# Keynes’ GTE

JM Keynes *General Theory of Employment, Interest and Money* Macmillan, 1936.

This challenges classical economics, which held that market economies had unique natural equilibria that were only disturbed by external shocks. Thus recessions were due to external shocks and recovery automatic. Sustained depressions were impossible and governments need not do anything to avoid them.

Technically, Keynes introduces the concept of a ‘multiplier’, the amount that an economy responds to a stimulus, and recognized the importance of liquidity preference. His use of the term ‘expectation’ differs from some current practice. In the General Theory, the certainty of making an adequate profit is more important than the probabilistic expectation.

Some regard Keynes as being an advocate of government spending in the face of an economic slow-down. But he actually advocated analysing the situation in terms of the actual multipliers at the time, and then seeking to increase the multiplier. Keynes makes a distinction between short and long-term issues, but notes that long-term expectations can impact on short-term behaviours. There can be conflicts between short-term and long-term issues. These depend on ‘animal spirits’ and so timing is unpredictable.

In Keynes’ time government spending has a large multiplier, hence his advocacy. In our time there are at least two important potentially high multiplier areas to be balanced:

- paying down the debt, via its impact of interest rates
- avoiding severe health and disorder issues, via impacts on confidence in government and costs and confidence by business.

The work focusses on investment decisions by business and governments, but much of it can inform broader theories.

## Book I – Introduction

### Ch. 2 The Postulates of Classical Economics

The classical theorists resemble Euclidean geometers in a non-Euclidean world, who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight-as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry. Something similar is required in economics.

## Book IV – The Inducement to Invest

This is the key part.

### Ch. 11 The Marginal Efficiency of Capital

Two types of risk affect the volume of investment which have not commonly been distinguished, but which it is important to distinguish. The first is the entrepreneur’s or borrower’s risk and arises out of doubts in his own mind as to the probability of his actually earning the prospective yield for which he hopes. If a man is venturing his own money, this is the only risk which is relevant.

That is, the probability of achieving the necessary return is more significant than the ‘rational’ expected utility. “In the long-run, we are dead.”

During a boom the popular estimation of the magnitude of … both borrower’s risk and lender’s risk, is apt to become unusually and imprudently low.

The fact that the assumptions of the static state often underlie present-day economic theory, imports into it a large element of unreality.

The book is full of such apt observations.

### Ch 12: The State of Long-Term Expectations

The state of long-term expectation, upon which our decisions are based, does not solely depend … on the most probable forecast we can make. It also depends on the

confidencewith which we make this forecast¾on how highly we rate the likelihood of our best forecast turning out quite wrong. If we expect large changes but are very uncertain as to what precise form these changes will take, then our confidence will be weak.”

A footnote refers to Keynes’ Treatise on Probability. ‘By “very uncertain” I do not mean the same thing as “very improbable”. ‘ Thus an individual venturing their own money will seek relative certainty, not just a probability, of return. This links to the later Allais ‘paradox’.

In practice we have tacitly agreed, as a rule, to fall back on what is, in truth, a

convention. The essence of this convention¾though it does not, of course, work out quite so simply¾lies in assuming that the existing state of affairs will continue indefinitely, except in so far as we have specific reasons to expect a change. This does not mean that we really believe that the existing state of affairs will continue indefinitely. We know from extensive experience that this is most unlikely. The actual results of an investment over a long term of years very seldom agree with the initial expectation. Nor can we rationalise our behaviour by arguing that to a man in a state of ignorance errors in either direction are equally probable, so that there remains a mean actuarial expectation based on equi-probabilities. For it can easily be shown that the assumption of arithmetically equal probabilities based on a state of ignorance leads to absurdities.…. the above conventional method of calculation will be compatible with a considerable measure of continuity and stability in our affairs,

so long as we can rely on the maintenance of the convention.… A conventional valuation which is established as the outcome of the mass psychology of a large number of ignorant individuals is liable to change violently as the result of a sudden fluctuation of opinion due to factors which do not really make much difference to the prospective yield; since there will be no strong roots of conviction to hold it steady. In abnormal times in particular, when the hypothesis of an indefinite continuance of the existing state of affairs is less plausible than usual even though there are no express grounds to anticipate a definite change, the market will be subject to waves of optimistic and pessimistic sentiment, which are unreasoning and yet in a sense legitimate where no solid basis exists for a reasonable calculation.

… Most, probably, of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as a result of animal spirits¾of a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities.

Keynes amplifies these ideas in his response to reviews of this book.

### Ch. 21 The Theory of Prices

The object of our analysis is, not to provide a machine, or method of blind manipulation, which will furnish an infallible answer, but to provide ourselves with an organised and orderly method of thinking out particular problems; and,after we have reached a provisional conclusion by isolating the complicating factors one by one, we then have to go back on ourselves and allow, as well as we can, for the probable interactions of the factors amongst themselves.This is the nature of economic thinking. Any other way of applying our formal principles of thought … will lead us into error. … Too large a proportion of recent “mathematical” economics are merely concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols.

This is good advice for any complex problem. Some of the reasons can be gleaned from his Treatise.

## Book VI

### Ch. 22 Notes on the Trade Cycle

The later stages of the boom are characterised by optimistic expectations as to the future yield of capital-goods sufficiently strong to offset their growing abundance and their rising costs of production and, probably, a rise in the rate of interest also.

It is of the nature of organised investment markets, under the influence of purchasers largely ignorant of what they are buying and of speculators who are more concerned with forecasting the next shift of market sentiment than with a reasonable estimate of the future yield of capital-assets, that, when disillusion falls upon an over-optimistic and over-bought market, it should fall with sudden and even catastrophic force.Moreover, the dismay and uncertainty as to the future which accompanies a collapse in the marginal efficiency of capital naturally precipitates a sharp increase in liquidity-preference¾and hence a rise in the rate of interest. ….It is this, indeed, which renders the slump so intractable. Later on, a decline in the rate of interest will be a great aid to recovery and, probably, a necessary condition of it. But, for the moment, the collapse in the marginal efficiency of capital may be so complete that no practicable reduction in the rate of interest will be enough. … it is not so easy to revive the marginal efficiency of capital, determined, as it is, by the uncontrollable and disobedient psychology of the business world. It is the return of confidence, to speak in ordinary language, which is so insusceptible to control in an economy of individualistic capitalism. This is the aspect of the slump which bankers and business men have been right in emphasising, and which the economists who have put their faith in a “purely monetary” remedy have underestimated.”

This clearly has relevance to the crises of 2007 et seq.

You are correct that Keynes intentionally links his magnum opus to his work on probability via two footnotes (one in Chapter 12, the other in Chapter 17, which refers back to the footnote in Chapter 12).

But out of curiosity Dr. David Marsay, what did you think of John Maynard Keynes’s mathematical model in

The General Theory?If you overlooked Keynes’s mathematical equations, then don’t worry. Just reread Book V of Keynes’s magnum opus – Chapter 19, the appendix to Chapter 19, Chapter 20, and Chapter 21. This is the most important part that has been overlooked by many economists.

Book V of

The General Theory(particularly Chapter 19 and its appendix) essentially counters Arthur Cecil Pigou’s 1933 book,The Theory of Unemployment. It demonstrates the special case of classical economics in what was at the time, state-of-the-art mathematical formulation in the economics profession: differential calculus and integral calculus.If you want more scholarly analysis on Book V of the GT, then please see the following sources.

http://hope.dukejournals.org/content/22/1/167.full.pdf+html

http://hope.dukejournals.org/content/26/4/697.full.pdf+html

http://cje.oxfordjournals.org/content/32/5/815

http://dx.medra.org/10.1400/121162

Thanks for the references, ‘Blue’. I am making some notes for a conference on mathematical finance, and your question is apt. I haven’t had time to follow up your references yet. The way I see it, Keynes’ model is appropriate as a counter to Pigou’s, but it follows from Russell’s ‘Human Knowledge’ (search my blog), which builds on Keynes’ Treatise, what perhaps ought to be obvious: that we shouldn’t take any model too seriously.

Keynes refers back to chapter 3 section II where he makes the important caveat that this is an equilibrium model. He also claims that “when employment increases aggregate real income is increased” and hence aggregate consumption. It is not obvious to me that this is necessarily true, although it may have been true back then. For example, in the UK an increased tendency for women to join the labour market has increased the supply of labour and hence diminished its price. Moreover, if income has increased over the past decades then so has income inequality, so increased employment may not have led to a ‘real’ increase in consumption: it could simply be that the cost of rare goods (old masters, houses with views) has gone up, with no increase in supply. It would be difficult to disentangle the effects, so Keynes’ assumption – if intended as a universal truth – calls for some justification.

I approve of Keynes’ overall approach, particularly the link to mathematics, not necessarily his assumptions or prescriptions.