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Karen works 50 hours per week. She can work legally as a book keeper and earn...

Karen works 50 hours per week. She can work legally as a book keeper and earn $50 per hour. Alternatively, she can work illegally by helping clients evade taxes for $150 per hour. Karen can only choose one occupation or the other. If she chooses illegal work, the probability of being caught is 0.3, and if caught, Karen will face a penalty of $150 per hour of illegal activity. (Note: if Karen is caught, she retains the proceeds from her illegal activity, but must pay the fine. Suppose Karen’s utility function is given by u(y) = y , where y is her weekly income. (a) Will Karen choose the legal or illegal activity? Explain. (b) Now suppose Karen has an additional option. She can undertake part time employment as a legal book keeper for 30 hours per week and devote 20 hours per week to illegal activities. Does Karen work only legally, only illegally, or both? Explain. (c) Suppose again that Karen can only choose to spend all her time legally or all her time illegally. If the police or justice system want to deter Karen from ever committing the illegal activity (given that her only choices are as given in earlier parts of this question), what is the minimum probability with which they must catch her committing the crime?

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