The arithmetic of discounting

Most current models of delay discounting multiply the nominal value of a good whose receipt is delayed, by a discount factor that is some function of that delay. This article reviews the logic of a theory that discounts the utility of delayed goods by adding the utility of the good to the disutility of the delay. In limiting cases it approaches other familiar models, such as hyperbolic discounting. In nonlimit cases it makes different predictions, generally requiring, inter alia, a magnitude effect when the value of goods is varied. A different theory is proposed for conditioning experiments. In it utility is computed as the average reinforcing strength of the stimuli that signal the delay. Both theories are extended to experiments in which degree of preference is measured, rather than adjustment to iso-utility values.