Efficient deterrence does not require that the wealthy should be able to buy Justice

It has been argued that it is inefficient to restrict the ability of the rich to buy better legal defense than the poor because such restrictions lead to overdeterrence of the wealthy, who have a higher opportunity cost of imprisonment. We show that the ability of the rich to buy a lower conviction probability can never lead to the expected sanction for a crime being the same at all income levels. Thus whilst a restriction on legal defense expenditure increases the proportion of individuals who are inefficiently overdeterred, it also reduces the proportion who are inefficiently underdeterred. Hence the efficiency implications are ambiguous.