Claire to be indifferent between legal and illegal activity

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Claire's utility from income is given by u = 10I – (0.001)I^2 . On her current job, she earns income of IL = 2,000 in legal work with certainty. Because Claire is responsible for handling significant amounts of cash, she has the opportunity to embezzle significant sums. Specifically, assume that she could embezzle an additional \$2,000 so that her illegal income would be II = 4,000 (\$2,000 from legal compensation and \$2,000 from embezzlement). However, if she engages in illegal activity, there is a specific probability that she will be caught and sanctioned. Assume the sanction involves loss of both the amount embezzled and half of her legal earnings so that her income if caught and sanctioned becomes I(I-s) = 1000. You can use a calculator for the calculations or enter the data into Excel so that you can copy the numeric inputs and short formulas from one part of the problem to another.

a. What probability of being sanctioned, pc, will cause Claire to be indifferent between legal and illegal activity? Solve this algebraically by setting the utility of legal work equal to the expected utility of illegal activity and solving for pc.

b. Assume that the sanction is increased so that I(I-s) if sanctioned equals 0. Under these circumstances, what probability of being sanctioned, pc, will cause Claire to be indifferent between legal and illegal activity?

c. Return to the assumptions of part (a), but now assume that there is a 10% chance of being sanctioned even if she does not engage in illegal activity. When this happens, the sanction is \$1000. (Thus, she ends up equally well off if “caught,” whether innocent or guilty.) Again, solve for the pc that makes Claire indifferent between legal and illegal activity. {Hint, now both legal and illegal activity involve some risk}. Please compare your answer to that in part (a) and comment on the effect of conviction of the innocent on the supply of crime.

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