So, if one plotted the demand for money against interest rate one would get the now well known textbook curve that slopes gently downward from all the money held at zero interest on bonds and asymptotically approaches zero money held at infinite interest. This description of liquidity preference has been severely criticized by Leontief and Miller. Tobin, inspired by Markowitz, saw Keynes liquidity preference curve in terms of portfolio theory, i.e., the maximization of utility in mean-variance space. Tobins theory satisfied Leontiefs critique and brought liquidity preference into harmony with the mainstream of economic thought of his time. He proposes the following lucid and enlightening explanation of the downward sloping money curve.
B is less than unity and represents the value weighted percentage of the portfolio held in bonds.
However, next year, the prevailing interest rate may change to R1. The assumption that g is normally distributed about an expected value of zero with a standard deviation of Sg leads to the following equations. Now we can substitute for B in the equation for expected value. The point determines the fraction of his liquid wealth he holds in money and that which he holds in bonds. Tobin wrestles with the fact that the relationship is reversed for riskophiles but offers no answers.