The Foundations of J M Keynes's IS-LM Model in Chapter 15 of the General Theory : Keynes's D-Z Model of Chapters 20 and 21

F. Modigliani presented a special case of Keynes's General Theory result in 1944 in his “Liquidity Preference and the Theory of Interest and Money”. Modigliani sought to provide the IS-LM model of Hicks's 1937 Econometrica interpretation of Keynes's chapter 15 IS-LM model with microeconomic foundations in the theory of the firm that included a production function and labor market. Modigliani overlooked the fact that Keynes had already done exactly that in his chapters 20 and 21 of the General Theory. Section 4 of Keynes's chapter 15 was the bridge connecting chapter 15 to chapters 20 and 21.Modigliani erred, however, in four ways. First, he used the theory of perfect competition, with its assumptions of perfect information and perfect prediction, and not Keynes's theory of pure competition. Second, Keynes defined p to be an expected price in the General Theory, whereas Modigliani defined his capital P to be an actual price. This led to his third mistake, which was to define the necessary and sufficient first and second order conditions for optimality, leading to a profit maximum, in the labor market, given decreasing returns, as being where the ACTUAL real wage of labor equaled the marginal productivity of labor. Keynes' condition is that it is the EXPECTED real wage of labor that equals the marginal productivity of labor. This leads directly to Keynes's Aggregate Supply Curve of multiple equilibria, which is a locus of the entire set of all possible D-Z intersections, which will lead to one Y value, whereas Modigliani is stuck with only one equilibrium. Modigliani thus has the equivalent of Keynes's Y-multiplier income expenditure model result from chapter 10 of the General Theory, but no D-Z model of expected prices and expected profits from chapters 20 and 21 of the General Theory. Modigliani's fourth mistake was that he replaced Keynes's uncertainty, a function of the weight of the evidence, with risk. This follows from Modigliani's acceptance of the de Finetti subjective theory of probability, where there is only risk and no uncertainty because all probabilities must be additive, precise probabilities, whereas for Keynes most probabilities must be non-additive, imprecise or indeterminate interval valued probabilities.Modigliani's paper thus becomes a special case of Keynes's General Theory analysis in chapters 20 and 21