The first screenshot is the question and the last two screenshots are the answers, please use the answers as they guidance to help you answer this question, please explain the first question step by step clearly and say how to approach this answer in the correct way! Please emphasise on the explanation part, eg what does the symbol alpha, dash, s mean, what theories have they used this questions, any reference study links? Thank you!

1. (a) With the continuity axiom we assume there is such a probability. If o; is sufficiently high the lottery will be preferred and if it is sufficiently small a; will be preferred so it does seem reasonable to assume that there is some value inbetween that gives indifference (even when the worst outcome is death or maybe not - you can express your own opinion!!!). In lotteries that only have the best or the worst outcomes, it is rational to prefer the one that has the higher probability of the best outcome (monotonicity). So you can't be indifferent between two lotteries if the probability of the best outcome is different. (b) utility 1 em 97 - 2 cm 0.8 1+25 cm 0:71 0.6 0.4 0.3 0.2 0 10 20 30 40 50 60 70 :90 100 wealth 64 149 25 36 EV = 85.6 CEN84 1Risk aversion can be illustrated by considering a lottery, say (((0.5, 0), (0.5, f100) and showing the expected utility (0.5) is less than the utility of the expected value (0.71). This will be true when the chord is below the curve. (c) EU(r) = 2x0.1+2x0.2+2x0.3+2x0.4+2 x0.5+-x0.6 = 0.35 EU(s) = - x 0.32 + - x 0.5 = 0.41 So they will prefer s to r. (d) Their preferences are not consistent with the axioms. (e) utility EU EUI u(w ) EV1 WAV -25 1 W 1 WAV -8 W + V Wealth WAV - 20 WtV - 10 Let w be the starting wealth. Before the change EU = 0.6U (w + v) + 0.4U(w +v -20) In the diagram EU is above U(w) so this person will choose to cheat. Both proposals give the same expected value, w tv - 10, but the second proposal has a lower expected utility (EU2). For this person, the first proposal will still not deter cheating (EV1 > U(w)).1. A student randomly picked from the class is asked to reveal the prob- ability as, for which are N (((l _ 0:17): 0): (053: 100) for amounts of money from 0 to 100. The values revealed are given in the table (a) (b) (1') 3;, 0 .85 10 .620 40 .670 100 a, 0 0.22 0.32 0.45 0.63 0.84 1 Is it reasonable to assume that there is such a probability for each amount of money? Why can't there be more than one probability for a particular amount of money? Do a rough sketch of the student's utility function (with 1cm for every 10 on the x-axis and 1cm for every 0.1 of utility on the y-axis). Show how you can use this diagram to demonstrate that the student is risk averse. According to expected utility theory, in a choice between 2 lotter- ies, the student will pick the one which gives the highest expected utility. Use the rough sketch to predict which lottery they will take in a choice between the lotteries r and s in section 1.2 of the notes. If they don't pick the one with the higher expected utility then in which sense can we say that they are irrational? Suppose that although we do not have this much information about every student, we do know that all students are risk averse. The School of Economics wants to deter cheating during exams. Suppose that at present there is a 0.4 chance of being caught cheating and a xed ne of .6 20 for those caught. There are two proposals. First, to increase the number of invigilators so that the probability of being caught rises to 50%. Second, to raise the ne to 25. Committing the crime is worth .81; (which you keep even when you are caught!!!) where 10