A taxpayer has income y that should be reported in full to the tax au- thority. There is a flat (proportional) tax rate r on income. The reporting technology means that that taxpayer must report income in full or zero income. The tax authority can choose whether or not to audit the taxpayer. Each audit costs an amount rp and if the audit uncovers under-reporting then the taxpayer is required to pay the full amount of tax owed plus a fine F .
1. Set the problem out as a game in strategic form where each agent (taxpayer, tax-authority) has two pure strategies.
2. Explain why there is no simultaneous-move equilibrium in pure strategies.
3. Find the mixed-strategy equilibrium. How will the equilibrium respond to changes in the parameters r, rp and F ?