When we combine assumptions that the utility function is additive and that one commodity is an inferior good (defined as one for which purchases decrease as income increases), we produce a case in which there are n-i inferior goods, each of which has diminishing marginal utility, and one normal commodity (defined as one for which purchases increase as money income increases), which has increasing marginal utility. This result is of considerable general interest. It provides an analytical method of evaluating the results of empirical studies of demand based upon additive utility functions written for blocks of commodities [2] [4] [7]. Unless such empirical studies produce a result in which all income elasticities are positive, they must produce a result in which there are n-i negative income elasticities and one positive income elasticity. In addition to the general demonstration mentioned above, this paper also presents what is apparently the first published specific utility function, together with its associated demand functions to illustrate the case of a commodity with a negatively sloping income consumption curve. This specific (additive) utility function can be subjected to a monotonic transformation by squaring it; such a transformation leaves the demand functions unchanged and, in our case, will produce an illustration of the case of an inferior good based on an assumption of dependence of the marginal utilities. I turn first to the general demonstration that the combined assumptions: (1) that the utility function is additive, and (2) that one good is inferior, imply that there are n-1 inferior goods (all with diminishing marginal utility) and one normal commodity (with increasing marginal utility). Assume the existence of a consumer with a utility function of the form:

In my model of the evolution of honesty,1 I assumed the existence of a signal-a blush, perhaps-extreme values of which served to identify some individuals as being honest with certainty. Joseph Harrington notes that without this assumption, honest individuals have difficulty invading a population initially dominated by defectors. For readers who do not wish to work through the algebra in his comment, the argument is easily summarized in nontechnical terms. Suppose two honest mutants, A and B, arrive in an uncountably large population consisting entirely of dishonest persons. And suppose that the probability that an honest person exhibits an intense blush is, say, 0.999, while the corresponding probability for everyone else is only 0.001. When A sees an intense blush on the face of B, what will then be his estimate of the probability that B is honest? Assuming that A knows the laws of elementary probability and corrects for the base rate of honest persons in the population, it will be zero. When virtually everyone in the population is dishonest, even a person with an intense blush will be pegged as dishonest, provided that even the smallest fraction of dishonest persons also shows an intense blush. With