One line of investigation in the problem of tax evasion has been introduced by B. Singh who studied the question of the ‘Optimum probability of detection’ which must be set (or be believed to be set) in order to induce the lax payer to declare income fully (‘complete honesty’). However, detection is costly and the achievement of an ‘optimum rate’ may therefore be ruled out on the grounds of economy. On the other hand, the penalty rate is set by legislative action, which is relatively costless. In contrast to Singh we take the probability of detection as given and study the ‘prohibitive penalty rate’, generally for any desired minimal level of evasion and more extensively where the desired evasion is zero. The formulae for the prohibitive rates are derived for each of three penalty functions, and the corresponding rates calculated for a selection of probabilities of detection on the basis of the current Australian taxation schedules. The calculations involved are simple and may be readily made for other countries. Copyright © 1979, Wiley Blackwell. All rights reserved
