Week 4 extra questions
1. A firm buying an input that costs $p knows that 4/5 of suppliers will provide a good input that the firm values at $100 and 1/5 of suppliers will provide a low quantity input that the firm only values at $60. The firm is matched with a potential input supplier in the market, but cannot tell whether it will supply a good or low quality product. At this point, the firm can opt to use a legal contract, at a cost of c that ensures the supply of a good input by all firms (given the threat of large fines following legal action) or it can opt not to use any contract. Without a legal contract, the firm will get the good input with a probability of 4/5 (and the low quality input with probability 1/5). What is the most the firm is willing to pay to use the legal contract?
a. 8 b. 10 c. 12 d. 16 e. 20
Consider a firm with a principal/boss (Donna) and an agent/worker (Angus). The firm needs to implement a decision regarding a new project, but there is some uncertainty about exactly what to do with the project. To find out more information, Angus can first expend either low (L) or high effort (H) in order to learn more about the project. If he put in Low effort, the game is over and the payoffs are $20 to Angus and $50 to the boss Donna. If Angus puts in High effort, Donna observes this and can then either Centralize the decision making (C) or opt to Delegate (D). Following High effort, if Donna opts to Centralize, the payoffs are $10 to Angus and $60 to Donna herself. If on the other hand Donna chooses to Delegate after having observed Angus put in High effort, the payoffs are $40 to both the boss and the worker.
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a. Draw the game tree of this game. What are the Nash equilibria and solve for all subgame perfect (SPE) equilibria. Explain your answer. (3 marks)
b. Now consider the case when Angus can ¡®buy¡¯ the operation from Donna. If this happens, Donna now has to move first, choosing either Centralize or Decentralize. Having observed Donna¡¯s choice, Angus can choose either Low or High effort. The payoffs are the same as they were in part a following any combination of actions. (For example, the payoffs following Low effort from Angus are always 20 and 50 to himself and Donna respectively. If Donna opted for Centralization and Angus chose High effort, the payoffs are 10 to Angus and 60 to Donna, respectively, and so on.) How much is Angus willing to pay to ¡®buy¡¯ the operation? Explain your answer. (3 marks)
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