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How much income will he conceal (i.e., fail to report) if the probability of being caught is 0.1? Leo, who has a utility-of-wealth function U

How much income will he conceal (i.e., fail to report) if the probability of being caught is 0.1?

Leo, who has a utility-of-wealth function U(w) = ln(w + 10), has $500 of income before tax and is taxed at a rate of 25% of earned income. If he is caught underreporting his income he will have to pay the taxes owed and in addition will pay a fine of $2 for every dollar of income he failed to report.

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