Magnitude effect Suppose that the utility function is given by u(z, t) = 8^TZ ^a, 0 < a < 1; Z, T is an outcometime pair, and 8 is a discount factor. Consider two alternative prizes z, zo z < zo. Suppose that a, b are the compensations required by the decision maker to delay the respective. rewards, z, zo, by one time period. Show that EDU implies that z/(z+a) = z /(z'+b'), while the magnitude effect implies that z'/(z'+b) < z/(z+a). 1
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- Optimal compensation. Ineffi Inc. is considering hiring Dr Jameela Knows- better to streamline its operations in Northern Montana. If successful, the project will yield a payoff of $100,000. If unsuccessful, it will bring a loss of $20,000. The outcome of the project crucially depends on Dr Knowsbetter's effort, which can take only two values: High or low. When effort is high, the project is suc- cessful with probability ph with probability pi at $15, 000. Exerting low effort costs her $10,000 less than that. In case it does not hire Dr Knowsbetter, Ineffi will have to turn to the next best candidate for the task, that is estimated to bring a net value of $20,000 to the company. If Dr Knowsbetter does not get this gig, she will go on a vacation in a Maldives' resort with her girlfriends. She values the vacation at $20, 000. Assume throughout that wage compensation must be non-negative. 0.9. When effort is low, the project is successful = 0.7. Dr Knowsbetter values the cost of exerting…Utility functions incorporate a decision maker’s attitude towards risk. Let’s assume that the following utilities were assessed for Danica Wary. x u(x) -$2,000 0 -$500 62 $0 75 $400 80 $5,000 100 Would a risk neutral decision maker be willing to take the following deal: 30% chance of winning $5,000, 40% chance of winning $400 and a 30% chance of losing $2,000? Using the utilities given in the table above, determine whether Danica would be willing to take the deal described in part a? Is Danica risk averse or is she a risk taker? What is her risk premium for this deal?Consider the following game, with a risk-neutral principal with preferences π = q - w hiring an agent 2, and the agent can = with preferences U = √w- - e.. The agent's reservation utility is given by U choose between an effort level of 0 or an effort level of 10. Output is either 0 or 400 and follows the following probability distribution, a function of effort level and some uncertain factor: Probability (q=0) Probability (q=400) 0.4 0.9 e=0 0.6 e-10 0.1 a) Illustrate this game of moral hazard using a fully labeled game tree with payouts.
- A manager is deciding whether to build a small or a large facility. Much depends on the future demand that thefacility must serve, and demand may be small or large. The manager knows with certainty the payoffs that willresult under each alternative, shown in the following payoff table. The payoffs (in $000) are the present values offuture revenues minus costs for each alternative in each event.What is the best choice if future demand will be low?Suppose that the expected value of weekly profits for an ice cream shop, before paying the manager, Amy, is where e is Amy's weekly avertime hours. Amy is risk-neutral but incurs a cost for working overtime. Thus, tatal expected surplus is What level of effort maximizes total surplus? The value of overtime that maximizes total surplus is e-hours. (Enter your response rounded to one decimal place.) E(x)=500+10c C(e)=² E(S)-[(x)-C(e).A clothing manutacturer must decide which of two clothing lines to emphasze for the spring season, her usual line or a budget line Her success with each line depends on the sta Budget Line Usual Line Strong Economy 15,000 35,000 In-between Economy 18,000 28,000 Weak Economy 27,000 10,000 Economists believe that there is a 5% chance of a strong economy next year, a 75% chance of a weak economy, and a 20% chance of an in-between economy Use the payoff m O A. Emphasize the usual line O B. Wait and see O C. Emphasize the budget line
- A new government lottery has been announced. Each person who buys a ticket submits an integer between 0 and 100. The winner is the person whose submission is closest to four-fifths of the average of all submissions. If ties occur, the price will be shared. If Chloe expects other players to select numbers randomly, what number should she choose? Chloe should choose the number (a)_____ if you expect all other players to exhibit the same depth of reasoning as Chloe, what number would you choose? you should choose the number (b)______Consider the St. Petersburg Paradox problem first discussed by Daniel Bernoulli in 1738. The game consists of tossing a coin. The player gets a payoff of 2^n where n is the number of times the coin is tossed to get the first head. So, if the sequence of tosses yields TTTH, you get a payoff of 2^4 this payoff occurs with probability (1/2^4). Compute the expected value of playing this game. Next, assume that utility U is a function of wealth X given by U = X.5 and that X = $1,000,000. In this part of the question, assume that the game ends if the first head has not occurred after 40 tosses of the coin. In that case, the payoff is 240 and the game is over. What is the expected payout of this game? Finally, what is the most you would pay to play the game if you require that your expected utility after playing the game must be equal to your utility before playing the game? Use the Goal Seek function (found in Data, What-If Analysis) in Excel.Suppose that a decision maker faced with four decisions alternatives and four state of nature developing the following profit payoff table: Outcomes Alternatives S1 S2 S3 S4 A1 14 9 10 5 A2 11 10 8 7 A3 9 10 10 11 A4 8 10 11 13 Use Maximax, Maximin, Criterion of realism (? = 0.55, and ? = 0.4), Laplace, and Minimax regret to find the best alternative.
- Behavioral evidence suggests that the likelihood of both fifirms choosing high prices can be increased if their executives can (A) engage in informal communications and signal their intention to keep high prices; (B) play mixed strategies; (C) use the K-level thinking; (D) none of the above.You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…CENGAGE MINDTAP News Analysis: Go for the Video Bonus While spending the weekend in New York City, Andrew, Beth, and their son, Darnell, are lucky enough to hail the Cash Cab for their taxi ride. During their ride, they win $100 for correct answers and receive only one strike for a wrong answer, so at the end of the ride they are eligible for the video bonus question. Their vacation budget before entering the cab was $400, and based on their understanding of the type of bonus question they'll be asked, they believe they have a 70% chance of getting the question right. As explained in the article, if they answer the video bonus question correctly, they will double their winnings, but if they miss the video bonus question, they will lose all of what they had previously won. Alternatively, they can choose not to play for the bonus and walk away with their winnings from the cab ride. The following graph shows the cab riders' utility as a function of their total vacation budget. For…