# Mark wants to maximize his expected utility. His preferences are represented by the utility function U(y) = y 1 2 where y is a monetary

Mark wants to maximize his expected utility. His preferences are represented by the utility function U(y) = y 1 2 where y is a monetary payoff. Mark is offered the following bet on the toss of a coin by Amanda; • If the coin comes up tails Amanda pays Mark £1, 000 • If the coin comes up heads Mark pays Amanda £1, 000 Mark’s initial capital is £10, 000 which he retains in its entirety if he does not take the bet. 1. What is Mark’s expected utility if he accepts the bet? 2. Will he accept the bet? Explain your answer. 3. Is Mark risk averse, risk neutral or risk loving? Explain your answer. 1 Amanda offers Mark an alternative bet whereby if the coin comes up tails Amanda gives him £10, 000 but if the coin comes up heads Mark gives Amanda his entire £10, 000. 4. Show that Mark does not accept this bet. Amanda offers Mark yet another alternative bet whereby Mark still loses his entire £10, 000 if the coin comes up heads, but if the coin comes up tails Amanda pays him£50, 000. 5. Does Mark accept this new alternative? Explain your answer. 6. Given that Mark loses his entire£10, 000 if the coin comes up heads, what is the smallest amount that Amanda has to pay Mark in the event of tails in order to persuade him to take the bet? All of these ways in which the poor cope with risk tend to be very costly. This has been well documented for agriculture: In India, poor farmers use farm inputs in a more conservative but less efficient way when they live in areas where rainfall is more erratic. Poor farmers’ profits rates go up by as much as 35 percent when they live in areas where the yearly rainfall pattern is very predictable. (a) Using the concepts studied last class, can you explain why poor farmers might choose to use farm inputs in a “less efficient way”? Does it mean that poor farmers are not rational? ( explain briefly. One or two sentences are enough) (b) Can you think of a possible Pareto improving trade between the farmer and some other economic agent? Explain briefly. (c) How do economists explain the fact that these Pareto improving trades are difficult to come about? Explain briefly Part B. (d) A farmer must choose whether to invest in the purchase of an input (say a fertilizer). By investing, the farmer faces the following income prospect (assume that he does not have any other source of income). Normal rain Little rain Invest $1000 $100 And by not investing Normal rain Little rain Not Invest $800 $200 Assume that the probability of the event “Little rain” is equal to α = 1 10 (and the probability of the event “Normal rain” is 1 − α = 9 10 ). If the farmer is risk neutral, will the farmer invest or not? Explain (e) Stop assuming that the farmer is risk neutral, but keep the same assumptions as in (1d). Assume that the farmer has preferences represented by the utility over monetary outcomes u(x) = 120 − 8000 x (1) Will a farmer with the above preferences invest or not? Explain (f) Now assume that a (risk neutral) insurance company offers the policy that pays $C if the event “Little rain” occurs. Assume that the policy is fairly priced: How much is the premium that the insurance company charges? (g) Keep assuming that insurance company offers a fairly priced policy. However the insurance company does not fix the coverage C, but lets the customer choose C. Under these assumptions, will the farmer with preferences described in the point (1e) invest or not? Will he buy insurance? If so, how much coverage C will he choose? (h) Now assume that there are two types of farmers: The farmer we met before (call him L) and a farmer who lives in a slightly different microclimate (call this farmer H). Assume that farmer H is identical to farmer L apart for one thing: In the microclimate in which farmer H lives, the probability of the event “Little rain” is equal to αH = 0.2. If the insurance company can distinguish between the two farmers and offer different insurance policies, what is the fair premium for the farmer H? Will he buy insurance? How much? will he invest? (i) Now assume that the insurance company cannot distinguish between the two types of farmers. And assume that the proportion of H farmers is equal to 0 < q < 1. Without making any calculations can you explain why in such a situation we can have "adverse selection". Be as clear as you can. Describe your target market. Consider both B2C (business to consumer) and B2B (business to business) customers, with as much detail as possible include demographics (factual data) and behavioral characteristics (attitudes and behaviors) when identifying your target market. At the end of this section, the audience should be convinced that you have selected a target market for your business that is suitable for e-commerce. Statement: The business is selling handmade knitwear. Pieces will include clothing articles, and accessories such as slippers, hats, headbands, etc. The people chosen as the target market are: Men, women, kids and pets (cats and dogs)

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