Individuals 1 and 2 are working together on a project. When 1 exerts effort e1 and 2 exerts effort e2, the outcome generated is X = 40e1 + 80e2. The utility %3D functions are such that individual 1 gets U1 = aX- (e1)", and individual 2 gets U2 = (1 – a)X – %3D - }(e2)*. |3D The value a E 0, 1 is the share of X that is given to individual 1. They can either set efforts cooperatively maximizing the total surplus defined as

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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1

Individuals 1 and 2 are working together on a project. When 1 exerts effort ei and 2
exerts effort e2, the outcome generated is X = 40e1 + 80e2. The utility
functions are such that individual 1 gets U1 = aX- (e1)*, and individual 2
|3D
U2 = (1– a)X - (e2)*.
gets
%D
The value a E 0, 1 is the share of X that is given to individual 1.
They can either set efforts cooperatively maximizing the total surplus defined as
U1 + U2.
Alternatively they choose their effort non-cooperatively whereby each individual
maximizes his/her own utility.
They cannot rely on any contract or threats.
QUESTIONS:
1-What is the value of the total surplus that is reached when 1 and 2 decide on
efforts cooperatively?
Enter your answer in blank #1. Do not use any comma.
2-What is the value of a that maximizes the total surplus when efforts are chosen
3-What is highest value of the total surplus that is reached when 1 and 2 set their
efforts non-cooperatively.
Enter your answer in blank #3. Do not use any comma.
Blank # 1
Blank # 2
Blank # 3
Transcribed Image Text:Individuals 1 and 2 are working together on a project. When 1 exerts effort ei and 2 exerts effort e2, the outcome generated is X = 40e1 + 80e2. The utility functions are such that individual 1 gets U1 = aX- (e1)*, and individual 2 |3D U2 = (1– a)X - (e2)*. gets %D The value a E 0, 1 is the share of X that is given to individual 1. They can either set efforts cooperatively maximizing the total surplus defined as U1 + U2. Alternatively they choose their effort non-cooperatively whereby each individual maximizes his/her own utility. They cannot rely on any contract or threats. QUESTIONS: 1-What is the value of the total surplus that is reached when 1 and 2 decide on efforts cooperatively? Enter your answer in blank #1. Do not use any comma. 2-What is the value of a that maximizes the total surplus when efforts are chosen 3-What is highest value of the total surplus that is reached when 1 and 2 set their efforts non-cooperatively. Enter your answer in blank #3. Do not use any comma. Blank # 1 Blank # 2 Blank # 3
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