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(a) The principal can opt to centralise the decision but before making her decision - given she does not know what the state of the economy is - she asks for recommendations from her two division managers. Centralisation means that the principal commits to implement a decision that is the average of the two recommendations she received from her managers. The recommendations are sent simultaneously and cannot be less than 0 or greater than 1. Assume that the state of the economy s = 0.7. What is the report (or recommendation) that Manager A will send if Manager B always truthfully reports s? (b) The principal is going to centralise the decision and will ask for a recommendation from both managers, as in the previous question. Now, however, assume that both managers strategically make their recommendations. What are the recommendations гA and гB made by the Managers A and B, respectively, in a Nash equilibrium? (c) What is the principal's expected utility (or loss) under centralised decision making (as in part b)? (d) Can you design a contract for both of the managers that can help the principal implement their preferred option? Why might this contract be problematic in the real world?

(a) The principal can opt to centralise the decision but before making her decision - given she does not know what the state of the economy is - she asks for recommendations from her two division managers. Centralisation means that the principal commits to implement a decision that is the average of the two recommendations she received from her managers. The recommendations are sent simultaneously and cannot be less than 0 or greater than 1. Assume that the state of the economy s = 0.7. What is the report (or recommendation) that Manager A will send if Manager B always truthfully reports s? (b) The principal is going to centralise the decision and will ask for a recommendation from both managers, as in the previous question. Now, however, assume that both managers strategically make their recommendations. What are the recommendations гA and гB made by the Managers A and B, respectively, in a Nash equilibrium? (c) What is the principal's expected utility (or loss) under centralised decision making (as in part b)? (d) Can you design a contract for both of the managers that can help the principal implement their preferred option? Why might this contract be problematic in the real world?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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(a) The principal can opt to centralise the decision but before making her decision - given she does not know what the state of the economy is - she asks for recommendations from her two division managers. Centralisation means that the principal commits to implement a decision that is the average of the two recommendations she received from her managers. The recommendations are sent simultaneously and cannot be less than 0 or greater than 1. Assume that the state of the economy s = 0.7. What is the report (or recommendation) that Manager A will send if Manager B always truthfully reports s? (b) The principal is going to centralise the decision and will ask for a recommendation from both managers, as in the previous question. Now, however, assume that both managers strategically make their recommendations. What are the recommendations rA and rв made by the Managers A and B, respectively, in a Nash equilibrium? (c) What the principal's expected utility (or loss) under centralised decision making (as in part b)? (d) Can you design a contract for both of the managers that can help the principal implement their preferred option? Why might this contract be problematic in the real world?
Transcribed Image Text:(a) The principal can opt to centralise the decision but before making her decision - given she does not know what the state of the economy is - she asks for recommendations from her two division managers. Centralisation means that the principal commits to implement a decision that is the average of the two recommendations she received from her managers. The recommendations are sent simultaneously and cannot be less than 0 or greater than 1. Assume that the state of the economy s = 0.7. What is the report (or recommendation) that Manager A will send if Manager B always truthfully reports s? (b) The principal is going to centralise the decision and will ask for a recommendation from both managers, as in the previous question. Now, however, assume that both managers strategically make their recommendations. What are the recommendations rA and rв made by the Managers A and B, respectively, in a Nash equilibrium? (c) What the principal's expected utility (or loss) under centralised decision making (as in part b)? (d) Can you design a contract for both of the managers that can help the principal implement their preferred option? Why might this contract be problematic in the real world?
3. Consider the following delegation versus centralisation model of decision making, loosely based on some of the discussion in class. A principal has to implement a decision that has to be a number between 0 and 1; that is, a decision d needs to be implemented where 0≤d≤1. The difficulty for the principal is that she does not know what decision is appropriate given the current state of the economy, but she would like to implement a decision that exactly equals what is required given the state of the economy. In other words, if the economy is in state s (where 0≤s≤1) the principal would like to implement a decision d = s as the principal's utility Up (or loss from the maximum possible profit) is given by Up = -|s-d. With such a utility function, maximising utility really means making the loss as small as possible. For simplicity, the two possible levels of s are 0.4 and 0.7, and each occurs with probability 0.5. There are two division managers A and B who each have their own biases. Manager A always wants a decision of 0.4 to be implemented and incurs a disutility UA that is increasing the further from 0.4 the decision d that is actually implement, specifically, U₁ = -0.4-d|. Similarly, Manager B always wants a decision of 0.7 to be implement, and incurs a disutility UB that is (linearly) increasing in the distance between 0.7 and the actually decision that is implemented - that is U₂ = -0.7-d. Each manager is completely informed, so that each of them knows exactly what the state of the economy s is. B
Transcribed Image Text:3. Consider the following delegation versus centralisation model of decision making, loosely based on some of the discussion in class. A principal has to implement a decision that has to be a number between 0 and 1; that is, a decision d needs to be implemented where 0≤d≤1. The difficulty for the principal is that she does not know what decision is appropriate given the current state of the economy, but she would like to implement a decision that exactly equals what is required given the state of the economy. In other words, if the economy is in state s (where 0≤s≤1) the principal would like to implement a decision d = s as the principal's utility Up (or loss from the maximum possible profit) is given by Up = -|s-d. With such a utility function, maximising utility really means making the loss as small as possible. For simplicity, the two possible levels of s are 0.4 and 0.7, and each occurs with probability 0.5. There are two division managers A and B who each have their own biases. Manager A always wants a decision of 0.4 to be implemented and incurs a disutility UA that is increasing the further from 0.4 the decision d that is actually implement, specifically, U₁ = -0.4-d|. Similarly, Manager B always wants a decision of 0.7 to be implement, and incurs a disutility UB that is (linearly) increasing in the distance between 0.7 and the actually decision that is implemented - that is U₂ = -0.7-d. Each manager is completely informed, so that each of them knows exactly what the state of the economy s is. B
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