Help me answer the following questions correctly.,,,

1. Nicholson problem 8.5 2. Bill is a Von-Neumann Morgenstern expected utility maximizer with a well-behaved, continuously differentiable utility function (i.e., no kinks or inflection points). Bill is presented with the following choices: A. $1,000 for sure B. 50% chance of $800 50% chance of $1,500 C. $500 for sure D. 50% chance of $400 50% chance of $900 Bill is indifferent between A and B and is also indifferent between C and D. (Note: this does not imply that he is indifferent between A and C or B and D.) Part 1. Is Bill risk neutral, risk averse, risk loving, or can't you tell? Explain. He is now faced with the following choice: E. $750 for sure F. 25% chance of $400 25% chance of $900 25% chance of $800 25% chance of $1,500 Part 2. Will Bill choose E or F, or is he indifferent between them, or is not possible to tell? (You must prove your answer) 3. Consider these four choices: A. $1,000,000 for sure B. .10 chance of $5,000,000 .89 chance of $1,000,000 .01 chance of $0 C. .10 chance of $5,000,000 .90 chance of $0 D. .11 chance of $1,000,000 .89 chance of $0 Before reading any further, choose which you prefer between A and B, and then choose which you would prefer between C and D. (The choice you make will not affect your grade.) It is commonly observed that people prefer A to B. and prefer C to D. Show that this pair of choices is inconsistent with expected utility maximization. 4. Suppose my utility function is given by: U = 100W where W is my wealth in thousands. My current wealth is $1,000. a. Characterize my relative risk aversion. b. Suppose I face a 0.1 chance of losing $100. Calculate my willingness to pay for an insurance policy that would pay me $100 in the event of such a loss. c. My utility is greatly augmented by my children. If they were to die, it would be reduced to: Calculate the loss of wealth that would be equivalent, in terms of its utility impact, to the death of my children.The problem: A. A policy maker for the Board of Health sits down to design the new national health plan. She reasons that since half of all Rothschildians get sick each year, the government should offer an actuarially fair full insurance policy that charges a premium of 1/2 Stiglitz and pays a benefit of 1 Stiglitz to any enrollee who gets sick (of course, the enrollee pays the premium regardless of whether or not she becomes ill). Given this premium, calculate who chooses to enroll in the plan: What is the expected illness probability of the most healthy and least healthy person to enroll in the plan? What is the average health of those who enroll in the plan? Does the plan break even, make money, or lose money in year 1, and by how much per person on average? B. In year 2, a different policy maker at the board of health (recall, the first has passed away) notes that something went wrong in the first year: the plan made/lost money (depending on your answer above). He reasons, "Clearly we set the premium too high/low in the first year. What we'll do is set the new premium to reflect our average cost from last year. This should straighten things out." What is the new premium? What is the expected illness probability of the most healthy and least healthy person to enroll in the plan? What is the average health of those who enroll in the plan? Does the plan break even, make money, or lose money in year 2, and by how much (per person average)? C. In year 3, a third policy maker observes that something is again amiss. The plan made/lost money again last year, although the intention was to break even. This policy maker suggests that the board fix the problem by setting the new premium at the average cost for year 2. What is the new premium? What is the expected illness probability of the most healthy and least healthy person to enroll in the plan? What is the average health of those who enroll in the plan? Does the plan break even, make money, or lose money in year 3, and by how much (per 2 person average)? D. In year 4, a fourth policy maker notes that something went wrong yet again. This policy maker has taken 14.03, however, and says, "Alas, I see the error of our ways! Every time we change the premium, a different pool of citizens enrolls in the plan. I wonder if there is a premium we could set so that the pool of citizens who enrolls at that price costs us on average exactly that price. That way, we'd break even and provide insurance to all those who want to buy it." After a few strokes of the pen, she shouts, "Eureka! There is." E. What is that premium? Hint: you can either solve this problem analytically (i.e., on paper with a simple equation) or with a spreadsheet by repeating the steps you used for A, B. and C until you get a convergent solution.An economy produces with the production technology T = F\"; EL] = K' {EL]\"2}3, where E is a labor augmenting technology. Population grows at 2% per year and E grows at 3% per year. The depreciation rate is 5% and the saving rate is 40%. The economy is in steady state. a. What is the growth rate of each of the following: KIEL, WEL, EL, V, WL. KEY, C b. At what rate do wages and the capital rerrtal rate grow? c. Find the steady state value of capital per effective worker d. In 214. L = IUD and E = 1:]. Find total output in 2014 and 2:115. e. If the economy wants to maximize consumption, should it save more or less? Find the consumption maximizing saving rate. f. Now assume a hurricane hits in 2014 and reduces labor to 9G. What happens to steady state output and capital {per effective worker]? What happens to output and capital today [both per effective worker and total}? What about their growth rates? g. Another country uses the same production technology, has the same level of total capital, but has fewer workers. If there is free mobility across countries [so wage rates are equalized}, what can we say about the value of E in the other country