In this case, the fraction of each type who dissembles on their income report becomes
The basic problem is this: When a taxpayer knows his own income but the revenue collector does not, the taxpayer may have an incentive to dissemble on his income report.
Thus, even taxpayers with large psychic costs of cheating may be induced to dissemble.
1] therefore has an incentive to dissemble on her income report, ceteris paribus.
1] ([Delta]) dissemble and the incentive compatibility condition is fulfilled for type 2 taxpayers.
2]([Delta]) respectively will dissemble and the incentive compatibility condition will not be fulfilled.
c], the population proportion of taxpayers who dissemble on their income reports is P([Delta]):
As either the audited proportion increases or the penalty increases, only taxpayers with low psychic costs are likely to file false reports, and overall, fewer taxpayers will dissemble.
With more progressive tax rates, even taxpayers with larger psychic costs will cheat and overall more taxpayers will dissemble.