For lack of a better term, I will refer to this phenomenon as “diminishing typical utility” (DTU). This is not exactly the same as diminishing marginal utility (DMU), at least DMU is often described. [See UPDATE below.] A person with DMU of sex might get utility of 12 from the first act, 9 from the second act, 7 from the third act, and so on. A person with DTU might get utility of 12 per act if he has sex once a week, 9 per act if he has sex twice a week, 7 per act if he has sex three times a week, and so on. Now, the same person might be subject to both DMU and DTU, but I suspect that DTU is the more important effect for a person having sex on a regular basis. For such a person, there is not a “reset” point – say, Sunday evening – at which marginal utility jumps back up to its initial high value. Instead, what matters is the frequency of sex in the cycle. A person who has sex twice a week will typically have waited about 3.5 days between acts, whereas a person who has sex seven times a week will have waited only about one day.
With DMU, having more frequent sex always increases your satisfaction (so long as the marginal utility is still positive). But with DTU, having more frequent sex creates offsetting effects: on the one hand, you enjoy the additional act, but on the other hand, each act has lower significance. So, if you’re a person with DTU of sex, how much sex should you have?
Calculus to the rescue! Let x equal your number of sex acts per time cycle (say, a week). Let s(x) equal your satisfaction per act of sex. DTU implies that s(x) has a negative first derivative, s'(x) < 0. Your total satisfaction from sex is xs(x). To maximize your satisfaction, find the first derivative (using the product rule) and set it equal to zero:
xs'(x) + s(x) = 0or, rearranging,
s(x) = – xs'(x)This optimal-sex-frequency condition has a nice interpretation. The left-hand side is the satisfaction you get from one act of sex considered in isolation. The right-hand side is the loss in satisfaction per sex act that results from increasing the frequency ( – s'(x)), multiplied by the number of sex acts whose satisfaction is reduced in that manner. So the condition says to increase your frequency of sex until the added satisfaction from having sex once more is exactly counterbalanced by the diminished satisfaction of all sex acts together.
(Aside for econ majors: This problem is mathematically equivalent to revenue maximization. To maximize revenue, expand output until the revenue received from your last unit – that is, the price – is just offset by the lost revenue from having lowered your per-unit price on all units in order to sell more units. Note, however, that revenue is not profit.)
However, the optimality equation above will only have a solution if greater frequency diminishes your satisfaction from each act, i.e., if s'(x) < 0. If you, like Steve, have s'(x) > 0, then the optimal response is what economists call a corner solution: have all the sex you possibly can.
Also, if sexual partners have different solutions to the maximization problem, then the stage may be set for a relationship cycle.
[UPDATE: In pondering a bit more, I've decided that DTU is actually a special case of DMU, but it doesn't fit with the usual description of DMU. Technically, marginal utility is defined as the change in total utility that results from an increase in quantity. With that definition, DTU is indeed a form of DMU, because the reduction in satisfaction per act is part of the change that results from an increase in quantity. But DMU is often described loosely as the satisfaction attributable to the very last unit of quantity -- e.g., the satisfaction you get from eating your third slice of pizza. If DMU is construed in this narrower way, then DTU appears to be a distinct phenomenon.]