Topic 7: Arbitrage 3. The stock PolarBear trades on both the South Pole Stock Exchange and the North Pole Stock Exchange. (a) Suppose the price on the North Pole is $18. What does the No-Arbitrage Condition say about the price on the South Pole? (Assume no trading costs.) (b) Suppose the price on the North Pole is $18 and the price on the the South Pole is $17? How can you make an arbitrage profit? (Assume no trading costs.) (c) Suppose that the price on the North Pole is $18, that buying or selling on the North Pole costs $2, and that buying or selling on the South Pole is free. What does the No-Arbitrage Condition say about the price on the South Pole?

1. consider a two-firm industry. firm 1 (the incumbent) chooses a level of output qı. firm 2 (the potential entrant) observes qı and then chooses its level of output q2. the demand for the product is p 100 q, where q is the total output sold by the two firms which equals qi +q2. assume that the marginal cost of each firm is zero. a) find the subgame perfect equilibrium levels of qi and q2 keeping in mind that firm 1 chooses qi first and firm 2 observes qi and chooses its q2. find the profits of the two firms-n1 and t2- in the subgame perfect equilibrium. how do these numbers differ from the cournot equilibrium? b) for what level of qi would firm 2 be deterred from entering? would a rational firm 1 have an incentive to choose this level of qi? which entry condition does this market have: blockaded, deterred, or accommodated? now suppose that firm 2 has to incur a fixed cost of entry, f> 0. c) for what values of f will entry be blockaded? d) find out the entry deterring level of q, denoted by q1', a expression for firm l's profit, when entry is deterred, as a function of f. for what values of f would firm 1 use an entry deterring strategy?