Part 1: In Seandinavia, the annual inverse demand for midrange consumer drones is given by: P=1,0001001Q where Q is the number of drones demanded, in drones per year, and P is the price of a drone, in (euro). Drogon. Ine is a monopoly seller of drones in Seandinavia. 1. Assume first that Drogon, Inc has a fixed cost of 2 million per year and constant marginal cost of 400 so that its total cost of producing and selling drones is: TC1=2,000,000+400qm where YDI is the number of drones produced and sold by Drogon, Inc, in drones per year, and TC1 is its tolal cost, in per year. For this monopoly case, calculate: Q1M the number of drones; P1M the price of a drone; and 1M, Drogon, Inc's profit, in per year. 2. Drogon, Inc considers investing in a new production technology and building a fully automated plant that would allow it to produce and sell drones at zero marginal cost. Its fixed cost, however, would jump to 20 million per year so that its total cost would be: TC2=20,000,000 Consider the case where Drogon decides to invest. For this new technology monopoly case, calculate: Q2M the number of drones produced; P2M the price of a drone; and 2M, Drogon, Inc' profit. 3. Will Drogon, Ine invest in the new production technology as in question 2 above, or will it continue using its old lechnology, as in question 1 abowe? Explain your answer. Part 2: Now assume that a British drone manufacturer Rhaegal, Inc considers entering the Scandinavian market for midrange consumer drones to compete with Drogon, Inc. Rhaegal, Inc can enter either with the old technology, with total cost TC1, as in question 1 above, or enter with new technology, with total cost TC2, as in question 2 above. 4. Post-entry, the nature of the competition in the duopoly will depend on the marginal costs of the two firms and thus on the technologies they use. a. If both firms use the same technology and have the same marginal costs, they will collude, charge the monopoly price, and split the output equally. What will be the price of a drone in the new-tech collusion case (when both firms use the new technology), P2Coll, and in the old-tech collusion case (when both firms use the old technology), P1Coll ? Calculate the outpul and the profit of a colluding lirm for the old-lech case (q1Coll;1Coll) and the new-lech case (q2Coll;2Coll). Hint: note that in the duopoly colusion case each firm bears its fixed cost separately b. If one firm uses the new technology and the other uses the old technology, collusion will be impossible, and the firms will engage in Bertrand competition with identical goods. For this case of Bertrand competition, calculate: PB the price of a drone; qoldB and qnewB the number of drones produced by the old-tech firm and the new-tech firm; oldH and 1iewB profits of the two firms. 5. Now assume that Drogon, Inc and Rhaegal, Ine play a secuential game. First, Drogon, Inc decides whether to use the new technology or the old technology. Next, Rhacgal, Ine learns about l)rogon, Inc's decision and makes one of three decisions: enter the market with the highcost technology; enter with the low-cost technology; do not enter the market. Note that you have already calculated the payoffs to the firms if Rhaegal, Inc enters in question 4a and 4b above. If Rhaegal, Ine does not enter, it gets zero payoff, while Drogon, Ine remains the sole seller of drones and you have already found its payoffis in questions 1 and 2 above. (a) Draw the tree of the game, depicting all nodes (firms' decision-making points); all decisions available at each node to the firm; and firms' payoffs for all possible outcomes. (b) Use backward induction to solve for the Nash equilibrium in this sequential game. Explain firms' decisions at each node of the tree. Will Rhaegel, Inc enter the market? (c) What is the effect of competition on the choice of technology by Dragon and the market price? To answer this question, compare the outcome of the game as in 5 (b) to the monopoly outcome as in 3 . Part 1: In Seandinavia, the annual inverse demand for midrange consumer drones is given by: P=1,0001001Q where Q is the number of drones demanded, in drones per year, and P is the price of a drone, in (euro). Drogon. Ine is a monopoly seller of drones in Seandinavia. 1. Assume first that Drogon, Inc has a fixed cost of 2 million per year and constant marginal cost of 400 so that its total cost of producing and selling drones is: TC1=2,000,000+400qm where YDI is the number of drones produced and sold by Drogon, Inc, in drones per year, and TC1 is its tolal cost, in per year. For this monopoly case, calculate: Q1M the number of drones; P1M the price of a drone; and 1M, Drogon, Inc's profit, in per year. 2. Drogon, Inc considers investing in a new production technology and building a fully automated plant that would allow it to produce and sell drones at zero marginal cost. Its fixed cost, however, would jump to 20 million per year so that its total cost would be: TC2=20,000,000 Consider the case where Drogon decides to invest. For this new technology monopoly case, calculate: Q2M the number of drones produced; P2M the price of a drone; and 2M, Drogon, Inc' profit. 3. Will Drogon, Ine invest in the new production technology as in question 2 above, or will it continue using its old lechnology, as in question 1 abowe? Explain your answer. Part 2: Now assume that a British drone manufacturer Rhaegal, Inc considers entering the Scandinavian market for midrange consumer drones to compete with Drogon, Inc. Rhaegal, Inc can enter either with the old technology, with total cost TC1, as in question 1 above, or enter with new technology, with total cost TC2, as in question 2 above. 4. Post-entry, the nature of the competition in the duopoly will depend on the marginal costs of the two firms and thus on the technologies they use. a. If both firms use the same technology and have the same marginal costs, they will collude, charge the monopoly price, and split the output equally. What will be the price of a drone in the new-tech collusion case (when both firms use the new technology), P2Coll, and in the old-tech collusion case (when both firms use the old technology), P1Coll ? Calculate the outpul and the profit of a colluding lirm for the old-lech case (q1Coll;1Coll) and the new-lech case (q2Coll;2Coll). Hint: note that in the duopoly colusion case each firm bears its fixed cost separately b. If one firm uses the new technology and the other uses the old technology, collusion will be impossible, and the firms will engage in Bertrand competition with identical goods. For this case of Bertrand competition, calculate: PB the price of a drone; qoldB and qnewB the number of drones produced by the old-tech firm and the new-tech firm; oldH and 1iewB profits of the two firms. 5. Now assume that Drogon, Inc and Rhaegal, Ine play a secuential game. First, Drogon, Inc decides whether to use the new technology or the old technology. Next, Rhacgal, Ine learns about l)rogon, Inc's decision and makes one of three decisions: enter the market with the highcost technology; enter with the low-cost technology; do not enter the market. Note that you have already calculated the payoffs to the firms if Rhaegal, Inc enters in question 4a and 4b above. If Rhaegal, Ine does not enter, it gets zero payoff, while Drogon, Ine remains the sole seller of drones and you have already found its payoffis in questions 1 and 2 above. (a) Draw the tree of the game, depicting all nodes (firms' decision-making points); all decisions available at each node to the firm; and firms' payoffs for all possible outcomes. (b) Use backward induction to solve for the Nash equilibrium in this sequential game. Explain firms' decisions at each node of the tree. Will Rhaegel, Inc enter the market? (c) What is the effect of competition on the choice of technology by Dragon and the market price? To answer this question, compare the outcome of the game as in 5 (b) to the monopoly outcome as in 3
