Tax Auditing Using Statistical Information about Taxpayers

A model of tax auditing in assumption, that tax authority have some statistical information about the distribution of income among population, is considered.
It is supposed that the true tax liability of each taxpayer takes its value from finite set. Dividing the range of possible tax payments on intervals, we make a correspondence between each interval and some group of taxpayers. The reported tax liability is the function of the true tax liability, which takes its values from the set of its argument's values. If the evasion was revealed, the taxpayer must pay the level of his evasion and penalty (marginal penalty rate assumed to be a constant). Tax evasions of the groups of taxpayers with the same level of income and the same level of rationality are investigated.
The tax authority assumed to get some statistical information, which can be considered as an indicator of the existing tax evasion. The information, mentioned above, is called a signal.
A taxpayer’s strategy is to make a decision to evade or not to evade, i.e. to declare his income level less or equal to his true income. A tax authority's strategy is to choose the audit probability.
The following results were obtained: the optimal audit strategies for each income-level group; the optimal audit strategies with consideration of the signals; the proposition about the optimal budget for tax auditing.