Dynamic Tax Evasion with Audits based on Conspicuous Consumption

We solve the problem of a representative agent who maximises the expected present utility of his intertemporal consumption under the as- sumption that an optimal fraction of his wealth is hidden to the tax au- thorities (we show conditions under which evasion is expedient). Evasion affects the capital dynamics in two ways: the growth rate of capital in- creases because some taxes are not paid, but when caught evading the consumer has to pay a fee (proportional to evasion). Consumption can be allocated between ordinary goods and so-called conspicuous goods. The latter are used by the Government for targeting the audit, since they are considered like an indicator of consumer's wealth. In fact, the probabil- ity to be caught is a function of the distance between the actual and the presumed consumption in conspicuous goods. We find a closed form solu- tion to the dynamic optimization problem and show how fiscal and audit parameters affect the optimal evasion and the optimal allocation between the two consumptions.