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econ 107 ps1a

# econ 107 ps1a - Economics 107 Suggested Solutions to...

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Economics 107 – Suggested Solutions to Practice Problems for Chapter 5 1 of 4 1. Firms setting prices in unison, dropping or raising more or less at the same time. Such practice might be due to explicit collusion forbidden by the law, but also by implicit collusion, a price leader, or simply supply and demand factors affecting all firms at the same time. The American Tobacco Case in 1946 is an example of the courts suspecting and convicting of collusion because of what looked like pricing parallelism (pp.141-142). 2a. Q M = 600; P M = 600 2b. Q 1 = Q 2 = 400; P = 400 3a. P* = 0 3b. Q* = 360 3c. Q M = 180 3d. P M = 45 3e. DWL = 4050 3f. Q B = 180 – 0.5Q J ; Q J = 180 – 0.5Q B 3g. Q B = 120 3h. P = 30 3i. Q B = 90 4a. Q 1 = 100, Q 2 = 100, P = 50, 1 = 5000, 2 = 5000 4b. Q = 150; P = 75, = 11250 (If the two firms share the market equally, then they will split the total output and total profits equally.) 4c. The market is more efficient when the firms compete (Cournot model) than when they collude (cartel model). The Cournot price is closer to marginal cost than the cartel price. 4d. Q 1 = 150, Q 2 = 75, P = 37.5, 1 = 5625, 2 = 2812.5 4e. The market output is higher in the Stackelberg case than in the Cournot case, and the market price is lower in the Stackelberg case than in the Cournot case. The leader firm increases profits by entering the market first, while the follower firm’s profits fall compared to the Cournot solution. 5a. 01 . 0 r 5b. 25 . 0 r 6a. Assume one firm prices at marginal cost ( MC ), then the other can price below MC and steal all the market but make a loss, or price higher than or equal to MC and make zero profit either way. Clearly, pricing at MC is best response since there is no better one (note that a best response does not have to be unique, i.e., there are many ways to obtain zero profits). This analysis is true for both firms so setting both prices at MC is a best response for both firms to each other and thus a Nash Equilibrium (NE). 6b. There are two cases in which at least one price is not at MC : Case 1: Assume there is a NE in which one firm prices below MC . Then the other firm would price anywhere above and get zero profits (the best it can do). As a result the first firm will lose money so it is not on a best response because it could at least make zero profits by pricing exactly at MC instead of below.

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