Uncertainty and Risk - DARP

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Microeconomics CHAPTER 8. UNCERTAINTY AND RISK Exercise 8.2 You are sending a package worth 10 000AC. You estimate that there is a 0.1 percent chance that the package will be lost or destroyed in transit. An insurance company o¤ers you insurance against this eventuality for a premium of 15AC. If you are risk-neutral, should you buy insurance? Outline Answer: No you should not. Your expected loss is 10 euros whereas the premium is 15 euros. cFrank Cowell 2006 116
Microeconomics Exercise 8.3 Consider the following de…nition of risk aversion. Let P := f(x ! ; ! ) : ! 2 g be a random prospect, where x ! is the payo¤ in state ! and ! is the (subjective) probability of state ! , and let Ex := P !2 !x ! , the mean of the prospect, and let P := f(x ! + [1 ]Ex; ! ) : ! 2 g be a “mixture” of the original prospect with the mean. De…ne an individual as risk averse if he always prefers P to P for 0 < < 1. 1. Illustrate this concept in (x red ; x blue )-space and contrast it with the concept of risk aversion used in the text 2. Show that this de…nition of risk aversion need not imply convex-to-theorigin indi¤erence curves. Outline Answer: 1. See Figure 8.1. x BLUE P P λ P x RED Figure 8.1: Nonconvex indi¤erence curve 2. Let P be the prospect and P its mean. P can be any point in the line joining them. The de…nition implies that moving along this line towards P puts the person on a successively higher indi¤erence curves. In Figure 8.1 it is clear that this condition is consistent with there being indi¤erence curves that violate the convex-to-the-origin property locally. cFrank Cowell 2006 117
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