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An option to buy Steps of the game: 1. Bernie and Sarah negotiate two prices, a baseline price po R+, and a price for exercising the option to buy an artwork that Sarah would produce, P. ER 2. Sarah observes the outcome of the negotiation in step 1. Then she chooses a quality level q E R. 3. If they failed to reach an agreement in step 1, then no money changes hands and Sarah keeps the artwork. But if they did manage to reach an agreement,... 4. Bernie observes q and decides whether to exercise his option to buy. If the parties agree in step 1, and then Bernie does exercise his option to buy, then the payoffs are: us = 4/9-Po - Pi us = pi + po-9. If the parties agree in step 1, but then Bernie does not exercise his option to buy, then Bernie still has to pay po, but Sarah now keeps the artwork. The payoffs are: ug = -Po us = Po +2V9-4 If parties do not reach an agreement in step 1, then the payoffs are: ug = 2/9-4 UB=0 Questions a) Draw the game tree b) Is there an environment of full verifiability in this game? Why or why not?@No, quality is not contractible. c) Consider the socially efficient (joint value maximising) outcome. Would Bernie exercise the option to buy the artwork in this outcome? What quality level would Sarah choose in this outcome? Yes he does; q = 4 d) Write down a condition for the contract under which Bernie actually exercise the option (ie, under which it would be sequentially rational for him to do so)? 479 P1 e) What quality level would Sarah choose if she anticipated that Bernie would exercise the option irrespective of quality? max, po + p1- q to get q = 0 f) What quality level would Sarah choose if she anticipated that Bernie would not exercise the option (no matter what the quality was)?Gmax, Po +2/9 - q to get q=1 ECON 339 2 of 3 g) Is there any contract that would implement the socially efficient level of quality? Explain. Bernie would only exercise his option for quality that was at least the socially efficient level when: P = 4/q* = 8 Faced with this level for P, Sarah would get 8 + po - 4 from q = 4, greater than the 2V1 + Po - 1 she would get from q=1. Consequently, she would choose q = 4, and Bernie would exercise his option. However, just because there is a contract that if adopted would implement a socially efficient outcome, doesn't mean that such a contract would actually be adopted. The question of whether it would be is addressed in the following question. h) Irrespective of you answer to the previous question, now assume that it is possible to implement the socially efficient outcome by setting Pi appropriately. Under this assumption, what value of po + Pi would the two parties agree on in step 1?@The GfT are 1/4 - 4 - 2V1 - 1] = 3. Consequently, ug = po + P1 - 4 = 1+0.5 x 3 Po + P1 = 4+1+ 3 = 6.5 2 Note that this is inconsistent with Pi = 8, Po 20. ************* ************** ECON 339 3 of 3 An option to buy Steps of the game: 1. Bernie and Sarah negotiate two prices, a baseline price po R+, and a price for exercising the option to buy an artwork that Sarah would produce, P. ER 2. Sarah observes the outcome of the negotiation in step 1. Then she chooses a quality level q E R. 3. If they failed to reach an agreement in step 1, then no money changes hands and Sarah keeps the artwork. But if they did manage to reach an agreement,... 4. Bernie observes q and decides whether to exercise his option to buy. If the parties agree in step 1, and then Bernie does exercise his option to buy, then the payoffs are: us = 4/9-Po - Pi us = pi + po-9. If the parties agree in step 1, but then Bernie does not exercise his option to buy, then Bernie still has to pay po, but Sarah now keeps the artwork. The payoffs are: ug = -Po us = Po +2V9-4 If parties do not reach an agreement in step 1, then the payoffs are: ug = 2/9-4 UB=0 Questions a) Draw the game tree b) Is there an environment of full verifiability in this game? Why or why not?@No, quality is not contractible. c) Consider the socially efficient (joint value maximising) outcome. Would Bernie exercise the option to buy the artwork in this outcome? What quality level would Sarah choose in this outcome? Yes he does; q = 4 d) Write down a condition for the contract under which Bernie actually exercise the option (ie, under which it would be sequentially rational for him to do so)? 479 P1 e) What quality level would Sarah choose if she anticipated that Bernie would exercise the option irrespective of quality? max, po + p1- q to get q = 0 f) What quality level would Sarah choose if she anticipated that Bernie would not exercise the option (no matter what the quality was)?Gmax, Po +2/9 - q to get q=1 ECON 339 2 of 3 g) Is there any contract that would implement the socially efficient level of quality? Explain. Bernie would only exercise his option for quality that was at least the socially efficient level when: P = 4/q* = 8 Faced with this level for P, Sarah would get 8 + po - 4 from q = 4, greater than the 2V1 + Po - 1 she would get from q=1. Consequently, she would choose q = 4, and Bernie would exercise his option. However, just because there is a contract that if adopted would implement a socially efficient outcome, doesn't mean that such a contract would actually be adopted. The question of whether it would be is addressed in the following question. h) Irrespective of you answer to the previous question, now assume that it is possible to implement the socially efficient outcome by setting Pi appropriately. Under this assumption, what value of po + Pi would the two parties agree on in step 1?@The GfT are 1/4 - 4 - 2V1 - 1] = 3. Consequently, ug = po + P1 - 4 = 1+0.5 x 3 Po + P1 = 4+1+ 3 = 6.5 2 Note that this is inconsistent with Pi = 8, Po 20. ************* ************** ECON 339 3 of 3