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 U P (or loss from the maximum possible profit) is given by U P ( ) 2 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 5 and 0 8 which occur with probability 0 4 and 0 6 respectively There are two division managers A and B who each have their own biases Manager A always wants a decision of 0 3 to be implemented and incurs a disutility A (0 3) 2 Similarly, Manager B always wants a decision of 0 8 to be implemented and incurs a disutility B (0 8 ) 2 Each manager is completely informed, so that each of them knows exactly what the state of the economy s is 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 8 What is the report (or recommendation) that Manager A will send if Manager B always truthfully reports s Explain your answer (4 marks) b) What if the principal instead delegates decision making entirely to manager A (that is, A can decide on her own d without any consultation) Does this make the principal better or worse off than with centralisation as in part a Provide some intuition for your answer (4 marks)

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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

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 U_P (or loss from the maximum possible profit) is given by U_P= ( )². 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 0.5 and 0.8 which occur with probability 0.4 and 0.6 respectively. There are two division managers A and B who each have their own biases. Manager A always wants a decision of 0.3 to be implemented and incurs a disutility A =(0.3)².Similarly, Manager B always wants a decision of 0.8 to be implemented and incurs a disutility B = (0.8 )². Each manager is completely informed, so that each of them knows exactly what the state of the economy s is.

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 = 0.8. What is the report (or recommendation) that Manager A will send if Manager B always truthfully reports s? Explain your answer. (4 marks)

b) What if the principal instead delegates decision-making entirely to manager A (that is, A can decide on her own d without any consultation). Does this make the principal better or worse off than with centralisation as in part a? Provide some intuition for your answer. (4 marks)