Consider the problem of an entrepreneur/borrower with no money and a project requiring L=200 to be carried out. Assume that the borrower cannot use his illiquid assets to finance the project. The entrepreneur Once the entrepreneur undertakes the project, she decides either to work hard or to shirk. • If she works hard, then she earns a high return R=$500 with probability p=0.75 and earns nothing with probability (1-p)=0.25. If she shirks, she earns a high return with probability q=0.25 and earns nothing with
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- 9) A risk-neutral individual with current wealth w has already decided investing all his wealth in a project that has two possible net wealth outcomes wn and we (with probabilities pr and pe, respectively) where wr > w > we > 0, PrPe E (0,1), and pr + Pe = 1. Before he invests, he realises that there is a source of information that tells the individual which outcome will be realised with truth, what is the value of this information for the individual? a) pe(@ – w;), b) (Pn – Pe)w, c) Phwn + PeWe – w, d) Pr(w – wn).One investment option will give a guaranteed income of $100,000. An alternative option is risky - there is a 80%chance of earning $62,500 and 20% chance of earning $250,000. A risk-averse person will choose the guaranteed income of $100,000 over the risky option. True O False2 Consider the two investments listed below with possible outcomes and probabilities: INVESTMENT (in $1000) SAFE RISKY INVESTMENT AMOUNTⓇ 40+ 40+ GOOD SCENARIO OUTCOME 45+ 80+ AVERAGE+ SCENARIO PROB OUTCOME 0.40* 0.40€ 42+ 45+ BAD+ SCENARIO PROB OUTCOME PROB 0.20 35+ 0.20 10+ 0.40€ 0.40+ b) a) Suppose I have utility function U(*) = (x)2. What is the expected utility from each investment? Which investment will I choose, if any? Show and explain your work and provide the intuition. c) What is the value of the risk premium for the SAFE investment? Show and explain your work and provide the intuition. d) What is the value of the risk premium for the RISKY investment? Show and explain your work and provide the intuition.< +
- Tasha is planning to invest in a farming project in 2022, but has a reservation given the different forecast (declined (D),the average (A) and takeoff (T)of the economy. She uses the following to guide her decision making. (i) there is 25% chance she will invest if there is a forecast of declined (ii) there is a 75% chance she will invest if there is a forecast of average growth and (iii) there is a 55% chance of investing if there is a forecast that economy will takeoff. Tashanna believes that for 2022 there is a 20% chance of decline and a 40% chance of average growth and a 40% chance the economy will take off. Based on these probabilities what is the chance that Tattiana will invest in the farming project if the stated forecast hold?An investor with capital x can invest any amount between0 and x; if y is invested then y is eitherwon or lost, with respectiveprobabilities p and 1− p. If p > 1/2, how much should be invested byan investor having a exponential utility function u(x) = 1 − e −bx ,b > 0.Suppose that the buyers do not know the quality of any particular bicycle for sale, but the sellers do knowthe quality of the bike they sell. The price at which a bike is traded is determined by demand and supply.Each buyer wants at most one bicycle.(ii) Assuming that each buyer purchases a bike only if its expected quality is higher than the price,and each seller is willing to sell their bike only if the price exceeds their valuation, what is theequilibrium outcome in this market?
- Subject 2 A bottle company ALPHA, is considering creating a new bottle of 0.25 lt. To decide whether to invest in this projector not, they performed market research that costed €5,000. The results indicated two possible scenarios that depend on the competitor's reaction to create a similar product and on the percentage of the faithful customers of ALPHA. ScenarioA has a 45% chanceto be realized, while scenarioB has a probability of 55%. For the project's realization the company must purchase specialmachinery that cost €80,000, while transportation and installation costs amount to €2,000. The useful life of the project is two years, and the machinery can be sold at the end of the useful life for €30,000.Table 1 presents the pertinenteconomic data. At the end of the second year the working capital is going to be recaptured. The tax rate is 25%, the weighted average cost of capital is 10% and the company fully depreciates fixed assets for tax purposes, using the straight-line depreciation…Suppose that there is limited commitment in the credit market, but lenders are uncertain about the value of collateral. Each consumer has a quantity of collateral H, but from the point of view of the lender, there is a probability a that the collateral will be worth p in the future period, and probability 1 - a that the collateral will be worthless in the future period. Suppose that all consumers are identical. (a) Determine the collateral constraint for the consumer, and show the consumer’s lifetime budget constraint in a diagram. (b) How will a decrease in a affect the consumer’s consumption and savings in the current period, and consumption in the future period? Briefly explain your results. Please do fast ASAP fastSuppose that the consumer is asked to contemplate a gamble with a probability of 60% of winning Birr 10,000 with a utility of 10 utils, and a 40% probability of winning Birr 15,000 with a utility of 12 utils. A. What will be the expected income and expected utility of the consumer? B. If the utility of this consumer from a risk free alternative which gives him an income equal to the expected income of the risky alternative given above is equal to 11 utils, is this consumer risk lover or risk averse? Why? Illustrate your answer with the help of a diagram
- efer to the following table showing the probability distribution of payoffs from an activity to answer the question below: Units Payoff Probability 1 $30 10% 2 40 25% 3 60 30% 4 50 20% 5 10 15% What is the expected value?Sam, after taking a $200 loan from the bank to finance an investment that pays $1000 50% of the time and $0 50% of the time at a 100% interest, discovers another riskier investment that pays out $5,000 but only 10% of the time, while the other 90% of the time it pays zero. Would the he want to switch to the riskier investment? Question 4 options: Yes because his return has increased No because his liability to the bank has increased No because his return has decreased None of the aboveMarcus is an expected utility maximizer with the Bernoulli utility function u(w) = √w. He faces a gamble in his wealth. In a good state he gets 81 and in a bad state he gets 9. He can take out an insurance plan which will leave him with a wealth of 49 in each state. (a) (b) (c) state? Is Marcus risk averse? Will he purchase the insurance if the probability of the states is ½ for each Let p denote the probability of the good state. For what value(s) of p will Markus be just indifferent between taking out the insurance and not taking it out? Show your working.