Proposition 2.6 Suppose that F is regular. Then an expected profit maximizing choice of q is given by the following: • If v (0) (0 -) c, then q(0) is the unique solution such that 1-F(@) 1- F(0) f(0) (4) =C. The corresponding expected profit maximizing t is given by t(0) = Ov(q(@)) – | vq(x))dr. Problem : Prove that the function q(@), @ <0<ö obtained by Proposition 2.6 is increasing if F is regular.
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- 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)Suppose Martha earns an of income 400 Birr currently, and her utility function is given by: U(m) = 4m, where m represents income. She has two options: Option 1: to buy a share. If she is successful her income will be 700 Birr and if she is not successful her income will be 100 Birr. Option 2: to do nothing and keep on earning 400 Birr. Assuming that success and failure are equally likely, a) What would be her expected income if she buys the share? b) What would be her expected utility of buying the share? c) Would Martha buy the share? Why? and Is Martha risk averse, risk lover or risk neutral?An executive at a publishing house has just been given two stock options as a bonus. Each option gives the executive the right (but not the obligation) to purchase one share of the publishing company's stock for $50, as long as he does it before the closing of the stock market tomorrow afternoon. When the executive exercises either option (recall, he has two), he must immediately sell the stock bought from the company at the market prize in effect at the time. An option can only be exercised once. The stock's price today is $55. The executive knows this price today before deciding what to do today. Hence, if he exercises either option today he is guaranteed a profit of $5 per option exercised. The stock price tomorrow will either be $45 or $65 with equal probability. The executive will know the price tomorrow before deciding what to do that day. This means that if he waits until tomorrow and the stock price rises to $65, he can exercise any remaining options for a profit of $15 per…
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- You are considering a $500,000 investment in the fast-food industry and have narrowed your choice to either a McDonald’s or a Penn Station East Coast Subs franchise. McDonald’s indicates that, based on the location where you are proposing to open a new restaurant, there is a 25 percent probability that aggregate 10-year profits (net of the initial investment) will be $16 million, a 50 percent probability that profits will be $8 million, and a 25 percent probability that profits will be −$1.6 million. The aggregate 10-year profit projections (net of the initial investment) for a Penn Station East Coast Subs franchise is $48 million with a 2.5 percent probability, $8 million with a 95 percent probability, and −$48 million with a 2.5 percent probability. Considering both the risk and expected profitability of these two investment opportunities, which is the better investment? Explain carefully.Suppose that instead Einar short sells 200 shares of German Power Weak Inc. at $40 each. NASDUCK now sets a margin requirement of 30%.(e) How much cash does Einar need to invest?(f) Calculate the margin call of NASDUCK if the price increases to $44.(g) Suppose the price falls to $25. How much cash can Einar take out from his margin account?(h) Suppose he takes out 50% of the amount in part (g). At what price threshold will Einar face a margin call by NASDUCK?Seung's utility function is given by U - C^(1/2), where C is consumption and C^(1/2) is the square root of consumption. She makes $50,625 per year and enjoys jumping out of airplanes. There's a 5% chance that in the next year, she will break both legs, incur medical costs of $30,000, and lose an additional $5,000 from missing work. a. What is Seung's expected utility without insurance? b. Suppose Seung can buy insurance that will cover the medical expenses but not the forgone part of her salary. How much would an actuarially fair policy cost, and what is the expected utility if she buys it? Policy cost: $___ Expected utility: ___ c. Suppose Seung can buy insurance that will cover her medical expenses and foregone salary. How much would such a policy cost if it's actuarially fair, and what is her expected utility if she buys it? Policy cost: $___ Expected Utility: ___