Keynes’s Use of Certainty Equivalent, Short Run Expectations in the General Theory, the Evidential Weight of the Argument, V(a/H)=W, 0≤w≤1, the Townshend -Keynes Exchanges of 1937–38, and Is-Lm: Rational Expectations Was a Special Case for Keynes if W=1 for Long Run Expectations

Abstract

The failure of all economists and philosophers in the 20th and 21st centuries to grasp the formal, technical analysis of the 'weight of the arguments' analysis in chapters 6 and 26 of Keynes’s A Treatise on Probability explains why the footnotes on pages 148 and 240 of the General Theory, the importance of which Keynes emphasized to Townshend in 1938, at the exact same time that Keynes was also engaged in a severe critique of Tinbergen’s misapplication of the limiting frequency interpretation of probability to business cycles using a multivariate normal probability distribution, have never been incorporated into Keynes’s theory of effective demand, the D-Z model, which served as the foundation for Keynes’s IS-LM(LP) model on pp .298-299 in Part IV of chapter 21 of the General Theory. Keynes’s certainty equivalence for the expectations embodied in Z=wN +P and D=pO incorporated expectations as a function of uncertainty, where uncertainty is a function of the evidential weight of the argument, w, which ranges from complete knowledge, w=1 to complete ignorance, w=0. This is very similar to A. Greenspan’s 2004 paper in the AER that specified a Continuum that ranged from complete ignorance to complete knowledge. The certainty equivalences for the P variable, expected profits, and the p variable, expected prices, were formalized directly from Keynes’s conventional coefficient,c. Y, realized aggregate income, is a function of the expectational D-Z locus, called by Keynes the aggregate supply curve (ASC). Once a particular Y value is specified, Keynes combined it with the long run nominal rate of interest, r, to specify the IS-LM(LP) model in (Y,r) space. Keynes showed that a severe problem of absolute liquidity preference would show up once the long run nominal rate reached 2% due to lack of confidence and fear of the future. Monetary policy would fail, leaving some type of fiscal policy as the only possible policy alternative in a severe recession or depression. In response to Townshend’s 1937-1938 pleas for guidance concerning the connection between Keynes’s theory of liquidity preference and the A Treatise on Probability’s logical theory of probability Keynes simply reiterated that Townshend needed to reread pages 148 and 240 of the General Theory, given Townshend’s own statement that he had read the A Treatise on Probability. The answer that Townshend never found appears on page 315 of the A Treatise on Probability in chapter 26, which is the mathematical complement and supplement to the initial logical treatment of the V relation provided by Keynes in chapter 6. Only in chapter 26 does Keynes make it clear that V(a/h)=w,0≤w≤1.