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:

The assumptions underlying the expectations theory of the determination of relative yields on default free securities differing only with respect term maturity may be summarized as follows:' 1. A set of identical expectations regarding future short term interest rates is held with complete confidence by the owners of a large proportion of the bond market's funds.2 2. There are no costs associated with trading in securities. 3. Investors maximize return over a horizon at least as long as the longest term security outstanding. These assumptions have been construed by I. Fisher, J. R. Hicks, and F. A. Lutz imply a market equilibrium in which the relation between yields at time t on securities maturing at times t+ 1 and t+n depends upon the yields expected prevail on one-period securities maturing at times t+2, t+3, * * , t+n. But it will be shown below that the traditional formulations rest upon an implicit fourth assumption: 4. Investors, when selecting their optimal portfolio at a given point in time, consider themselves bound hold each security purchased until maturity.3 The primary purpose of the present paper is demonstrate that assumption 4 is necessary the results of Fisher, Hicks, and Lutz and that, if we discard this assumption in a world of zero transactions costs and risk indifference-the FisherHicks-Lutz world-equilibrium relationships depend only upon interest rate expectations one period in the future rather than upon interest rate expectations several periods into the future. In other words, the traditional theory, in which investors are assumed forecast rates to Kingdom come [13, p. 18], implicitly requires that they be precluded from disposing of securities prior maturity. A theory of the term structure of rates in which investors are not so constrained, but which retains assumptions 1-3, must involve only oneperiod forecasts. This is shown in Part II after an examination in Part I of the underpinnings of the traditional theory. Some concluding comments are contained in Part III.