Chapter 15 Two firms are engaged in Bertrand competition. There are 30,000 peopl
ID: 1125234 • Letter: C
Question
Chapter 15 Two firms are engaged in Bertrand competition. There are 30,000 people in the population, each of whom is willing to pay at most 20 for at most one unit of the good. Currently, both firms have a constant marginal cost of 8. a. What is the equilibrium in this market? What are the firms' profits? b. Suppose that one firm can adopt a new technology that lowers its marginal cost to 3. What is the equilibrium now? How much would this firm be willing to pay for this new technology? Suppose the new technology mentioned in (b) is available to both firms. The cost to a firm of purchasing this technology is 40,000. The game is now played in two stages. First, the firms simultaneously decide whether to adopt the nevw technology or not. Then, in the second stage, the firms set prices simultaneously. Assume that each firm knows whether or not its rival acquired the new technology when choosing its prices. What is (are) the Nash equilibrium (equilibria) of this game? (What does your answer suggest about why firms c. engage in patent races?) Why is innovation so important from a macroeconomic point of view? What policies can - Dives long- run gowth incentives for R.D countries implement to encourage more innovation? t policies n captal accumulaton t OVExplanation / Answer
(a) What is the equilibrium in this market? What are the firms’ profits?
Answer: The firms will charge p = 8 and earn profit= 0.
(b) Suppose that one firm can adopt a new technology that lowers its marginal cost to 3. What is the equilibrium now? How much would this firm be willing to pay for this new technology?
Answer: The firm with the lower cost technology charges a fraction of a cent less than p = 8 and sells to all 30,000 customers. Its profits are = [(8- 3) * 30, 000] = 150, 000. It would be willing to pay up to 150,000 for this technology.
(c) Suppose the new technology mentioned in (b) is available to both firms. The cost to a firm of purchasing this technology is 40,000. The game is now played in two stages. First, the firms simultaneously decide whether to adopt the new technology or not. Then, in the second stage, firms set prices simultaneously. Assume that each firm knows whether or not its rival acquired the new technology when choosing its prices. What is (are) the Nash equilibrium (equilibria) of this game?
Answer: There are two pure-strategy equilibria: (1) firm 1 invests in the low-cost technology and firm 2 does not, and (2) firm 2 invests in the low-cost technology and firm 1 does not. It is not an equilibrium for both firms to invest or for neither firm to invest. (There is also a mixed strategy equilibrium in which each firm invests with probability 0.5.)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.