Day-fines are a type of fine, common in many European countries, in which the amount of the fine is based on both the severity of the offense and the income of the offender; thus, an investment banker will be fined more than a fast food worker for the same offense.
This system is not widely used in the United States, but it has seen some use:
The New York Times reported on an experiment with day fines which took place in 1988 in Staten Island, which was a partnership between the local courts and District Attorney, and the Vera Institute of Justice. In addition to Staten Island, day fines experiments have also been piloted in Maricopa County, Arizona; Bridgeport, Connecticut; Polk County, Iowa; four counties in Oregon; and Milwaukee, Wisconsin. An additional project was set up for Ventura County, California, but never ultimately implemented. According to the National Center for Access to Justice, Oklahoma is the only state in the U.S. that "has taken one or more specific steps to mandate, encourage or facilitate courts’ use of individualized fines (“day fines”) that are scaled according to both the severity of the offense and the individual’s economic status."
However, it seems to me that it could possibly violate the Equal Protection Clause of the Fourteenth Amendment:
[No state shall] deny to any person within its jurisdiction the equal protection of the laws.
Since the hypothetical investment banker is fined more than the fast food worker, despite the fact that their offenses were the same, it seems that the banker may be able to claim that the fine violates the Fourteenth Amendment.
As a possible counterargument, the state could claim that because the fines are designed to have equal effects on everyone, taking into consideration their financial circumstances, there is no equal-protection issue. However, I don't see how this claim could be made without requiring all fines to be day-fines, and it's highly unlikely that the vast majority of fines imposed in the United States are actually unconstitutional and no one has noticed this.
Has the constitutionality of day-fines in the United States ever been challenged under the Equal Protection Clause, or any other part of the Constitution?