In this question, we will study Renee's incentives when it comes to reporting unobserved income to the tax authority. Renee works as a dance teacher. Some of her students pay her in cash at the end of a class. Accordingly, Renee has the opportunity to earn cash income (in addition to other forms of payments that she reports) that are not reported to the Australian Tax Office (ATO). Her cash income is rather variable. Suppose that in a good year (G), she earns a high income, so her tax liability to the ATO is $5,000. In a bad year (B), she earns a low income, and her tax liability to the ATO is $0. The ATO knows that the probability of Renee's having a good year is 0.6, and the probability of her having a bad year is 0.4, but it doesn't know for sure which outcome has resulted for Renee this tax year. In this game, first Renee decides how much income to report to the ATO. If she reports high income (H), she pays the ATO $5,000. If she reports low income (L), she pays the ATO $0. Then the ATO has to decide whether to audit Renee