The owner of the Jets is going to offer a contract to a free agent player, Hapoleon. If signed, Hapoleon can give the Jets high effort or low effort. High effort costs Hapoleon $2 million and low effort costs Hapoleon nothing. The Jets’ owner cannot observe Hapoleon’s effort directly. Hapoleon has a guaranteed offer of $10 million from another team, the Sharks. If Hapoleon signs with the Jets, the team can be profitable or not and the Jets’ owner can observe that. If Hapoleon gives high effort, then the probability the Jets are profitable is 80 percent, but if Hapoleon gives low effort, then the probability the Jets are profitable is 40 percent. Hapoleon is the typical risk neutral player and his utility is given by u w() = w . a. If effort were observable, describe the contingent contract the Jets’ owner should offer Hapoleon. As already stated, effort is not observable. The Jets’ owner is optimistic that he can sign Hapoleon. b.Calculate Hapoleon’s expected payoff if he signs with the Jets and gives high effort. c. Calculate Hapoleon’s expected payoff if he signs with the Jets and gives low effort. d. Use parts (b) and (c) to derive Hapoleons’s incentive compatibility constraint (ICC) for choosing high effort over low effort. e. Use part (b) to derive Hapoleon’s participation constraint (PC) if the Jets’ owner wants him to give high effort. f. Derive Hapoleon’s PC if the Jets’ owner wants him to give low effort. g. Briefly explain your answer to part (f). h. Use the ICC and PC in parts (d) and (e) to calculate the optimal wage levels, wH and wL that the Jets’ owner should offer Hapoleon to get him to sign with the Jets and give high effort. i. Calculate the optimal wage levels, wH and wL , that the Jets’ owner should offer Hapoleon to get him to sign with the Jets and give high effort if Hapoleon’s disutility from high effort increases to $3 million. j. Determine the optimal wage levels, wH and wL , that the Jets’ owner should offer Hapoleon to get him to sign with the Jets and give high effort if instead Hapoleon’s disutility from low effort increases to $1 million. k. Determine the optimal wage levels, wH and wL , that the Jets’ owner should offer Hapoleon to get him to sign with the Jets and give high effort if instead the probability of high profits given high effort increases to 90 percent. l. Determine the optimal wage levels, wH
The owner of the Jets is going to offer a contract to a free agent player, Hapoleon. If signed, Hapoleon can give the Jets high effort or low effort. High effort costs Hapoleon $2 million and low effort costs Hapoleon nothing. The Jets’ owner cannot observe Hapoleon’s effort directly.
Hapoleon has a guaranteed offer of $10 million from another team, the Sharks. If Hapoleon signs with the Jets, the team can be profitable or not and the Jets’ owner can observe that.
If Hapoleon gives high effort, then the probability the Jets are profitable is 80 percent, but if Hapoleon gives low effort, then the probability the Jets are profitable is 40 percent.
Hapoleon is the typical risk neutral player and his utility is given by u w() = w .
a. If effort were observable, describe the contingent contract the Jets’ owner should offer Hapoleon.
As already stated, effort is not observable. The Jets’ owner is optimistic that he can sign Hapoleon.
b.Calculate Hapoleon’s expected payoff if he signs with the Jets and gives high effort.
c. Calculate Hapoleon’s expected payoff if he signs with the Jets and gives low effort.
d. Use parts (b) and (c) to derive Hapoleons’s incentive compatibility constraint (ICC) for choosing high effort over low effort.
e. Use part (b) to derive Hapoleon’s participation constraint (PC) if the Jets’ owner wants him to give high effort.
f. Derive Hapoleon’s PC if the Jets’ owner wants him to give low effort.
g. Briefly explain your answer to part (f).
h. Use the ICC and PC in parts (d) and (e) to calculate the optimal wage levels, wH and wL that the Jets’ owner should offer Hapoleon to get him to sign with the Jets and give high effort.
i. Calculate the optimal wage levels, wH and wL , that the Jets’ owner should offer Hapoleon to get him to sign with the Jets and give high effort if Hapoleon’s disutility from high effort increases to $3 million.
j. Determine the optimal wage levels, wH and wL , that the Jets’ owner should offer Hapoleon to get him to sign with the Jets and give high effort if instead Hapoleon’s disutility from low effort increases to $1 million.
k. Determine the optimal wage levels, wH and wL , that the Jets’ owner should offer Hapoleon to get him to sign with the Jets and give high effort if instead the probability of high profits given high effort increases to 90 percent.
l. Determine the optimal wage levels, wH and wL , that the Jets’ owner should offer Hapoleon to get him to sign with the Jets and give high effort if instead the probability of high profits given low effort increases to 50 percent.
m.Determine the optimal wage levels, wH and wL , that the Jets’ owner should offer Hapoleon to get him to sign with the Jets and give high effort if instead the Sharks’ offer increases
to $11 million.
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