Question 6. Consider a taxpayer with exogenous income 3; > 0 who faces a tax rate t, where 0

Question 6. Consider a taxpayer with exogenous income y > O who faces a tax rate t, where O < t < 1. She is asked to report an income level a; to the government and pay taxes according to the report, i.e., tr. If the taxpayer is honest, she will report x = y, but she may cheat by reporting a lower income O < x < y. Let z = y a; represent the amount by which income is understated. The government does not know the true income y and must enforce compliance through a system of audits and penalties. Assume that the enforcement policy, known by the taxpayer, is to audit reports with probability p, where p e (O, 1) is constant. If there is an audit, we assume that the government always ends up learning the true income of this individual y. If the taxpayer is caught cheating, she must pay a penalty O on each dollar of income evaded, Oz, in addition to the evaded tax. Assume that the taxpayer is risk averse, meaning her utility is increasing and concave in income, and that she maximizes expected utility. 1. For any z, where O z < y, write the income the taxpayer will receive in each one of the two possible situations, i.e., there is an audit and if there is no audit (notice that the choice variable for the consumer is z) 2. Calculate the minimum value of t such that she does choose to cheat. 3. Suppose that an inner solution exists, and denote it by z* e (O, y). Prove that z* decreases in the probability of being audited, p, and in being fined, 0. What's the effect of the tax rate t on