Q2. Preferences and utility Let's assume that country A prefers not to make additional concessions (outcome C1) to country B than granting those concessions (outcome C2), but a continued war (outcome C3) would be worse than making the additional concessions (C2). The following utility function over the outcomes specifies the intensity of preferences for country A over the outcomes: u(C1) = 1, u(C2) = 0.3, and u(C3) = 0. Country A can choose to refuse concessions (action A1) or allow concessions (action A2). The outcome that will occur is a function of the "type" of country B's leader. If country A refuses concession (A1), country B will not initiate a war (outcome C1) if country B's leader is amicable, while it will enter a war (outcome C3) if the leader is belligerent. There is a probability p(S1) = 0.6 that country B's leader is amicable and a probability p(S2) = 0.4 that country he's belligerent. If country A allows concession (A2), both in case of country A is amicable p(S1) and belligerent p(s2), outcome (C2) is realized. Q3. What is the expected utility of action A1? EU(A1)=0.30 EU(A1)=0.40 EU(A1)=0.60 EU(A1)=0.70 EU(A1)=0.72 Q2. Preferences and utility Let's assume that country A prefers not to make additional concessions (outcome C1) to country B than granting those concessions (outcome C2), but a continued war (outcome C3) would be worse than making the additional concessions (C2). The following utility function over the outcomes specifies the intensity of preferences for country A over the outcomes: u(C1) = 1, u(C2) = 0.3, and u(C3) = 0. Country A can choose to refuse concessions (action A1) or allow concessions (action A2). The outcome that will occur is a function of the "type" of country B's leader. If country A refuses concession (A1), country B will not initiate a war (outcome C1) if country B's leader is amicable, while it will enter a war (outcome C3) if the leader is belligerent. There is a probability p(S1) = 0.6 that country B's leader is amicable and a probability p(S2) = 0.4 that country he's belligerent. If country A allows concession (A2), both in case of country A is amicable p(S1) and belligerent p(s2), outcome (C2) is realized. Q3. What is the expected utility of action A1? EU(A1)=0.30 EU(A1)=0.40 EU(A1)=0.60 EU(A1)=0.70 EU(A1)=0.72 Q4. What is the expected utility of action A2? EU(A2)=0.30 EU(A2)=0.40 EU(A2)=0.60 EU(A2)=0.70 EU(A2)=0.72 Q5. What action should country A choose? Action A1 Action A2 Q6. What action should country A choose if u(C2) were equal to 0.5 rather than 0.3? Action A1 Action A2 Q7. What action should country A choose if u(C2) were equal to 0.3 but p(S1) were equal to 0.25 (and p(S2) = 0.75)? Action A1 Action A2
Q2. Preferences and utility Let's assume that country A prefers not to make additional concessions (outcome C1) to country B than granting those concessions (outcome C2), but a continued war (outcome C3) would be worse than making the additional concessions (C2). The following utility function over the outcomes specifies the intensity of preferences for country A over the outcomes: u(C1) = 1, u(C2) = 0.3, and u(C3) = 0. Country A can choose to refuse concessions (action A1) or allow concessions (action A2). The outcome that will occur is a function of the "type" of country B's leader. If country A refuses concession (A1), country B will not initiate a war (outcome C1) if country B's leader is amicable, while it will enter a war (outcome C3) if the leader is belligerent. There is a probability p(S1) = 0.6 that country B's leader is amicable and a probability p(S2) = 0.4 that country he's belligerent. If country A allows concession (A2), both in case of country A is amicable p(S1) and belligerent p(s2), outcome (C2) is realized. Q3. What is the expected utility of action A1? EU(A1)=0.30 EU(A1)=0.40 EU(A1)=0.60 EU(A1)=0.70 EU(A1)=0.72 Q2. Preferences and utility Let's assume that country A prefers not to make additional concessions (outcome C1) to country B than granting those concessions (outcome C2), but a continued war (outcome C3) would be worse than making the additional concessions (C2). The following utility function over the outcomes specifies the intensity of preferences for country A over the outcomes: u(C1) = 1, u(C2) = 0.3, and u(C3) = 0. Country A can choose to refuse concessions (action A1) or allow concessions (action A2). The outcome that will occur is a function of the "type" of country B's leader. If country A refuses concession (A1), country B will not initiate a war (outcome C1) if country B's leader is amicable, while it will enter a war (outcome C3) if the leader is belligerent. There is a probability p(S1) = 0.6 that country B's leader is amicable and a probability p(S2) = 0.4 that country he's belligerent. If country A allows concession (A2), both in case of country A is amicable p(S1) and belligerent p(s2), outcome (C2) is realized. Q3. What is the expected utility of action A1? EU(A1)=0.30 EU(A1)=0.40 EU(A1)=0.60 EU(A1)=0.70 EU(A1)=0.72 Q4. What is the expected utility of action A2? EU(A2)=0.30 EU(A2)=0.40 EU(A2)=0.60 EU(A2)=0.70 EU(A2)=0.72 Q5. What action should country A choose? Action A1 Action A2 Q6. What action should country A choose if u(C2) were equal to 0.5 rather than 0.3? Action A1 Action A2 Q7. What action should country A choose if u(C2) were equal to 0.3 but p(S1) were equal to 0.25 (and p(S2) = 0.75)? Action A1 Action A2
Chapter2: Productions Possibilities, Opportunity Costs, And Economic Growth
Section: Chapter Questions
Problem 10SQ
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Q2.
Preferences and utility
Let's assume that country A prefers not to make additional concessions (outcome C1) to country B than granting those concessions (outcome C2), but a continued war (outcome C3) would be worse than making the additional concessions (C2). The following utility function over the outcomes specifies the intensity of preferences for country A over the outcomes: u(C1) = 1, u(C2) = 0.3, and u(C3) = 0.
Country A can choose to refuse concessions (action A1) or allow concessions (action A2). The outcome that will occur is a function of the "type" of country B's leader.
If country A refuses concession (A1), country B will not initiate a war (outcome C1) if country B's leader is amicable, while it will enter a war (outcome C3) if the leader is belligerent. There is a probability p(S1) = 0.6 that country B's leader is amicable and a probability p(S2) = 0.4 that country he's belligerent.
If country A allows concession (A2), both in case of country A is amicable p(S1) and belligerent p(s2), outcome (C2) is realized.
Let's assume that country A prefers not to make additional concessions (outcome C1) to country B than granting those concessions (outcome C2), but a continued war (outcome C3) would be worse than making the additional concessions (C2). The following utility function over the outcomes specifies the intensity of preferences for country A over the outcomes: u(C1) = 1, u(C2) = 0.3, and u(C3) = 0.
Country A can choose to refuse concessions (action A1) or allow concessions (action A2). The outcome that will occur is a function of the "type" of country B's leader.
If country A refuses concession (A1), country B will not initiate a war (outcome C1) if country B's leader is amicable, while it will enter a war (outcome C3) if the leader is belligerent. There is a probability p(S1) = 0.6 that country B's leader is amicable and a probability p(S2) = 0.4 that country he's belligerent.
If country A allows concession (A2), both in case of country A is amicable p(S1) and belligerent p(s2), outcome (C2) is realized.
Q3.
What is the expected utility of action A1?
- EU(A1)=0.30
- EU(A1)=0.40
- EU(A1)=0.60
- EU(A1)=0.70
- EU(A1)=0.72
Q2.
Preferences and utility
Let's assume that country A prefers not to make additional concessions (outcome C1) to country B than granting those concessions (outcome C2), but a continued war (outcome C3) would be worse than making the additional concessions (C2). The following utility function over the outcomes specifies the intensity of preferences for country A over the outcomes: u(C1) = 1, u(C2) = 0.3, and u(C3) = 0.
Country A can choose to refuse concessions (action A1) or allow concessions (action A2). The outcome that will occur is a function of the "type" of country B's leader.
If country A refuses concession (A1), country B will not initiate a war (outcome C1) if country B's leader is amicable, while it will enter a war (outcome C3) if the leader is belligerent. There is a probability p(S1) = 0.6 that country B's leader is amicable and a probability p(S2) = 0.4 that country he's belligerent.
If country A allows concession (A2), both in case of country A is amicable p(S1) and belligerent p(s2), outcome (C2) is realized.
Let's assume that country A prefers not to make additional concessions (outcome C1) to country B than granting those concessions (outcome C2), but a continued war (outcome C3) would be worse than making the additional concessions (C2). The following utility function over the outcomes specifies the intensity of preferences for country A over the outcomes: u(C1) = 1, u(C2) = 0.3, and u(C3) = 0.
Country A can choose to refuse concessions (action A1) or allow concessions (action A2). The outcome that will occur is a function of the "type" of country B's leader.
If country A refuses concession (A1), country B will not initiate a war (outcome C1) if country B's leader is amicable, while it will enter a war (outcome C3) if the leader is belligerent. There is a probability p(S1) = 0.6 that country B's leader is amicable and a probability p(S2) = 0.4 that country he's belligerent.
If country A allows concession (A2), both in case of country A is amicable p(S1) and belligerent p(s2), outcome (C2) is realized.
Q3.
What is the expected utility of action A1?
- EU(A1)=0.30
- EU(A1)=0.40
- EU(A1)=0.60
- EU(A1)=0.70
- EU(A1)=0.72
Q4. What is the expected utility of action A2?
- EU(A2)=0.30
- EU(A2)=0.40
- EU(A2)=0.60
- EU(A2)=0.70
- EU(A2)=0.72
Q5.
What action should country A choose?
- Action A1
- Action A2
Q6.
What action should country A choose if u(C2) were equal to 0.5 rather than 0.3?
- Action A1
- Action A2
Q7.
What action should country A choose if u(C2) were equal to 0.3 but p(S1) were equal to 0.25 (and p(S2) = 0.75)?
- Action A1
- Action A2
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