I. BY introducing liquidity preference into the theory of interest Mr. Keynes has provided us with an analytical apparatus of great power to attack problems which hitherto have successfully resisted the intrusion of the economic theorist. In this paper I propose first to elucidate the way in which liquidity preference co-operates with the marginal efficiency of investment and with the propensity to consume in determining the rate of interest and to point out how both the traditional and Mr. Keynes's theory are but special cases of a more general theory. Further I propose to show how the analytical apparatus created by Mr. Keynes can be used to handle the problem which bothered the underconsumption theorists since the time of Malthus and Sismondi. 2. The economic relations by which the rate of interest is determined can be represented by a system of four equations.' The first of these equations is the function relating the amount of money held in cash balances to the rate of interest and to income. This is the liquidity preference function. If M is the amount of money held by the individuals, r their total income and i the rate of interest we have2 M=-L(i, n (I) It is convenient to take M and r as measured in terms of wage-units, or of any other numeraire. Thus r is the real income while M is the real value of the cash balances, both