Let 100 -100 A = 300 -300 200 -200 be an asset payoff matrix. You are 'greedy': 'more is better' in at least one state. (a) Suppose that a broker offers you to sell asset 2 at a price of AED 300. What should the price of asset 1 be for the Law of One Price to hold, if at all possible? Explain. (b) Can the prices you found under (a) be part of a financial equilibrium? Explain. (c) Give no arbitrage prices q1, q2 consistent with an implicit riskfree discount rate of p= 0.
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- Are derivatives similar to insurance in that both have an indefinite life spans, allow for the transfer of risk from one party to another or allow for the transformation of the underlying risk itself? First explain why one or more of the options above are correct. Secondly explain why, if any of the remaining options are incorrect. Your justification/s should be one sentence for each of the points above, in bullet point format.Suppose there exist n = 1000 firms that seek to gain access to a small niche market that is regulated. Suppose that one firm will obtain access and that will get that firm an additional R = $50,000 in profits. Each firm already receives $1 million in profits from other ventures. a. Suppose the probability of winning the rents is linear in investment, each firm has an equal chance of winning and they are all risk-neutral. How much will each firm invest in rent-seeking? Are the rents fully dissipated? b. Suppose instead that the probability of winning changes with the amount invested in rent-seeking, so that each firm’s odds of gaining access are π(n,I) = I1/2 /n. Is the probability of winning increasing or decreasing in investment? Are there diminishing returns to rent-seeking? c. How much will each firm invest in rent-seeking? Are the rents fully dissipated, less than fully dissipated, or more than fully dissipated?You have bought a car for $50,000. You were so excited. However, you then found out that the car you bought decreases in value by 8% each year. You finally decide to sell your car after 7 years. How much will your car be worth after 7 years? Explicit: a1= r= f(n)= f( )=
- Prospect Y = ($6, 0.25 ; $15, 0.75) If Will's utility of wealth function is given by u(x)=x0.25, what is the value of CE(Y) for Will? (In other words, what is Will's certainty equivalent for prospect Y?) (The certainty equivalent represents the maximum amount a person would be willing to pay to acquire a risky prospect, and equivalently, the lowest price for which they would be willing to sell a risky prospect if they already owned it) (Note: The answer may not be a whole number; please round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)Millicent’s utility function is U(w) = W0.5 , where W is her wealth. She owns a “pure water” producing firm that will be worth GH100 or 0 Ghana cedis next year with equal probability. a. Suppose her firm is the only asset she has. What is the lowest price at which she will agree to sell her pure water? (Hint: price=amount that will give her the same expected utility) b. Assume that she has GH200 safely stored under her mattress, find the new lowest price at which she will agree to sell her “pure water” producing firm c. From your answers in parts (a) and (b), what is the relationship between her wealth and her degree of risk aversion?A4 The Suboptimality of Lower-Than-Cost Reserve Prices: A seller chooses to sell an object by means of a Vickrey auction. If trade occurs, the seller incurs a positive opportunity cost (i.e. c > 0). There are n > 1 bidders participating in the auction. Suppose that the all of the bidders play according to a symmetric and increasing BNE strategy. Show that the seller is always better off by setting the reserve price equal to her cost (i.e. r = c) than by setting the reserve price below her cost (i.e. r < c).
- An investor has a power utility function with a coefficient of relative risk aversion of 3. Compare the utility that the investor would receive from a certain income of £2 with that generated by a lottery having equally likely outcomes of £1 and £3. Calculate the certain level of income which, for an investor with preferences as above, would generate identical expected utility to the lottery described. How much of the original certain income of £2 the investor would be willing to pay to avoid the lottery? Detail the calculations and carefully explain your answer.1.a. What is the purpose of understanding: .contingent claims? .contingent strategies?b. How is the concept of "states of the world" useful in making decisions underrisk? Under uncertainty?c. What is meant by a unit contingent claim and why is this concept useful infinancial economics?d.Suppose that we can describe the world using two states and that two assets areavailable, asset K and asset L. We assume the assets' future prices have thefollowing distributions:Consider the constant relative risk aversion utility of wealth function from Chapter 3 for an investor with gamma parameter equal to 0.25: U(W) = W^(0.25)/(0.25) = 4W^(0.25). Suppose this investor is faced with a 50-50 bet to receive nothing or to receive 1000 dollars. What's a fair price for this bet to the investor? I.e., what is the certainty equivalent wealth (CEW) associated with this bet, for this investor
- The demand curve and supply curve for one-year discountbonds with a face value of $1,000 are represented by thefollowing equations:Bd: Price = -0.8 * Quantity + 1100Bs: Price = Quantity + 680a. What is the expected equilibrium price and quantityof bonds in this market?b. Given your answer to part (a), what is the expectedinterest rate in this marketAngie owns an endive farm that will be worth $90,000 or $0 with equal probability. Her Bernouilli utility function is u(w) =√w, where w is her wealth level (sum of initial wealth and the worth of the endive farm). 1. Suppose her firm is the only asset she has, that is, she has no initial wealth. What is the lowest price P at which she will agree to sell her endive farm before she knows how much it will be worth? 2. Redo part (1) assuming that she has $160,000 in her bank safe. 3. Compare and discuss your results in parts (1) and (2). What relationship can you find between Angie’s initial wealth level (zero versus $160,000) and her risk aversion?5 Expected Utility formulation was initially proposed as a solution to the St. Petersburg paradox (or, its predecessor). However, does it really solve all such paradoxes? More specific, consider an individual whose “little Bernoulli” utility functions is, a la Cremer, given by u(x) = x1/2. Construct a lottery similar to St. Petersburg lottery in that your lottlery, too, gives a finite prize with probability one, but not only the expected value, but also the expected utility of your lottery (calculated using the u(.) above) is not finite. Discuss how that violates EU as a solution for the St. Petersburg paradox.