33 (b) (c) (d) (e) functions. negative them. Find the best response function of each partner. Draw the best response Solve for the Nash equilibrium of this game. 1 Now assume that b = -. (This implies that the effort levels have synergies.) Solve for the best response functions in this case and draw Solve for the Nash equilibrium of this game. Now suppose that the partners can write a contract on effort levels. That is, they can determine the effort levels which would maximize the firm's revenue net of total effort costs. Briefly explain whether you would expect the effort levels they choose to specify in the contract to be higher or lower than the effort levels you found in parts (b) and (d).

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Solve part D and E only
(a)
(b)
(c)
(d)
(e)
functions.
negative
them.
Find the best response function of each partner. Draw the best response
Solve for the Nash equilibrium of this game.
1
- -
2°
Now assume that b - (This implies that the effort levels have
synergies.) Solve for the best response functions in this case and draw
Solve for the Nash equilibrium of this game.
Now suppose that the partners can write a contract on effort levels.
That is, they can determine the effort levels which would maximize the firm's
revenue net of total effort costs. Briefly explain whether you would expect the
effort levels they choose to specify in the contract to be higher or lower than the
effort levels you found in parts (b) and (d).
Transcribed Image Text:(a) (b) (c) (d) (e) functions. negative them. Find the best response function of each partner. Draw the best response Solve for the Nash equilibrium of this game. 1 - - 2° Now assume that b - (This implies that the effort levels have synergies.) Solve for the best response functions in this case and draw Solve for the Nash equilibrium of this game. Now suppose that the partners can write a contract on effort levels. That is, they can determine the effort levels which would maximize the firm's revenue net of total effort costs. Briefly explain whether you would expect the effort levels they choose to specify in the contract to be higher or lower than the effort levels you found in parts (b) and (d).
Two business partners jointly own a firm and share equally the revenues.
They individually and simultaneously decide how much effort to put into the firm. Let
s₁ and s2 denote the effort choices of partner 1 and partner 2, respectively. Assume
si € [0, 4]. The cost of effort is given by s? for i E {1, 2}. The firm's revenue is given by
4(81 +82 + bs182) where 0 ≤ b ≤. (Note that the parameter b reflects the synergies
between the effort levels. b> 0 implies that the more one partner works, the more
productive the other partner is.) The payoffs for partners 1 and 2 are:
u₁ (81, 82)
u2 (81, 82)
-
=
1
[4(81 +82 +68182)] − 8²
-
1
[4(81 +82 + bs182)] – $²
Transcribed Image Text:Two business partners jointly own a firm and share equally the revenues. They individually and simultaneously decide how much effort to put into the firm. Let s₁ and s2 denote the effort choices of partner 1 and partner 2, respectively. Assume si € [0, 4]. The cost of effort is given by s? for i E {1, 2}. The firm's revenue is given by 4(81 +82 + bs182) where 0 ≤ b ≤. (Note that the parameter b reflects the synergies between the effort levels. b> 0 implies that the more one partner works, the more productive the other partner is.) The payoffs for partners 1 and 2 are: u₁ (81, 82) u2 (81, 82) - = 1 [4(81 +82 +68182)] − 8² - 1 [4(81 +82 + bs182)] – $²
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