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- 1. A woman with current wealth X has the opportunity to bet an amount on the occurrence of an event that she knows will occur with probability P. If she wagers W, she will received 2W, if the event occur and o if it does not. Assume that the Bernoulli utility function takes the form u(x) = -e-rx with r>0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA?1. A woman with current wealth X has the opportunity to bet an amount on the o ccurrence of an event that she knows will occur with probability P. If she wager s W, she will received 2W, if the event occur and if it does not. Assume that t he Bernoulli utility function takes the form u(x) = -e-TX with r> 0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA?Economists John Maynard Keynes and John Hicks argued that, if hedgers tend to holdshort positions and speculators tend to hold long positions, the futures price of an assetwill be below the expected spot price. This is because speculators require compensationfor the risks they are bearing. They will trade only if they can expect to make money onaverage. Hedgers will lose money on average, but they are likely to be prepared toaccept this because the futures contract reduces their risks This is from John Maynard Keynes. My question is i dont understand this statement. Why is the future price of an asset to be below the expected spot price if speculators are the main determinant of the future price, they have a long contract which means they will earn money if the spot price is above the expected spot price
- A person's utility function is given by U(x, y, z) = 7xyz, where x, y, z denote then number of units of three commodities X,Y, and Z that the person consumes. The pricesr per unit of X,Y, and Z are 5 euro, 1 euro, and 3 euro respectively. If ther person has a budget of 270 euro, the person's utility is maximised when they consume units of X, units of Y, and units of Z. The person's maximum utility is If the person's budget is increased to 271 euro, then using the method of lagrange multipliers we find that the maximum utility is approximatelySituation 1 Suppose you have won $1000 on a game show. In addition to these winnings, youare now asked to choose between Option A: 50% chance of winning $1000 and 50% chance of winning nothing Option B: winning $500 for sure. Situation 2 Suppose you have won $2000 on a game show. In addition to these winnings, youare noW asked to choose between Option C: 50% chance of losing $1000 and 50% chance of losing nothing Option D: losing $500 for sure. They found that respondents are much more likely to choose Option B in the first case and Option C in the second case. Suppose the respondents are not indifferent between options. Show that their choices are inconsistent with the Expected Utility Theory.In the field of economics, utility is a measure of how much benefit consumers derive from certain goods or services. From a finance standpoint, it refers to how much benefit investors obtain from portfolio performance. Then, what is the meaning of utility maximization? For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). в Iу SРaгagraph 10pt A I Arial ... P O WORDS POWERED BY TINY > I! > !!! >
- 2. Alice believes that her car would cost £12500 to replace if it was stolen or damaged. Based on crime statistics for the area she lives in, she believes that the probability of her car being stolen or damaged is 0.15. (i) Alice's utility function is given by U(w) = ln(w) for w > 0 and she as £35000 in the bank. Calculate how much Alice would be prepared to pay (in a single payment) to insure her car against theft or damage (ii) Repeat the calculation in the previous part but now assume Alice has £500000 in the bank.Im confused which one is correct: option A or option D??Assume Person A is offered the following game: If they want to participate in the game, theywill need to pay £5. If they participate, they can choose between Option A and Option B.Option A consists of spinning a roulette wheel with 37 different numbers (18 red, 18 black,and 1 green). If the outcome is red, the participant receives £10 and £0 otherwise. Option B isa fair coin flip that yields £5 when heads comes up and £10 when tails comes up.(a) What is the expected value of Option A?(ii) What is the expected value of Option B?(iii) What is the expected value of participating in the game and choosingOption A?(iv) What is the expected value of participating in the game and choosingOption B?(v) How much would the game need to cost to make it a fair game when youchoose Option A?(vi) How much would the game need to cost to make it a fair game when youchoose Option B?(b) Person A chooses to participate in the above described game. Which of thefollowing options can be true regarding…
- For a given option portfolio, you are long vega (value increases as volatility goes up), and short theta (as time passes your options portfolio loses money). Are you net long or short options? Net long, because as volatility goes up and it increases in value and as time passes you lose value. Net short, because as volatility goes up and it decreases in value and as time passes you increase value. not consistent you are long one and short the other, so can't tell completely independent derivatives, its apples and oranges and no reflection on your portfolio4) Luke is planning an around-the-world trip on which he plans to spend $10,000. The utility from the trip is a function of how much she spends on it (Y ), given by U(Y) = InY a). If there is a 25 percent probability that Luke will lose $1000 of his cash on the trip, what is the trip's expected utility. b). Suppose that Luke can buy insurance to fully against losing the $1,000 with a actuarially fair insurance. What is his expected utility if he purchase this insurance. Will he purchase the insurance? c). Now suppose utility function is U(Y) = Y/1000 What is his expected utility if he purchase the insurance in b). Will he purchase the insurance?an entrepreneur is setting up a storage facility which will provide storage bothat peak times and off peak times.The entrepreneur need to decide how much money storage Q1 t to supply at peak times, and how much storage Q2 to supply off peakit also needs to decide how to set up capacity K, where capacity is such that both K is equal or plus Q1 and K is equal or plus Q2The peak period demand fan storage is given by PI=7200 -Q1 and the off peak is give by P2=5400 -Q2 where P1 and P2 are the prices for units of storage at peak times and off peak respectively.the variable cost is 200 per unit of storage supplied and capacity costs are 100 per unit. Hence profits fpr the entrepreneurs are given by:(7200-Q1) Q1+ (5400-Q2) Q2 - 200 (Q1+Q2)-100 K where Q1 is less or equal K and Q2 is less or equal Ka) write down the Kuhn-Tucken conditions for this proble. b) Find the optimal outputs and capacity for this problemc) now suppose there is a substancial increqse in capacity costs, which rise to 2000…