Finding The Value Of The Safe Salary Essay Discussion Paper

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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) = 0.3

*200,000 + 0.7*50,000 = 65,000 Finding The Value Of The Safe Salary Essay Discussion Paper- Explanation for step 2

Final answer

**The Final answer is EV(L2) = 0.3**

**200,000 + 0.7****50,000 = 65,000**

Finding The Value Of The Safe Salary Essay Discussion Paper