BUSS 230 Homework Solution, Spring 2012

BUSS 230: Managerial Economics Spring 2011-2012 Assignment 3 Solution Question 1 (8 points) a) Therefore output Q = 10. b) Calculate the firm’s total profit at the above determined price and output levels c) If the fixed cost increased to 1200, the MC doesn’t change and therefore the optimal Q and P won’t change. However, the TP will decrease by 200 and thus the TP will be equal to 50 dollars. Page 2 of 16 d) New firms can enter the market, which is likely if firms are earning a positive economic profit in the short-run. New firms will be attracted by these profit opportunities and will choose to enter the market. The entry of new firms leads to an increase in the supply of differentiated products, which causes the firm's market demand curve to shift to the left. As more firms enter the market, the firm’s demand curve will continue shifting to the left until it is just tangent to the average total cost curve at the profit maximizing level of output . At this point, the firm's economic profits are zero, and there is no longer any incentive for new firms to enter the market. Thus, in the long-run, the competition brought about by the entry of new firms will cause each firm in a monopolistically competitive market to earn normal profits, just like a perfectly competitive firm. Question 2 (6 points) Firm 2 Advertize Don’t Advertize Firm 1 Advertize 5 , 3 6, 5 Don’t Advertize 4,5 2,3 a) Firm 1 has a dominant strategy which is to advertize Firm 2 doesn’t have a dominant strategy. Page 3 of 16 b) The Nash Equilibrium is for Firm 1 to advertize and for Firm 2 to not advertize. Therefore, Firms 1 and 2’s profits will be 6 and 5 respectively. c) No it is not a prisoners’ dilemma as both firms are better off using the strategy which is for Firm 1 to advertize and Firm 2 to not advertize. Question 3 (12 points) Assume “Crystal Picture Film” company operates in a perfectly competitive market for movie production. a) The demand faced “Crystal Picture Film” is D = MR = P = $8 since the company operates in a perfectly competitive market. Page 4 of 16 b) The market price of a movie P = $8. c) The supply of “Crystal Picture Film” is the part of MC curve that is above the shut down point. d) The breakeven point for “Crystal Picture Film” is where MC intersects ATC at Q=200. e) The shutdown point for “Crystal Picture Film” is where MC intersects AVC at Q=160. f) Profit is maximum where MR = MC at Q=200. From the figure, “Crystal Picture Film” is breaking even. Therefore, short-run economic profit is zero. “Crystal Picture Film” will operate in the short-run to minimize its losses since P > AVC. Question 4 (12 points) a) so b) so c) d) Profit maximized when so Q = 110 at Page 5 of 16 Total profit: e) so Q =110, same result as in the profit maximizing method. f) The assumed market structure in this problem is that of a perfect competition. Question 5 (8 points) a) Ocida is a monopoly, so profit is maximized when MR = MC. so so Q =47 and P=$1.43 Total profit : . b) Ocida and Lorca form an equal market-sharing cartel. Demand faced by each firm = half the market demand so or For Ocida MR’ = MC1, so Page 6 of 16 Solving for Q1 yields a value of 28.85. Substitute in yields P1=$1.08. Total profit = .2 Similarly for Lorca, MR’ = MC2 Solving for Q2 yields a value of 0.69 and a corresponding value for P of $2.954. Total profit = (a loss). Lorca has therefore no incentive to enter the market. c) To maximize profit, set so so Therefore, hence Setting Solving for Q yields 54. Substituting Q in the demand equation, we obtain a market price of $1.20. Plugging the value of Q into the equation of MR gives us a value of: Page 7 of 16 For Ocida: so therefore . For Lorca: so therefore . d) Lorca will do better in the second market. Question 6 (8 points) a) b) Page 8 of 16 c) Solving the two equations simultaneously yields: QF= 164.67 & QC = 166.67 d) Question 7 (10 points) a) b) Since Firm 2 has a higher leverage, we would expect its breakeven point to be higher because of higher overheard costs. c) Page 9 of 16 d) Since Firm 2 has a higher operating leverage, its degree of operating leverage would be larger. e) Q = 7 is closer to the breakeven point than Q =8. Question 8 (8 points) Payoff Matrix 400 300 400 (20,20) (10,60) 300 (60,10) (15,15) a) If Hallmart charges $400, Bullseye will charge $300 If Hallmart charges $300, Bullseye will charge $300 Therefore, Bullseyes optimal strategy is to charge $300 If Bullseye charges $400, Hallmart will charge $300 If Bullseye charges $300, Hallmart will charge $300 Therefore, Hallmarts optimal strategy is to charge $300. b) The Nash Equilibrium is where each store charges $300. c) As shown in Part (a), the dominant strategy for each store is to charge a price of $300. Page 10 of 16 d) Although each store will follow its dominant strategy and set a price of $300, they would each do better by cooperating and charging a price of $400. One of the problems that might arise is that one of the stores might cheat and lower its price to gain a higher payoff. Question 9 (16 points) From the demand function: or Obtain the marginal revenue function The marginal cost for the two firms in this industry is: Rewrite the marginal cost functions: Therefore or Also, the total cost functions can be obtained by integrating the marginal cost functions without a constant since the fixed cost is equal to zero. so so Page 11 of 16 a) As can be seen from the figure below, the optimal production for the cartel is 70 units. This is obtained at the intersection of the marginal revenue (MR) and the marginal cost (MC) curves. Solving the equation yields Q =70 (as can be seen in the graph). At Q = 70, And Setting MC1 = MR = 12, Solving this equation yields Q1 = 56. Similarly, setting MC2 = MR = 12, 0 5 10 15 20 25 30 35 40 45 0 20 40 60 80 100 120 140 160 180 200 D MR SMC Page 12 of 16 Solving this equation yields Q2 = 14. ( ) b) Per unit profits for firm 1 = Total profits for firm 1 = 0 2 4 6 8 10 12 14 16 18 20 0 10 20 30 40 50 60 70 80 90 100 MC1 ATC1 MR 0 2 4 6 8 10 12 14 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 MC2 ATC2 MR Page 13 of 16 Per unit profits for firm 2 = Total profits for firm 2 = c) The market demand function is . The half-share market faced by each duopolist is then or . . Setting And Setting And Total output of the industry = . d) Profit for firm 1 = Page 14 of 16 Profit for firm 2 = Question 10 (12 points) a) so so Horizontal summation of and gives: Page 15 of 16 b) Setting Solving the equation yields a value of QL= 40. Plugging QL = 40 into the leader’s demand function gives a price of From the equation for MCF, when the price is $8.50, the followers will produce At price P = $8.50, the total demand is 0 2 4 6 8 10 12 14 16 18 20 22 24 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 DT SMCF MCL DL MRT MRL MCT Page 16 of 16 c) Setting MRT = MCT, we get: Solving the equation yields QT = 54. Plugging this value into the market demand function DT gives us a market price of And a marginal revenue of Setting MCL = MRT, we can solve for QL: Solving the equation yields a value of QL = 36.8, say 37. Setting MCF = MRT, we can solve for QL: Solving the equation yields a value of QF = 17.33, say 17. Verify that QL + QF = QT.