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Finding The Value Of The Safe Salary Essay Discussion Paper The football player Rheuma Kai has the choice between two contracts. The first contract guarantees a safe annual salary of 240,000 Euro. The second one pays based on his performance. If his team wins the championship with a probability of 30%, he will receive 450,000 Euro, or otherwise only 150,000 Euro. His utility function is estimated as: (piecewise defined) u(x)=⎩⎨⎧​10001​x​21​+(302000x−2000​)23​​,0≤x≤250000,250000≤x≤500000​ a) How high is his expected salary in both cases? b) Which contract will he choose? c) How high should the safe salary be, so that he will choose against the performancebased contract? 00)=10001​240,000​,u(450,000)=21​+(396850450.000⋅250.000​)23​  b) E∪[L1​]=10001​240000​=0.49E∪[Lx​]=0.7(10001​150000​)+0.3(21​+396050450000−200000​)3/2=0.53→E∪[L2​]>E∪[L1​]→ Choose L2​ (performance based)  Finding The Value Of The Safe Salary Essay Discussion Paper ORDER YOUR PAPER NOW ​ Expert Answer This solution was written by a subject matter expert. It's designed to help students like you learn core concepts. Step-by-step 1st step All steps Answer only Step 1/2 In the given question Part (A) and Part (B) of the question is solved and we are asked to solve the part (C) with the reference. Explanation for step 1 To solve part C), we need to find the value of the safe salary that would make Rheuma Kai indifferent between the two contracts, i.e., the expected utility from the safe contract should be equal to the expected utility from the performance-based contract. Step 2/2 Let S be the safe salary that Rheuma Kai would choose if offered both contracts. Then, the expected utility from the safe contract is: EU(S) = U(S) = 1000V(S-240,000) The expected utility from the performance-based contract is: EU(L2) = 0.3U(450,000- S) + 0.7U(150,000 - S) We want to find the value of S such that EU(S) = EU(L2). That is, 1000V(S-240,000) = 0.3U(450,000- S) + 0.7U(150,000 - S) Substituting the piecewise definition of U(x), we get: 1000V(S-240,000) = 0.3(450,000- S-250,000)+ 0.7(150,000 - S-250,000) Simplifying the equation: 1000V(S-240,000) = 0.3(200,000 - S) - 0.4S 1000V(S-240,000) = 60,000 - 0.3S - 0.4S 1000V(S-240,000) = 60,000 - 0.7S 1000V(S-240,000) + 0.7S = 60,000 Dividing both sides by 0.7V(S-240,000) + 0.7, we get: S = (60,000)/(0.7V(S-240,000) + 0.7) We can solve this equation numerically using iterative methods or graphical methods. One possible approach is to substitute a guess value for S, compute the left-hand side of the equation, and compare it with the right-hand side. If they are close enough, we accept the guess as the solution. Otherwise, we update the guess and repeat the process until convergence. For example, let's start with a guess value of S = 250,000. Then, we have: S = (60,000)/(0.7V(S-240,000) + 0.7) S = (60,000)/(0.7V(10,000) + 0.7) S = (60,000)/(0.7*31.62 + 0.7) S ≈ 465,222 This value of S is higher than the expected value of the performance-based contract, which is: EV(L2) = 0.3200,000 + 0.750,000 = 65,000 Finding The Value Of The Safe Salary Essay Discussion Paper Explanation for step 2 Therefore, Rheuma Kai would still prefer the performance-based contract over the safe contract with a salary of 465,222 Euro. We can repeat the process with different guess values until we find the value of S that makes Rheuma Kai indifferent between the two contracts. Final answer The Final answer is EV(L2) = 0.3200,000 + 0.750,000 = 65,000 Finding The Value Of The Safe Salary Essay Discussion Paper
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Finding The Value Of The Safe Salary Essay Discussion Paper
The football player Rheuma Kai has the choice between two contracts. The first contract guarantees a safe annual salary of 240,000 Euro. The second one pays based on his performance. If his team wins the championship with a probability of , he will receive 450,000 Euro, or otherwise only 150,000 Euro. His utility function is estimated as: (piecewise defined)  a) How high is his expected salary in both cases? b) Which contract will he choose? c) How high should the safe salary be, so that he will choose against the performancebased contract?  

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Expert Answer

This solution was written by a subject matter expert. It's designed to help students like you learn core concepts.

Step-by-step

Step 1/2
In the given question Part (A) and Part (B) of the question is solved and we are asked to solve the part (C) with the reference.
  • Explanation for step 1
To solve part C), we need to find the value of the safe salary that would make Rheuma Kai indifferent between the two contracts, i.e., the expected utility from the safe contract should be equal to the expected utility from the performance-based contract.
Step 2/2
Let S be the safe salary that Rheuma Kai would choose if offered both contracts. Then, the expected utility from the safe contract is: EU(S) = U(S) = 1000V(S-240,000)
The expected utility from the performance-based contract is:
EU(L2) = 0.3U(450,000- S) + 0.7U(150,000 - S)
We want to find the value of S such that EU(S) = EU(L2). That is,
1000V(S-240,000) = 0.3U(450,000- S) + 0.7U(150,000 - S)
Substituting the piecewise definition of U(x), we get:
1000V(S-240,000) = 0.3(450,000- S-250,000)+ 0.7(150,000 - S-250,000)
Simplifying the equation:
1000V(S-240,000) = 0.3(200,000 - S) - 0.4S
1000V(S-240,000) = 60,000 - 0.3S - 0.4S
1000V(S-240,000) = 60,000 - 0.7S
1000V(S-240,000) + 0.7S = 60,000
Dividing both sides by 0.7V(S-240,000) + 0.7, we get:
S = (60,000)/(0.7V(S-240,000) + 0.7)
We can solve this equation numerically using iterative methods or graphical methods. One possible approach is to substitute a guess value for S, compute the left-hand side of the equation, and compare it with the right-hand side. If they are close enough, we accept the guess as the solution. Otherwise, we update the guess and repeat the process until convergence.
For example, let's start with a guess value of S = 250,000. Then, we have:
S = (60,000)/(0.7V(S-240,000) + 0.7)
S = (60,000)/(0.7V(10,000) + 0.7)
S = (60,000)/(0.7*31.62 + 0.7)
S ≈ 465,222
This value of S is higher than the expected value of the performance-based contract, which is:
EV(L2) = 0.3200,000 + 0.750,000 = 65,000 Finding The Value Of The Safe Salary Essay Discussion Paper
  • Explanation for step 2
Therefore, Rheuma Kai would still prefer the performance-based contract over the safe contract with a salary of 465,222 Euro. We can repeat the process with different guess values until we find the value of S that makes Rheuma Kai indifferent between the two contracts.
Final answer
The Final answer is EV(L2) = 0.3200,000 + 0.750,000 = 65,000
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