Consider the simultaneous move game between taxpayer and tax inspector

Question 2 [16 pts.) Consider the simultaneous move game between a taxpayer and a tax inspector. The taxpayer chooses whether to truthfully report his taxable income or to underreport it. The tax auditor chooses whether or not to audit the income report. The cost of auditing is c :> 1, and the ne (including tax payment} imposed ifthe taxpayer is caught cheating is F (with F >- c >- 1). With a truthful report the taxpayer has to pay a tax of 1 unit ofincome. The payoffs are given in the Table 1, where the rst number in each cell denotes the tax inspector's payoff and the second number is the taxpayer's payoff: Table 1 Truthful re -ort a) (4 p15.) Calculate the pure strategy Nash equilibria (if any). Sh ow ALL STEPS. b) (2 p15.) Briey explain why (Audit,Under report) is not a pure strategy Nash equilibrium. :1 [6 pts.) Calculate the mixed strategy Nash equilibria [of any). Show ALL STEPS. d) [2 pts.) Calculate the responsiveness of the optimal probability of audit, p\