Equilibrium and Economic Theory (Routledge Studies in the History of Economics)

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This book considers the treatment of equilibrium by several of the most important schools of thought in economics, including:
* neoclassical economics,
* the neo-Ricardian economics,
* Post-Keynesian economics - both those who follow Joan Robinson in denying any interpretative role to equilibrium in economic theorizing and those who use the notion of equilibrium, but re-defined from a Classical or Keynesian perspective.

Equilibrium and Economic Theory (Routledge Studies in the History of Economics) Review

The authors of this book understand what the basic conflict is when discussing concepts such as equilibrium,disequilibrium,shifting equilibrium,temporary equilibrium,interpemporal equilibrium,etc.from a neoclassical view as opposed to Keynes's view.They understand that the major differences concerning the conept of equilibrium have to do with the impact of Keynes's concept of uncertainty and uncertain expectations as opposed to the neoclassical concept of mathematical risk represented by the standard deviation of a normal probability distribution.Unfortunately,none of the authors is able to give a formal,mathematical,technical analysis of the differences existing between Keynes and neoclassical economists because they lack an understanding of Keynes's technical modeling of uncertainty in the A Treatise on Probability (1921)under the heading " the weight of the evidence ".

The neoclassical view is based on the Subjectivist,Bayesian approach to probability which postulates that all decision makers base all of their decisions on the linear and additive concept of the purely mathematical laws of the probability calculus.This will insure that their degress of belief are coherent,i.e.,consistent with conjunctive(unions) and disjunctive(intersections)outcomes calculated on the assumption of a completely specified sample space of all outcomes.Specifing a unique probability distribution is identical to claiming that the set of all possible outcomes is known before any decision is made.It follows that a stochastic analysis will result in one stable,unique equilibrium to which all disequilibriums will converge over time in the limit because all decision makers who are rational are coherent.This is the modern ,neoclassical view of equilibrium. Modern DSGE macroeconomic theory is then based on assuming that all outcomes are normally(log normally)distributed.This theory is identical to rational expectations theory,real business cycle theory,the Monetarism of Milton Friedman and the Chicago school,New Classical economics,etc.

Unfortunately,this is a very special case.Keynes proved that such results are a limiting case that can only occur if all probabilities are sharp,unique,linear,additive, point estimates whcih have a weight of the evidence of 1 wherw w is an index defined on the interval [0,1].I will append an appendix demonstrating Keynes's analysis.Keynes integrated this analysis into his modeling in chapters 20 and 21 of the GT.There is a set(locus) of expected D=Z outcomes.Each one of the expected outcomes ia a possible equilibrium.The set of all possible expected equilibriums forms a set of multiple equilibria.Only one of the set of multiple equilibria(D=Z)will turn out to be the actual equilibrium.This is determined by the income expenditure model of chapter 10 based on taking the limit of the multiplier process.

The neoclassical equilibrium can only occur if w=1(additivity holds) and all probability preferences are linear.Vast amounts of empirical and experimental evidence, gathered by psychologists starting in the late 1940's by Preston and Baretta and continuing in the work of Tversky and Kahneman,Einhorn and Hogarth,Slovic and Lichtenstein,Gardenfors and Sahlin,etc.,established that real world decision makers are using a non linear,non additive approach to decison making.Keynes was the first to postulate such a theory of decision making in history.

I append Keynes's 1921 A Treatise on Probability(TP) form of the analysis below for the interested reader.It can be found in sections 6-8 of chapter 26.The technical details can be found on p.315 and in footnote 2 on p.315 .Keynes presented a very precise analysis demonstrating that an analysis of uncertainty introduced non additivity and non linearity into the formal representation of decision making. The subjectivist, Bayesian approach regards probability as another name for the purely mathematical laws of the probability calculus that requires additivity and linearity. The Subjectivist approach makes the crucial error of conflating probability theory with decision theory.Keynes realized that ,due to the impact of the weight of the evidence (confidence)on decision makers ,as well as the optimism-pessimism of the decision maker,decision theory would have to be able to take into account the importance of non linearity and non additivity. The concept of expected value or utility is crucial to the Ramsey-De Finetti approach.Keynes demonstrated that expected value or expected utility can ,at best,be a special case only of a much more general theory .
The Ramsey-De Finetti approach is the mathematical translation of Jeremy Benthem's Benthamite Utilitarian approach.Bentham's approach was that the whole can not be anything more than the sum of the individual ,atomic parts. However, this requires the assumptions of additivity and linearity.Bentham assumed also that all decision makers can calculate the odds.Keynes showed that this was not the case. Keynes's demonstration ,taken from chapter 26 of his A Treatise on Probability(1921;TP),of the special case nature of any expected value(utility) approach ,based on the purely mathematical laws of the probability calculus,shows this to be a very special case when w=1. Bentham claimed that all individuals have the capability to calculate the odds and outcomes and act on the expected utility (the probability times the utility of the outcome) in a rational way.This can be expressed by the following ,where p is the probability of success,q is the probability of failure, and A is the outcome:

Maximize pA.

The modern version of this is to Maximize pU(A),where p is a subjective probability that is additive,linear,precise,and exact and U(A) is a Von Neumann-Morgenstern Utility function. The goal is to

Maximize pU(A).

The modern name for Benthamite Utilitarianism in neoclassical economics is SEU theory(Subjective Expected Utility). Therefore,a microeconomic foundation based on Utility Maximization is just Benthamite Utilitarianism updated with modern mathematical probability techniques.Modern macroeconomics is all disguised SEU theory.

Keynes rejected Benthamite Utilitarianism as a very special case that would only hold under the special assumptions of the subjectivist, Bayesian model-that all probabilities were additive,linear,precise,single number answers that obeyed the purely mathematical laws of the probability calculus.

Keynes specifies his conventional coefficient of risk and weight,c, model in chapter 26 of the TP on p.314 and footnote 2 on p.314,as a counter weight to the Benthamite Utilitarian approach of Ramsey.

Essentially, Keynes's generalized model is given by

c=2pw/(1+q)(1+w),

where w is Keynes's weight of the evidence variable that measures the completeness of the relevant, available evidence upon which the probabilities p and q are calculated.(Benthamite Utilitarians always assume that the value of w is always 1.)w is an index defined on the unit interval between 0 and 1,p is the probability of success,and q is the probability of failure.p+q sum to 1 if they are additive.This requires that w=1.Keynes's c coefficient can be rewritten as

c=p [1/(1+q)][2w/(1+w)].

Now multiply the above by A or U(A).One obtains

cA =p[1/(1+q) ][2w/(1+w)] A or

cU(A)= p[1/(1+q)][2w/(1+w)]U(A).

The goal is to Maximize cU(A) as opposed to the special Ramsey case of Maximize pU(A).
If w = 1 and all probability preferences are linear,then one obtains Ramsey's special result and a unique,stable convergent,macroscopic employment equilibrium will occur.Otherwise,no such equilibrium will occur.The equilibriums will generally be Keynes's unemployment equilibriums .

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