Problem 4 (20 points): Ward Edwards recognized that his utility for money was no

Question

Problem 4 (20 points): Ward Edwards recognized that his utility for money was not linear, and that his risk aversion would therefore influence his decision. Use the following risk assessments to plot ward's utility function. Assume U(SO) = 0 and U($25) = 1. His certain equivalent was S6 for a His certain equivalent was $3 for a His certain equivalent was $11 for His certain equivalent was $6 for a gamble consisting of a 0.25 chance of SO and 0.75 chance of S25 His certain equivalent was $3 for a gamble consisting of a chance of $0 and chance of $6 His certain equivalent was $11 for a gamble consisting of a 0.4 chance of $6 and 0.6 chance of $25. 1.0 0.8 0,7 04 03 9.1 0.0 1237 11 12 1315 16 17 I 19 2 21 22 23 24 2 Using the above utility function, determine Ward's preferred course of action by computing the certain equivalent for each alternative shown below 54 0.3 S9 s9 0.4 si0

Explanation / Answer

Using the theory of Mathematical expectation we calculate the probable utility

For equivalent $6 : Expected utility is U X Value + U1 X Value

                                   0.25 X $0 + 0.75 X 25= 18.74

Similarly for equivalent $3 : the expected value would be 4

And for equivalent $ 11 : the expected value would be 17.4

It is known as assumed that U($0)=0 and U($25)=1

The equivalents would now be converted on the basis of this assumption:

Since $25 is 1 , thus $6 would be 0.24

Since $25 is 1 , thus $3 would be 0.12

Since $25 is 1 , thus $11 would be 0.44

We thus get the three co-ordinates for the non-linear utility function as :

(18.74, 0.24); (4,0.12) and (17.4,0.44)

Plotting these on the graph above we get the required function

For the given extensive game depicted we need to get the expected values for each possible strategy:

If he opts for YES: his expected returns would be

For LOW: 0.3 X 4= 1.2

For BASE 0.4 X 9= 3.6

For HIGH 0.3 X 15= 4.5

And for NO

It is $10

Given the transformation above on the basis of utility conversions the highest returns would be with NO where the returns are $10 > 1.2,3.6 and 4.5

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