Economics of discriminatory sentencing

The legal and social professions have long been concerned with the problem of whether the fact that those incarcerated in prison tend to be drawn from the ranks of the poor unemployed and low social status is indicative of willful discrimination against the underprivileged. In this paper we apply the traditional analytical tools of economics to develop the conditions required for an efficient tradeoff between the probability of conviction and the length of prison sentence for both rich and poor. We show that the generally accepted approach of equal punishment for equal crimes tends to "overdeter" the rich and "underdeter" the poor, which results in a gross overrepresentation of the poor in the prison population. In order to eliminate this overrepresentation, the poor must receive a more severe sentence than the rich for an equivalent crime. This appears to contradict normal definitions of "equity" and we address this issue. We also show that an increase in the total crime budget when used efficiently must always result in longer sentences but can, under appropriate conditions, require a lower probability of apprehension.