(f) The reason students don't cheat is only related to an expected utility calculation, discuss! 2. Our student in question 1 faces a probability of 0.4 that their laptop will be stolen. They have .8 100 and will have to spend 36 to replace it. Let W2 be their wealth when their computer is stolen and W1 when it is not. So without insurance we have W1 2 100 and W2 2 64. (a) (b) (C) (61) Use the rough sketch in 1b) to nd the certainty equivalent of the lottery they are facing. On an accurate sketch the marginal utility at 100 is % and at 64 is %. Check that this is close to what you have on your sketch. Sketch the indifference curve for their expected utility that goes through the point (100, 64} (with wealth when the computer is stolen on the yaxis and wealth when it is not stolen on the zit-axis). Hint: it will also go through the certainty equivalent calculated in part a) on the 45 degree line. Using the accurate marginal utilities from part a), show that for expected utility, the marginal rate of substitution of wealth in state 2 for wealth in state 1 at the point (100, 64) is %. How would you explain this to a 10 year old? Explain why risk aversion implies that the marginal rate of sub- stitution is diminishing. What is the MRS at the 45 degree line? A student randomly picked from the class is asked to reveal the prob- ability a, for which mi~(((1_ aaola (at: 100) for amounts of money from 0 to .f,' 100. The values revealed are given in the table (a) (b) (d) (8) 22,; 0 5 10 20 40 70 100 or, 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 xaxis 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 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 1: (which you keep even when you are caught!!!) where 10