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Unformatted text preview: Answers to practice problems Question 1. Part a) If none of the B’s speak language A, then the payoff for an A to learn language B is $400, since he is able to speak to 400 more people if he learns language A. If none of the A’s speak language B, then the gain to a type B from learning language A is $600. The outcome where nobody learns the other groups language will be a Nash equilibrium only if when nobody knows the other language, nobody finds it worthwhile to do so. This will be the case if C A > $400 and C B > $600. Part b) First we note that it will never be efficient for both groups to learn the other language, since if one group is bilingual, the other group can speak to and understand them. The total cost of making all the A’s bilingual is 600 C A and the total cost of making all the B’s bilingual is 400 C B . Therefore in order for it to be efficient for the A’s to become bilingual, it must be that 600 C A ≤ 400 C B , or equivalently, C A ≤ (2 / 3) C B . If this is the case, it is more efficient to make the A’s bilingual than the B’s. But for it to be efficient for the A’s to become bilingual rather than have nobody become bilingual, it needs to be that total benefits to making the A’s bilingual exceed total costs. Total costs are 600 C A . The total benefits of making the A’s bilingual are 600 × 400+400 × 600 since 600 type A’s each gain $400 from being able to talk to the 400 B’s and since 400 type B’s each gain $600 from being able to talk to the 600 A’s. So benefits exceed costs if 600 × 400 + 400 × 600 > 600 C A . Divide both sides of this inequality by 600 and combine terms and you find $800 > C A . We see that if 600 < C A < C...
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This note was uploaded on 12/25/2011 for the course ECON 100c taught by Professor Bergstrom,t during the Fall '08 term at UCSB.
- Fall '08