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Wildcat Co. has to decide whether or not to drill and oil well. It has $100 current income. Drilling would cost $100; if oil were struck, the company would receive $200 for the oil. If the field is dry, nothing is recovered.
(a) Suppose Wildcat’s utility function is U=y where y is income. Suppose the probability of striking oil is 0.6. Should Wildcat drill? At what probability would Wildcat be just indifferent between drilling or not?
(b) Now suppose the utility function is U=2y1/2. Is Wildcat risk adverse? Using this function, answer question (a).
(c) Suppose for $20, Wildcat could run a test that would determine for certain whether the field is wet or dry. The probability of a positive test is 0.6. Would the Wildcat with the utility as in (a) do the test? (Assume that if the field is wet, they can borrow at zero interest the extra $20 needed to drill– to be repaid immediately.) What is the maximum
amount Wildcat would pay for the test?
(d) Answer (c) using U=2y1/2.. For which utility
function does the company value the test higher? Offer an explanation for your answer.

Respuesta :

PNaik

a.  The probability of striking oil is 0.6.should not drill. thus indifferent p must be 1 certainty of   strike oil needed.

b. Now suppose the utility function is U=2y1/2 risk adverse.

c. the maximum amount Wildcat would pay for the test is 0.

d. the company will value the the test higher in case of U =[tex]2Y^{\frac{1}{2} }[/tex]  become it leads to even lower welfare.

What is probability?

Probability means the possibility of the outcome of some random event. The purpose of this term is to control the degree to which some event is likely to occur. For example, what is the chance of getting heads when we flip a coin? The answer to this question is based on the number of possible outcomes. Here it is possible that the result is either heads or tails. So the probability of getting a head  is 1/2.

Probability is a measure of the probability of an event. It measures the certainty of an event. The probability formula  is given;

P(E) = number of favourable outcomes / total number of  outcomes

P(E) = n(E)/n(S)

Here

n(E) = number of favourable events for event E

n(S ) ) ) = results total number

Therefore,

a. U=y

probability of striking oil = 0.6

expected value = 0.6x(200-100)+0.4(0-100)

                          = 0.6(100)+0.4x100

                          = 60-40

                          = 20  No EV>100 should not drill.

U(100)= U(EV)

thus U (100)= 100

U(EV) = P(200-100)+(1-P)+(-100)

         = 100P+100P-100

         = 200-100

To be different U(100)= U(EV)

                             100 = 200P

                                  P = 1

thus indifferent p must be 1 certainty of   strike oil needed.

b. U=2y1/2.

    U'  = [tex]2\times\frac{1}{2}^{\frac{1}{2} } }[/tex]

  U'' = -[tex]-\frac{1}{2} Y^{\frac{3}{2} }[/tex]<0

Therefore risk adverse

U(100) = 2X[tex]100^{\frac{1}{2} }[/tex]\= 20

U(EV) =[tex]2(200-100)^{\frac{1}{2 }[/tex]

To be indifferent

[tex]20 = 2(200P-100)^{\frac{1}{2} }[/tex]

[tex]10 = (200P-100)^\frac{1}{2}[/tex]

100= 200P-100

200=200P

P=1 required.

c. now EV = 0.6X(200-100-20) +0.4X 100-20

                  = 0.6X80+0.4X80

                  = 80

U(EV)<U(income= 100)

therefore will not take rest

He would be willing to pay U(EV)-U(income)<0

would be willing to pay 0.

d.  U=2y1/2

        =[tex]2 (0.6\times80+0.4\times60)^{\frac{1}{2 }[/tex]

        = [tex]2\times 80^{\frac{1}{2} }[/tex]

U(EV) = 17.84

U(100)=20>U(EV)

Therefore will not take that.

the company will value the the test higher in case of U =[tex]2Y^{\frac{1}{2} }[/tex]

Become it leads to even lower welfare.

To learn more about probability refer;

https://brainly.com/question/11234923

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