) – pA + pB qB = (1/2) – pB + pA Let the firms marginal costs be constant, given by cA and cB. It can be shown that the best response function for firm A is pA = (1/4)(1 + 2pB + cA) and for firm B is pB = (1/4)(1 + 2pA + cB)
(a) Graph the two best-response functions. Find the Nash equilibrium assuming cA = cB = 0 algebraically and indicate it on a graph.
(b) Indicate on the graph how an increase in cB would shift the best–response functions and change the equilibrium.
Page 2 (c) Indicate on the graph where the analogue to the Stackelberg equilibrium might be, with firm A choosing price first and then firm B. Is it better to be the first or the second mover when firms choose prices? QUESTION 12.8 – p. 447 Consider a two-period model with two firms, A and B. In the first period, they simultaneously choose one of two actions, ENTER or DO NOT ENTER. Entry requires the expenditure of a fixed cost of 10. In the second period, whichever firm enter play a pricing game as follows. If no firm enters, the pricing game is trivial and profits are zero. If only one firm enters, it earns the monopoly profit of 30. If both firms enter, they engage in competition as in the Bertrand model with homogeneous products. (a) Using backward induction, fold the game back to the first period in which firms make their choice of ENTER or DO NOT ENTER. Write down the normal form for this game. (b) OMIT (c) OMIT
QUESTION 12.2 – pp. 445 – 446 Suppose demand is Q = 10,000 – 1,000P and marginal cost is constant at MC = 6. From the given demand curve, one can compute the following marginal revenue curve: MR = 10 - 500/Q (a) Graph the demand, marginal cost, and marginal revenue curves. (b) Calculate the price and quantity associated with point C, the perfectly competitive outcome. Compute industry profit, consumer surplus, and social welfare. (c) Calculate the price and quantity associated with point M, the monopoly or perfect cartel outcome. Compute industry profit, consumer surplus, social welfare and deadweight loss. (d) Calculate the price and quantity associated with point A, a hypothetical imperfectly competitive outcome, assuming that it lies at a price halfway between C and M. Compute industry profit, consumer surplus, social welfare and deadweight loss. QUESTION 12.4 – p. 446 Consider the model of Bertrand competition with differentiated products. Let the demand curves for firms A and B be given by qA = (1/2) – pA + pB qB = (1/2) – pB + pA Let the firms marginal costs be constant, given by cA and cB. It can be shown that the best response function for firm A is pA = (1/4)(1 + 2pB + cA) and for firm B is pB = (1/4)(1 + 2pA + cB)
(a) Graph the two best-response functions. Find the Nash equilibrium assuming cA = cB = 0 algebraically and indicate it on a graph.
(b) Indicate on the graph how an increase in cB would shift the best–response functions and change the equilibrium.
Page 2 (c) Indicate on the graph where the analogue to the Stackelberg equilibrium might be, with firm A choosing price first and then firm B. Is it better to be the first or the second mover when firms choose prices? QUESTION 12.8 – p. 447 Consider a two-period model with two firms, A and B. In the first period, they simultaneously choose one of two actions, ENTER or DO NOT ENTER. Entry requires the expenditure of a fixed cost of 10. In the second period, whichever firm enter play a pricing game as follows. If no firm enters, the pricing game is trivial and profits are zero. If only one firm enters, it earns the monopoly profit of 30. If both firms enter, they engage in competition as in the Bertrand model with homogeneous products. (a) Using backward induction, fold the game back to the first period in which firms make their choice of ENTER or DO NOT ENTER. Write down the normal form for this game. (b) OMIT (c) OMIT
