In this paper we have derived the demands for securities, under the assumption that (1) individuals choose their portfolios so as to maximize expected utility, (2) their utility functions are quadratic in the value of wealth, and (3) all individuals have the same probability distributions of future prices. This latter assumption probably is the most unrealistic one, but could be modified somewhat without affecting some of our conclusions. We have shown that, given these assumptions, the ratio of the quantity of security j to that of security j is the same for all individuals independently of their wealth and the parameters of their utility functions (providing that some of each security is held by every individual). The ratios of money holdings to wealth will differ among individuals, however. We also have shown that the elasticities of aggregate demand depend only upon the expected "yields" and the variances and covariances of the probability distributions of future prices. These demand relations were used in analyzing a problem in debt management, namely, "how can the composition of the government debt be altered in a way such as to hold gross national product a constant?" The answer to this question together with that to "how can the composition of the debt be altered in a way such as to keep the total current value of government debt a constant" leads us to conclude that--given our assumptions--variations in interest costs probably are so small that they can be neglected.