Dougie’s car is worth $10,000. Dougie is a careless fellow who leaves the top down, thekeys in the ignition, and his fanny pack in the front seat. As a result, the probability of his carbeing stolen is 0.3. If his car is stolen, he will never get it back (the fanny pack is a knockoff,assume that it has a value of zero). Dougie has $20,000 in other wealth and his utility functionfor wealth is 𝑢(𝑤) = 2𝑤^0.5. Suppose that Dougie can buy $K worth of insurance at a price of$.35K a) Write down Dougie’s von Neuman-Morgenstern utility function. (u(c1, c2, π1, π2) = π1ν(c1) + π2ν(c2))

1. A property development company takes on one new project each year, investing all of its capital in that year’sproject. If the project is successful, the company makes a profit of $1million. If the project is unsuccessful,the company is ruined (loses all its money) and ceases to exist. The success or failure of each project isindependent of all previous ones. The probability that a project is unsuccessful when x million dollars isinvested (for x = 1, 2, 3, . . .) is 1/(x + 1) 2 . Let X n million dollars be the company’s total capital after nprojects.(a) Write down the transition probabilities for the Markov chain (X n ).(b) Show that when X 0 = i, the probability h i of eventual ruin is 1i+1

Josh is looking to buy a second hand car. Josh is risk averse. The cars all sell for $3,500 but there is an 6 percent chance that the car will be worth $1,000, a 53 percent chance it will be worth $3,000 or a 41 percent chance that the car is worth an unknown amount. What must the unknown value be if the expected value is to equal $3,500? Give your answer to the nearest whole dollar (with no decimal points, spaces, $ signs, or commas in your answer).

June is relocating from Canberra to Sydney and hasengaged a removalist company to bring her household goods by truck fromher house in Canberra to her new residence in Sydney. Suppose she faces thefollowing uncertainty, either the truck makes the journery from Canberrato Sydney without incident and unloads her household goods in Sydneywith nothing lost and nothing damaged, or, the truck crashes and all herhousehold goods are damaged beyond repair. Let M denote her overall(money) wealth in the event that nothing is lost and M L denote herwealth in the event the truck carrying her household goods crashes. AssumeM > L > 0.(a) (5 points) Let (x1; x2)  (0; 0) denote Juneís state-contingent wealth,where x1  0 is her wealth in the state in which the truck does notcrash and x2  0 is her wealth in the state in which the truck doescrash. Draw a graph with the horizontal axis measuring the quantityx1 and the vertical axis measuring the quantity x2 and plot Juneísstate-contingent wealth if she does not take out any insurance

Barney backs his truck into a telephone pole, causing $3,000 worth of damage to his truck.  Barney files a claim with his auto insurance.  His collision deductible is set at $500.  To get his car fixed, how much money will Barney receive from his insurance company? a$0 b$2,000 c$2,500 dThere is not enough information

Josh's club at school is selling suckers for a fundraiser. They sold the suckers for $.50$.50 a piece but had to pay a shipping cost of $30$30. The function for their sucker sales is P(s)=.50s−30𝑃(𝑠)=.50𝑠−30, where s𝑠 is the number of suckers sold and P𝑃 represents the profit made. If they sold 150150 suckers, how much profit would they make? Josh's club would make $$ Answer 1 Question 20 for selling 150150 suckers.