below are questions with correct answers. please explain for each why we choose this specific input and mathematical detailed steps till we for the salutation. (how we got x)

D15. Peter has a current wealth of $90,000, including his brand new Cadillac which is worth $50,000. His son just got a driver's license and Peter is contemplating whether to (i) let his son borrow the Cadillac, or (ii) buy him a used car as a gift. Peter estimates that the likelihood that his son will total the Cadillac is around 10% and the used car will cost somewhere between $5,000 and $6,000.

D15b. (1 point) What is the maximum amount that Peter would be willing to pay to buy his son a used car as a gift?

E(X) = (90,000 - x)^0.5 = 290, implying x = $5,900.

D16. Simone is planning an around-the-world trip on which she plans to spend $10,000. The utility from the trip is a function of how much she actually spends on it (x), given by: u(x) = ln(x)

D16b. (1 point) Now, suppose that Simone can buy insurance against losing the $1,000 (say, by purchasing traveler's checks) at the actuarially fair price of $250. What is her expected utility if she purchases this insurance? Again, use your calculator and round to the third decimal point.

E(X) = ln(10,000 - 250) = 9.184, implying x = 9.185

D16c. (1 point) What is the maximum amount that Simone would be willing to pay to insure her $1,000?

E(X) = ln(10,000 - x) = 9.184, implying x = 260

S15. A weapons producer, acting as a monopolist, sells guns to two countries (A and B) that are at war with each other. The guns can be produced at a constant marginal cost of $10. The demand for guns from the two countries can be represented as: Q_A = 100 - 2P and Q_B = 80 - 4P.

S15b. What price will it charge to each country?

To solve, find marginal revenue for each and set equal to marginal cost of $10.

MRA = 50 - QA = 10 or QA = 40 and PA = 30.

S15c. (1 point) What price will it charge to each country?

MRB = 20 - (1/2)QB = 10 or QB = 20 and PB = 15.