An investor with initial wealth $20000 and utility function U(x) = In(x) is considering an investment that has a 80% chance of gaining r% and a 20% chance of losing s%. (1) Find in terms of r and s the certainty equivalent of this investment. (2) If s = 10, find the range of values of r for which the investor will avoid this investment.
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- Suppose that there are two types of workers: high and low. Employers cannot distinguish between different types during an interview. Employers value high type at $200,000 and low type at $100,000. Employers are in a competitive market (i.e. zero profit applies). High type workers have a reservation wage of 140,000 and low type workers have a reservation wage of 80,000. Suppose that 50% of all workers are high type. The productivities, reservation wages, and the probabilities are common knowledge). What wage would the employers offer? Please explain the solution!Farmer Brown faces a 25% chance of there being a year with prolongeddrought, with zero yields and zero profit, and he faces a 75% chance of a normal year, with good yields and$100,000 profit. These probabilities are well-known. Suppose that an insurance company offered a droughtinsurance policy that pays the farmer $100,000 if a prolonged drought occurs. Assume that the farmer’sutility function is u(c) = ln(c). He has initial wealth of $40,000. What is the economic intuition on why X > Y? Confine your answer to at most three sentences.The investor is considering how to optimally invest 1000 euros in stocks and bonds. Let's assume that the optimal decision is made based on expected utility. Suppose the investor has a utility function u(x)=ln(1+x), where x is their wealth. Let y be the proportion invested in stocks and 1−y be the proportion invested in bonds. By investing in stocks, the investor earns 1% with a probability of 39.5% and 4% with a probability of 60.5%. By investing in bonds, the investor earns a certain 2.8%. What proportion of the investment will the investor allocate to stocks and what proportion to bonds?
- An individual has a utility function U(W)= √w. where W is the level of wealth.They have been offered a gamble with a payout of 100 with a probability of 0.31 and a payout of ￡35 with a probabiity of 1-031.The Certainty Equivalent of this gamble is:Q1) An expected utility maximiser owns a car worth £60000£60000 and has a bank account with £20000£20000. The money in the bank is safe, but there is a 50%50% probability that the car will be stolen. The utility of wealth for the agent is u(y)=ln(y)u(y)=ln(y) and they have no other assets.2.4 The opening 2018 World Cup odds against being the winning team specified by espn.com were 9/2 for Germany, 5/1 for Brazil, 11/2 for France, 20/1 for England, and 7/1 for Spain. Find the corresponding prior probabilities of winning for these five teams.
- Question 2An investor is to purchase one of three types of real estate, as illustrated inFigure below. The investor must decide among an apartment building, anoffice building, and a warehouse. The future states of nature that willdetermine how much profit the investor will make are good economicconditions and poor economic conditions. The profits that will result fromeach decision in the event of each state of nature are shown in Table below: Assume that it is now possible to estimate a probability of 0.60 that goodeconomic conditions will exist and a probability of .40 that poor economicconditions will exist. a) Determine the best decision by using expected opportunity loss. b) Develop a decision tree, with expected values at the probability nodes. c) Compute the expected value of perfect information."Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $1,480,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.The probability of a small box office earning $203,000 is 0.27. The probability of a medium box office of $1,660,000 is 0.49, and the probability of a large box office of $2,950,000 is 0.24.Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $20,000 to get the novel evaluated by the movie critic.The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.If the movie will have a large box office, there is a 0.75 probability the critic will have a favorable opinion.If the movie will have a medium…"Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $1,460,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.The probability of a small box office earning $210,000 is 0.27. The probability of a medium box office of $1,530,000 is 0.64, and the probability of a large box office of $3,190,000 is 0.09.Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $21,000 to get the novel evaluated by the movie critic.The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.If the movie will have a large box office, there is a 0.61 probability the critic will have a favorable opinion.If the movie will have a medium…
- Mf. Mean variance utility defines risk using certainty equivalent wealth. The lower the certainty equivalent wealth, the lower the mean variance utility. uestion Select one: O True O False Under constant relative risk aversion, the lower the certainty equivalent wealth is than the average wealth of a lottery the riskier the lottery. Select one: O True O False Given a normally distributed risky asset and a risk free asset, a person with a lower CRRA risk aversion coefficient will put less in the risk free asset than a person with a higher CRRA risk aversion. Select one: O True O False Greater risk aversion means a plot of utility vs. wealth would look less curved. Select one: O True O False The greater the wealth, the less the utility of the next dollar of wealth. Select one: O True O False People don't like risk because it means they get poorer when they're poorer and richer when they're rich. In fact, a financial security…True/False a. Consider a strategic game, in which player i has two actions, a and b. Let s−i be some strategy profile of her opponents. If a IS a best response to s−i, then b is NOT a best response to s−i. b. Consider the same game in (a). If a IS NOT a best response to s−i, then a does NOT weakly dominates b. c. Consider the same game in (a). If a mixed strategy of i that assigns probabilities 13 and 23 to a and b, respectively, IS a best response to s−i, SO IS a mixed strategy that assigns probabilities 32 and 13 to a and b, respectively. d. Consider the same game in (a). If a mixed strategy of i that assigns probabilities 13 and 23 to a and b, respectively, is NOT a best response to some strategy profile of her opponents, s−i, NEITHER is a mixed strategy that assigns probabilities 32 and 13 to a and b, respectively. e. Consider the same game in (a). If a IS a best response to s−i, SO IS any mixed strategy that assigns positive probability to a. f. Consider the same game in (a). If a…Suppose that an individual is just willing to accept a gamble to win or lose $1000 if the probability ofwinning is 0.6. Suppose that the utility gained if the individual wins is 100 utils. What is expected gains/loss.
