Category Archives: Notes

Keynes, The General Theory: Chapter 13

John Maynard Keynes,The General Theory (BN Publishing, 2008), pp. 165–174.

The General Theory of the rate of interest

I.

Chapter 11 deals with the marginal efficiency of capital (MEC); here, Keynes will explain his unique approach to the theory of interest: the liquidity preference theory. To put the two concepts in relation to each other, Keynes harks back to supply and demand. The MEC is what decides the demand for loanable funds, while interest is what decides the supply of loanable funds. Traditionally, interest is said to be a function of the relationship between the MEC and time preference, but Keynes doesn’t believe this to be true.

II.

Keynes essentially divides the concept of time preference into two ancillary ideas: (i) the propensity to consume; and, (ii) liquidity preference: “in what form he will hold the command over future consumption which he has reserved” (p. 166). Does the person want to retain some high degree of immediate command — like cash — or is he willing to part with command for some amount of time? It’s the concept of liquidity preference that traditional theories of interest neglect.

Why can’t the rate of interest be a return on waiting or saving? Let’s suppose two forms of savings are available: holding cash and a time deposit. The latter pays interest, while the former does not. Yet, an individual might choose to increase his demand for money, rather than store it in a time deposit, and earn no interest. Rather, the rate of interest is the price of “parting with liquidity;” specifically, it’s the inverse proportion between a stock of money and “what can be obtained for parting with control over the money in exchange for debt for a stated period of time” (p. 167).

Therefore, the rate of interest measures how unwilling those with cash are to part with control over it. So, rather than equilibrating the supply of and demand for loanable funds, it equilibrates demand for money with the supply of money. Given this, we can say that the rate of interest is determined by liquidity preference and the quantity of money. Or, where M is money, L is liquidity preference, and r the rate of interest: M = Lr.

While most of this concern will be answered in chapter 15, what determines liquidity preference?  Why might someone prefer liquid command over interest payments? Keynes’ answer, “[U]ncertainty as to the future of the rate of interest.” In other words, if there is uncertainty as to the interest that investment into a long-term bond will pay, such that there may be a loss, an individual may refer to simply hold cash. As such, the decision to part with liquidity is made when the expected gain is higher than the expected gain of holding money, meaning that when there is high uncertainty the rate of interest will have to increase. Now, knowing that expectations will diverge, we can say that interest will balance at the equilibrium point between “bears” (hold cash; sell bonds) and “bulls” (buy bonds).

To recap,

  • The Transaction Motive: the need for cash to fulfill current transactions during personal and business exchanges;
  • The Precautionary Motive: the desire for security;
  • The Speculative Motive: The objective of securing profit by “knowing better than the market” (p. 170).

As with earlier chapters, he mentions that organized markets suffer the burden of destabilization at the hands of speculators. Let’s say that liquidity preference due to the transaction and precautionary motives leads to demand for cash y, such that total cash x – y is equal to the amount of cash available to satisfy the speculative motive (z). The rate of interest and price of bonds have to be set where liquidity preference due to the speculative motive is equal to z. Suppose the quantity of money increases, then the price of bonds has to rise to the point where it persuades the marginal speculators to become bearish, and thus sell their bonds in exchange for holding cash. As a matter of simple arithmetic: X = Y + Z; assuming Y remains the same, ↑M must lead to ↑Z. Alternatively, if Z is negligible, then an ↑M will cause a ↓r (↑Y).

Why, though, can we generally assume a liquidity preference schedule such that ↑M leads to ↓r? Keynes gives two reasons,

  1. The more r falls, usually the more money will be held due to the transaction motive. If a fall in r leads to an increase in income, money held due to the transaction motive will rise proportionally with the increase in income;
  2. A fall in r may change the amount of cash held due to the speculative motive.

There maybe a time when increases in the quantity of money may not reduce the rate of interest further (or “will exert a comparatively small influence” [p. 172]). It occurs when an increase in M causes high uncertainty with regards to the future state of r. Liquidity preference will rise due to stimulation of the precautionary motive and it may lead a “mass movement” (p. 172) to cash. Here Keynes make the great observation that for changes in the money stock to change the rate of interest, there has to exist some degree of variation in expectations. The more heterogeneous expectations are, the more stable the cash–bond market.

III.

Keynes sees this relationship between the stock of money (and changes in this stock), bond prices, and the rate of interest as the main artery by which money exerts its influence over the economy. For example, while we may expect an ↑M to cause a ↓r, this may not occur if ↑L>↑M. Similarly, while a ↓r may be expected to cause a ↑I, this may not occur if there is a simultaneous ↓MEC greater than the ↓r. Just the same, a ↑I will not lead to higher employment if there is a ↓MPC. Finally, to maintain r in the face of ↑money wages and ↑O, there will have to be a ↑L.

IV.

This is a minor note, relating this chapter and liquidity preference to what Keynes called “the state of bearishness” in his Treatise on Money. The difference is that the “state of bearishness” is a functional relationship between the “price of assets and debts, taken together, and the quantity of money” (pp. 173–174). The error there is a confusion between the results of a change in the rate of interest and a change in the MEC.

V.

Liquidity preference is not just hoarding in the sense of cash holdings; the decision to hoard is taken into consideration along with “the advantages” of parting with liquidity. No less, equating hoarding with only the demand for money is meaningless if we consider that all money has to be held by someone. So, while the public doesn’t choose how much to hoard, since the public doesn’t choose the quantity of money, the public does “choose” the rate of interest, in the sense that interest is set where “the aggregate desire to hoard becomes equal to the available cash” (p. 174). As Keynes eloquently states,

The habit of overlooking the relation of the rate of interest to hoarding may be a part of the explanation why interest has been usually regarded as the reward of not-spending, whereas in fact it is the reward of not-hoarding.

— p. 174.

Keynes, The General Theory: Chapter 12

John Maynard Keynes,The General Theory (BN Publishing, 2008), pp. 147–164.

The state of long-term expectations

I.

We now know that the rate of investment depends on the relationship between the rate of interest (which will be covered in the next chapter) and the marginal efficiency of capital. The latter, in turn, is a relationship between supply price (minimum income necessary to justify investment) and prospective yield. This chapter will focus on what influences the prospective yield.

This latter concept is dictated by two categories: what we know and what we don’t know (future oriented uncertainty). The first is made up of things like the stock of capital goods and the state of existing consumer demand. The second is composed of factors like the future stock of capital goods, future preferences and consumer demand, and future wages. In other words, future uncertain factors which will influence the profitability of the investment. This Keynes refers to as the “state of long-term expectations.”

II.

Keynes argues that it would be “foolish” to form expectations on the basis of the very uncertain (different from the very improbable; ftn. #1, p. 148); what we are most (or somewhat) confident about is likely to be more important. This causes a further degree of asymmetry (Keynes uses the word disproportionate), and therefore the entrepreneur is simply likely to project the present state of affairs into the future. The state of long-term expectations depends not only on the forecast made, but on the confidence placed on the prediction.

This brings us to the idea of the “state of confidence.” This is a major factor in determining the marginal efficiency of capital, or the investment demand schedule. However, the “state of confidence” is an empirical variable, in that “not much can be said about [it]… a priori” (p. 149). For the rest of the chapter, to simplify discussion, we will assume that the rate of interest is fixed and that all impact on the marginal efficiency of capital is wrought by changes in confidence.

III.

The knowledge available to accurately plan investments is scarce; this uncertainty, or radical ignorance of the future, shrouds production. Entrepreneurs who try to predict the future state of affairs in five or ten years are “in the minority and their behavior does not govern the market” (p. 150).

There was a time when entrepreneurs embarked upon investment only as a way of life, where long-term yields were largely unknown and even once investments were completed few knew whether the yield was below, on par with, or above the prevailing rate of interest. Entrepreneurship is partly skill and partly chance; Keynes suggests that if human nature had no inclination towards risk-taking, there might not even be much long-term investment.

Something which distinguishes old investments from modern investments is that the latter were mostly irrevocable. However, given modern stock markets and other forms of information transmission, investments can be revised even on a daily basis. This adds to the complexity, though. The stock exchange gives an opportunity to purchase existing investments, or start a new one and then sell it at an “intermediate profit” on the stock market. Also, equity prices are not just influenced by “professional” entrepreneurs, but by all market agents who partake in it.

(Ftn. 1, p. 151 might interest some. In Treatise on Money, Keynes suggested that a rise (fall) in the price of equities is analogous to a fall (rise) in the rate of interest. He revises this here, arguing that instead a rise (fall) in the price of equities is analogous to a rise (fall) in the marginal efficiency of capital. The implications are the same, however.)

IV.

In practice, entrepreneurs rely on a convention: that present conditions will continue, unless we have reason to expect change. This doesn’t mean that they actually think there will be no change, rather it is an assumption that that present valuations are correct. As long as this convention remains intact, we can expect stability. Therefore, short-term investments run lesser risk: they are “liquid” for the entrepreneur and “fixed” for the community. That is, they don’t run the risk of being inadequate five or ten years down the road.

V.

What are some of the factors which affect the “contemporary problem of securing sufficient investment” (p. 153)?

  1. Since the stock market allows non-managers and non-owners to purchase equity, or part of the investment, the knowledge surrounding that particular investment falls in quality;
  2. Day-to-day fluctuations in the equity prices tend to excessively influence the market —  in other words, stock market prices represent an inherent instability in modern investment markets;
  3. The mass of “ignorant” (p. 154) investors will be subject to waves of optimism, or alternatively pessimism;
  4. “Expert” investors, rather than forecasting the state of future yields, instead aim at predicting future valuation of equity prices in accordance with how the “ignorant” masses will value them.

We see, then, the “anti-social” (p. 155) character of equity markets, where speculators follow the ignorant masses in valuing investments. Keynes argues that there is a paradox between the object of liquidity for the individual and the illiquidity of investment for the community (this is also where Keynes mentions “time and ignorance” [p. 155]). Modern equity markets undermine the necessity for long-term, stable investment. Investors don’t choose the best investment, but what they think others will recognize as the best investment.

Why are long-term investors no longer prevalent in markets? These run a higher risk than short-term prediction, and require much more work; intelligent investing, therefore, tends to concentrate in the short-term. Investors are also running against their biological clock, making short-term profits more lucrative than long-term profits of equal value. Finally, successful long-term investors have no advantage in public relations, meaning that in bad times they will be treated equally as poorly as other, more rash investors.

The fifth and final factor discussed (although, here it’s labeled [1]),

  1. The “state of credit” (p. 158): the confidence banks have in borrowers.

VI.

Two definitions (p. 158),

(i) “Speculation:” “…forecasting the psychology of the market.”

(ii) “Enterprise:” “…the activity of forecasting the prospective yield of assets over their whole life.”

While speculation need not necessarily be predominate over enterprise, as investment markets organize and evolve speculation gradually becomes a more important activity. Fore the reasons established above, Keynes sees the growth of financial markets in this way as a negative outgrowth of the capitalist system. For this reason, he proposes means — such as higher taxes on gains — to make equity markets more expensive to access. However, the problem is that there is also advantage that the expected liquidity of equity makes investors more willing to take risks, which is fundamental. No less, where money can be hoarded, these kinds of assets are attractive alternatives.

Keynes proposes directing more spending towards consumption, since if there is a pessimists’ mood then the individual might rather choose to neither invest nor consume.

VII.

Apart from speculation, there is also the problem of “spontaneous optimism.” This is the famed “animal spirits” — the sudden urge to do something positive; to choose action over inaction. But, these are not mathematical calculations; i.e. it would be analogous to claiming the driving force being emotional and psychological impulse rather than instrumental rationality. As such, a loss in this optimism may cause damage in that it will reverse the trend of investment. It exaggerates both booms and busts; it therefore behooves society to create an environment that promotes and stimulates good feelings and optimism (p. 162: Keynes on regime uncertainty). Keynes’ basic point is that the instrumental rationality of an omniscient rational being is not something proper to assume.

VIII.

What factors mitigate radical ignorance?

In many investments, due to both compound interest and capital obsolescence, short-term investing may actually be preferable to its long-term ilk. Some long-term investments (e.g. housing and apartments) can enjoy the safety of long-term contracts, which spread the risk between investor and client. Otherwise, other long-term investments — such as utilities — may enjoy “natural monopoly” privileges, giving some sense of security in prospective yields. Also, there is public investment, in areas which are seen to be socially desirable. With the state of long-term expectations properly considered, we must turn to the rate of interest which also plays a heavy role in deciding the rate of investment.

Keynes, The General Theory: Chapter 11

John Maynard Keynes,The General Theory (BN Publishing, 2008), pp. 135–146.

The Marginal efficiency of capital

I.

A man buys capital-assets, also buying the right to the returns yielded from selling its output: the prospective yield.  We also have the supply price, which is the minimum return an entrepreneur requires to induce him to invest (also called a replacement cost).  The relationship between these two variables is the marginal efficiency of capital; that is, where income earned from the use of capital is equal to its supply price.  These terms are all forward looking, in the sense that they are values based on entrepreneurial expectations.

Typically, the rate of investment will be set at the point where the marginal efficiency of capital is equal to the rate of interest.  Therefore, the inducement to invest relies both on the investment demand-schedule and the rate of interest — this supposedly becomes clearer as we push through Book IV (the next one hundred pages).

II.

Let’s compare Keynes’ “marginal efficiency of capital” (MEC) to other familiar terms with similar meanings, such as “marginal productivity” or “yield.”  In defining these terms, Keynes notes that there exist “three ambiguities,”

  1. What matters?  The increase in physical output per unit of time that the marginal unit of capital brings about?  Or, the increase in value as a result of the employment of the marginal value unit of capital?  Keynes seems to favor the second choice, given that defining capital and output in real terms is difficult, and he can’t reduce the relationship by means of arithmetic;
  2. Is the MEC an absolute quantity or a ratio;
  3. Should we consider the increment discussed in (1) related only to one point in time — as in a static model —, or should we consider the MEC of the marginal unit over its entire productive life (necessarily bringing in expectations)?

In a couple of brief paragraphs Keynes discusses the relationship between the marginal efficiency of capital and the rate of interest.  The MEC doesn’t decide the rate of interest; rather, the rate of interest decides the volume of investment, given the MEC.  In other words, if the rate of interest is 3%, entrepreneurs won’t invest unless they expect an increase in output of at least 3%.  Keynes also notes that the MEC is mostly analogous with Irving Fisher’s term “the rate of return over cost,” where this latter term implies that an investment won’t take place unless the rate of return over cost is greater than the rate of interest.

III.

Keynes again emphasizes the importance of prospective yields; i.e. the expectations of profits.  That is, today’s marginal efficiency of capital has as much to do with how much the entrepreneur expects to get in return from its use tomorrow as much as today.  The expectation of all in the MEC of a particular unit of capital will decrease its value today.  Keynes has a paragraph on changes in the value of money, suggesting that an expectation in the fall in the value of money will increase MEC — this isn’t necessarily true (the rise in the value of money could be caused by an increase in output). This leads to a discussion of Irving Fisher’s theory of real and nominal interest rates.  Keynes notes that what changes in money value do is change the MEC, not the rate of interest.

Also, an expectation of a fall in the rate of interest might depress the present MEC, given that entrepreneurs might further expect to have to compete with new production willingly made at a lower return.  In other words, this kind of expectation might lead to an expectation of a fall in the value of output.  This may be partially offset, though, by a present reflection of this expectation (in the present rates of interest).  Keynes notes that understanding the impact of expectations on the marginal efficiency of capital is important to understand how “violent fluctuations” in expectations explain industrial fluctuations.

IV.

There are two (potentially three) types of risk that affect the volume of investment,

  1. The entrepreneur’s risk associated with the probability of actually achieving the prospective yield;
  2. In the world of financial intermediation, there also exists “lenders’ risk:” the probability of default;
  3. Unexpected change in the value of money.

V.

Keynes again emphasizes the principal take away from the chapter: the marginal efficiency of capital depends heavily on expectations — more so than any other factor, including the rate of interest.  In passing, largely to justify his continued re-statement of the just mentioned point, he also notes that durable capital equipment is the influence of today on tomorrow (a point that Hayek uses, largely against Keynes, in “Investment That Raises the Demand for Capital”).

Keynes, The General Theory: Chapter 10

John Maynard Keynes,The General Theory (BN Publishing, 2008), pp. 113–131.

The Marginal Propensity to Consume and the Multiplier

Keynes, in this chapter, borrows from earlier work of his (Arthmar and Brady [2011]) and from R.F. Kahn’s “The Relation of Home Investment to Unemployment,” and I think is integral to understanding Keynesian capital theory (i.e. the relationship between consumption and investment).  As the chapter’s title suggests, Keynes will take us through the logic of the multiplier, which is a ratio between income and investment.  Therefore, allowing for some abstractions, it is also a ratio between total employment and primary employment (that directly employed by investment).  No less, it establishes a precise relationship, given the propensity to consume, between aggregate employment and income and the rate of investment.

He offers a brief description of the argument offered by R.F. Kahn, who is usually credited as the originator of the idea.  Assume the marginal propensity to consume to be given; employment will be a function of the net change in investment.  This chapter is dedicated to elucidating this idea (or an application of it, with some subtle alterations), and providing a foundation by defining terms.

I.

Remember that fluctuations in income come from changes in employment (a given level of employment assumes a certain level of output and a certain level of nominal income).  If we assume diminishing marginal returns with increases in output, this means that wages will rise both nominally and in real terms.  Keynes holds that real wages and nominal wages will move in the same direction (this is also established in chapter 2), which allows him to posit (since measuring real wages is difficult) that changes in income can be measured in wage-units, Yw, and used as an index. (Keynes, though, argues that nominal wages might fall or rise in greater proportion than real income!)

Knowing that increases in Yw outstrip increases in consumption (Cw), the following relationship holds true: Yw > Cw.  This allows us to define the marginal propensity to consume (MPC) as dCw/dYw.

The MPC, in turn, tells us how increases in income will have to divided between consumption and investment.

∆Yw = ∆Cw + ∆Iw (i.e. the change in income is equal to the sum of the change in consumption and the change in investment).

∆Yw = k∆Iw, where 1 – 1/k is the MPCk is therefore the “investment multiplier.”

II.

Kahn’s multiplier — that Keynes defines as k’ and calls the “employment multiplier” — measures the ratio between the increase in total employment associated with increases in primary employment in the investment industries.  Formally, this would suggest the following: if ∆Iw leads to change in employment ∆N2, the increase in total employment is ∆N = k’∆N2.

k does not equal k‘, since the supply functions between different industries differ; i.e k’ is properly applied to a single industry (or supply function), where as k is aggregated across industries (implied by the fact that it relates to total income Yw).  Despite this reality, it is easier, writes Keynes, to just assume k = k‘ (the model can be changed to show the more realistic possibility of a divergence between ∆Yw/∆N and ∆Iw/∆N2.

What the multiplier suggests is that if society consumes 9/10 of their income then multiplier k is 10.  So, for example, if the government were to build a pyramid that employed h workers (primary employment), then total employment (everything else being equal) would be 10h.  This assumes, of course, that ∆Cw is positive as Yw rises.  Here, I think, we see a very important rationale in Keynes’ model that reflects on his vision of the relationship between consumption, savings, and investment.  If I am reading pp. 117–118 correctly, the temporal sequence is as such: ↑I ⇨ ↑Y ⇨ ↑C,↑S; but, were the ∆Sw is enough to cover the previous ↑I.  In other words, in a two time period model, It would be funded by St+1.  The “secondary employment,”  by the way, is that which is stimulated in the consumer industries thanks to a rise in income.

What this means is, according to Keynes, assuming a high MPC a minor negative changes in investment can lead to broad decreases in unemployment, but minor positive changes in investment can cause broad rises in employment (towards full employment).  Comparatively, a low MPC would mean smaller changes in employment.  Where MPC is measured between 0 and 1, it therefore seems better to increase consumption, so that a relatively minor increase in investment can have greater effects on ” secondary employment.”

III.

All of what we have discussed so far assumes a net increase in investment.  In reality, though, the economy is complex.   For example, if we apply the multiplier to a public works, then we have to assume that this project didn’t cause some offset (a decrease in investment) elsewhere and it didn’t change the MPC.  What are some factors that need consideration?

  1. Depending on how public works are financed, it may raise the rate of interest and therefore dissuade private investment (crowding out?) — assuming monetary policy doesn’t try to assuage this consequence.  No less, related inflation will increase the cost of capital goods and reduce their marginal efficiency, requiring a fall in the rate of interest;
  2. Given the prevailing “confused psychology” (calculation chaos?), government spending can reduce confidence, which can in turn increase liquidity preference and/or decrease the marginal efficiency of capital;
  3. If part of increased income is spent on foreign goods, then part of the multiplier will benefit these other countries.  But Keynes is insightful enough that to the extent that this stimulates economic activity there, it may actually be beneficial to us.

Depending on the volume of public works, we also have to account for changes in the MPC.  Increases in income will tend to decrease the MPC, which in turn will decrease the multiplier.  We also have to account for distributional forces: entrepreneurs might accrue a disproportional amount of new income, and their MPC may be lower than that of workers.  Also, the unemployed may be living on “negative saving” (i.e. consuming their savings) and when they are re-employed their MPC might fall as they try to replenish their savings or repay loans.

Remember what Keynes believes the implications of the multiplier are: it is what explains the differences in magnitudes between the consequences on investment and the consequences on employment as a whole.

IV.

Now that we’ve dealt with possible alterations in net investment, another case we have to deal with is: what if changes in investment aren’t “foreseen sufficiently in advance” by consumer good industries?  This introduces us to the concept of time lags, where an unforeseen increase in capital goods production will manifest the multiplication of aggregate demand over time.  However, notes Keynes, an unforeseen increase in the production of capital goods will only gradually increase aggregate investment and it may cause the MPC to deviate and then finally return back to normal.  But, the theory of the multiplier still applies — despite the fact that it’s an instantaneous relationship — in that the effect is equal to the increment in investment times its value; this relationship holds again when a new increment in aggregate investment occurs due to the time-lag.

To illustrate the point, let’s assume that an increase in capital goods production is entirely unforeseen, such that there is no increase in the production of consumer goods.  Income earners in the capital goods industries will increase consumption, raising the prices of these goods and increasing the incomes of profit earners, who have a lower MPC, and depleting the existing stocks of consumer items.  There is therefore a reduction in MPC and the multiplier, meaning that increases in aggregate investment is less than the total increase in investment in the capital goods industry.  Everything balances out, though, when the consumer goods industries replenish their stocks to meet the increase in demand, the MPC rises, and there is an increase in aggregate investment bringing it to the level of former production of capital goods.

Keynes writes that this concept of the time-lag does play a role in his business cycle theory, but is inconsequential with regards to the validity of the multiplier theory.  Also, unless the consumer goods industries are fulling employing their fixed capital, there’s no reason to assume that there will be a great time lag between capital good production and consumer good production.

V.

Let’s explore the relationship between the marginal propensity to consume and the average propensity to consume.

Assume that in a community where 5 million workers are employed 100% of income is consumed.  The output of +100,000 workers would lead to a consumption of 99%; +100,000 workers 98%; +100,000 workers 97%’; etc.  10,000,000 represents full employment.  The multiplier at the margin is 100/n when 5,000,000 + 100,000n workers are employed; further, n(n + 1)/2(50 + n) is invested.  So, when 5,200,000 men are employed, the multiplier is 100/2 = 50; investment is 2(2 + 1)/2(50 + 2) = .06 (rounded up).  Let’s say that investment falls by two-thirds; employment would only fall by around 2%.

Yet, when 9 million workers are employed the marginal multiplier is 100/([9m – 5m]/100k = 40) = 2½.  Much lower MPC, much lesser fluctuations in employment, right?  Wrong.  Investment is now at 40(40 + 1)/2(50 + 40) = 1640/180 = ~9% (rounded down) of total income.  So, if investment falls by two thirds then employment will fall by 44%!

The ratio of the proportional change in total demand to the proportional change in investment is: (∆Y/Y)/(∆I/I) = (∆Y/Y)([Y-C]/[∆Y – ∆C]) = (I – C/Y)/(1 – dC/dY).

All of this leads Keynes to some conclusions: (a) public works pay for themselves in countries with high unemployment and high MPC, but not where an economy is approaching full employment, and (b) as an economy approaches full employment, increases in investment will garner fewer and fewer increases in employment.  Also, in an interesting application to the Great Depression in the United States, Keynes suggests that the low MPC he computes might be due to high corporate savings.

VI.

As established in chapter two, if there exists involuntary unemployment it means that the marginal disutility of labor is less than the utility of the marginal product.  This suggests that even “wasteful” government spending may increase wealth (this is where the infamous “pyramids” and hole digging comments are made).  So, the government could bury bank notes underground and employ people to dig them up and positively create wealth, even though alternative forms of investment might be preferred (e.g. building houses).  The comment on digging holes is actually an analogy to gold mining, which Keynes notes is often considered a positive endeavor, but really not that different from digging holes for money.  He notes that periods during which mining is high are periods of growth, yet where there is no gold available usually there is stagnant growth.  What all of this is actually is is a somewhat sarcastic discussion of how people find such unproductive ventures to add to wealth, but yet oppose more sensible projects.

Two pyramids, two masses for the dead, are twice as good as one; but not so two railways from London to York.

— p. 131.

Keynes, The General Theory: Chapter 9

John Maynard Keynes,The General Theory (BN Publishing, 2008), pp. 107–112.

I.

This is a very short chapter that covers the “subjective factors” behind the marginal propensity to consume (MPC).  After, there is one more chapter on the MPC and the multiplier; then, we go into my personal favorites: the marginal efficiency of capital (MEC), interest rate theory, and long-term expectations.

Keynes lists eight “main motives… which lead individuals to refrain from spending out of their incomes,”

  1. Uncertainty (“precaution”);
  2. Foreseen changes in income in relation to anticipated needs (“foresight”);
  3. Time preference (“calculation”);
  4. To enjoy “gradually increasing expenditure” (“improvement”);
  5. To enjoy a “sense of independence” (“independence”);
  6. To carry out speculative or business projects (“enterprise”);
  7. To provide a large inheritance (“ostentation”);
  8. Out of preference for frugality (“miserliness;” “avarice”).

Keynes calculates that roughly 1/3 to 2/3 of income is held by government and business institutions, mainly for the following four reasons,

  1. “The motive of enterprise:” To provide for future investment, without incurring debt or having to raise capital on the market;
  2. “The motive of liquidity:” Largely, for uncertainty; to have liquidity available for unforeseen expenses;
  3. “The motive of improvement:” To increase income;
  4. “The motive of financial prudence…:”   Related to the second, I think.  It is to cover costs, including supplementary and user costs.

Sometimes, though, there can be consumption over income (or dis-saving or “negative saving”).  Keynes includes things like spending savings at an older age and unemployment insurance.  In any case, these subjective factors are less important than the objective factors, because it is the latter which are the most relevant at any given point in time (since the subjective factors can be considered as “given”).

II.

Since subjective factors change slowly, we can assume that it is more important to study how changes in income affect consumption, rather than how the MPC changes within the same level of income.

Quite paradoxically, Keynes writes that while moderate changes in the rate of interest will have a small influence on the propensity to consume, changes in the rate of interest will have an important influence on the rates actuallyconsumed and saved.  But, it usually works in the opposite way that people expect: increases in the rate of interest may reduce the propensity to consume, but it will also reduce the quantity of savings.  Why?  Because “aggregate savings is driven by aggregate investment,” and a high rate of interest will discourage investment.  So, a high rate of interest will reduce incomes, and therefore reduce savings (since forces always work to equalize S and I).  In other words, both saving and consumption (spending?) will decrease.  In fact, we can tell by how much incomes are bound to decrease by looking at the height of the rate of interest, since the former will fall to the point of equalizing S and I.

Here we see the general theory re-stated in part:  the more we save, the higher the rate of interest relative to the marginal efficiency of capital, and the less that is spent, the greater will be the shock to our incomes.  We also see an early introduction to one of Keynes’ unique insights: the rate of interest is not governed by the marginal propensity to consume or the rate of capital accumulation, but can be much higher than these allow for.

Keynes, The General Theory: Chapter 8

John Maynard Keynes,The General Theory (BN Publishing, 2008), pp. 89–106.

I.

Terms defined, we are ready to go back to building back towards Keynes’ general theory.  This chapter, as its title suggests, discusses the marginal propensity to consume (there is also a short second chapter broadly on the same subject that will be covered in a follow-up post).  More generally, it is the first chapter of a series that will look almost exclusively on the aggregate demand function; remember from chapter three, and restated here: proceeds expected from employing N men.

Proceeds = sum spent on consumption at the given level of employment + that spent on investment at same time.  Here Keynes will spend most of his time explaining what decides the former: the propensity to consume.  A new function is introduced (C), related to employment (N).  Going on his choice of units (chapter 4), however, Keynes changes the function a bit to (Cw) as related to income in terms of wage-units (Yw). Keynes admits that maybe Yw is difficult to relate to N (the level of employment), given that different forms of employment may lead to variations in Yw (something he says he will return to in chapter twenty, where he will explain his employment function in further detail).  But, more or less, Yw is sufficiently determined to N to make the argument that follows.  This argument is that the propensity to consume is a “functional relationship X between Yw, a given level of income in terms of wage-units, and Cw the expenditure on consumption out of that level of income, so that

Cw = Yw or C = W × X(Yw)

What society consumes depends on,

  1. Income;
  2. “Other objective attendant circumstances;
  3. “The subjective needs and the psychological propensities and habits.”

In short hand, relevant factors are put into two categories: objective and subjective factors.  This chapter deals with the former.  Since the latter is a historical study (or a psychological one) and not an economic one, the juice of Keynes’ MPC relies on changes in the objective factors.

II.

What are these objective factors that can influence MPC?

(1)  Changes in wage-units:  C is more of a function of real income than nominal income, but the former will fluctuate with regards to changes in wage-units (when total output increases, though, real income will rise at a progressively lesser rate, due to decreasing returns).  Consumption is in some way proportional to changes in real income, since as real income changes consumption tends to change in the same direction.

(2)  Change in difference between income and net income:  Before, Keynes had established that consumption is based on net income (income minus supplementary costs [V]).  While he doesn’t put much importance on this factor, his basic point is that changes in income that do not manifest in net income should not be considered, and changes in net income that do not manifest in income should.  In any case, we will return to net income at some later in these notes.

(3)  Windfall changes in capital-values not allowed for in net income:  Remember, windfall changes are like supplementary costs, but unexpected (illustratively: non-insurable changes).  These are important to figuring consumption, because they are unstable and unexpected.  Keynes posits that this is more relevant for the “wealth-owning class,” but I’m not sure why.

(4)  “Changes in the rate of time-discounting, i.e. in the ratio of exchange between present goods and future goods:”  Not exactly the same as the rate of interest, according to Keynes, but approximate to it.  According to the Classicals, a high rate of interest will cause consumption to fall, but Keynes says this is not proven and perhaps doubtful.  He says that “short-period” changes will not affect the rate of consumption, for all practical purposes.  Related to (3), he writes that they may be relevant when they relate to the value of securities and other forms of these types of asset investments.  Changes in the rate of interest might have an effect if they fluctuate wildly or dramatically, or if it pays to have a life annuity over saving money (if the rate of interest is low enough).  Lastly, maybe extreme uncertainty and its effects on consumption might be relevant to this factor.

(5)  Changes in fiscal policy: Government policy can effect MPC.  For example, taxes on unearned income (capital-profits, death-duties, etc.), and redistribution policies, can all increase the rate of consumption.  On the other hand, payment of debt through sinking funds will decrease consumption.

(6)  Changes in expectation of changes between present and future income:  For society as a whole, Keynes contends that this is not likely to be a major factor (since it will average out between individuals).

When not considering changes in wage-units, Keynes suggests that MPC is essentially stable.  Other factors may cause a fluctuation in MPC, but not likely (or may be secondary).  That is, the volume of output (income) is the most concerning factor.

III.

Time to talk about the shape of the consumption function.  Since we “know” a priori (but, through experience…?) some aspects of human nature, we also know that as income rises so does consumption, but not by the same amount.  More mathematically, this means that the ∆Cw and ∆Yw are of the same sign; where dCw/dYw is positive, but less than one.  Keynes posits that while savings will rise during increases in income, they will decrease during falls in income (during “short periods,” like during fluctuations of employment), because he believes individuals would rather maintain their present living standards.  A fall in consumption due to a fall in income, if any, would be, at best, imperfect.

As already stated in the third chapter, Keynes repeats that increases in the absolute level of income will “widen the gap between” income and consumption — i.e. an increase in savings.  He rationalizes this through his belief that an individual has primary needs of higher priority than saving, but once these are met that there is less incentive to presently consume increases in income.  He argues that economic stability lies in this rule being true.  On the other hand, again, a fall in income will lead to a proportionally higher fraction of income to be presently consumed, which Keynes believes to be a stabilizing function during periods of fluctuations in employment.  In any case, the most important conclusion here is that an increase in income will necessitate an increase in investment.

IV.

Employment is a function of expected consumption and expected investment, and consumption is a function of net income (which is consumption + net investment), or more accurately net investment.  This focus on net investment is important, because as savings increase these might exceed investment to maintain capital (or protect against depreciation).  So, an even greater quantity of investment is necessary to stabilize income.  This is true also if depreciation isn’t accounted for (example [p. 99]: a house that depreciates is a drag on employment, made good only when the house is replaced).

This can be a problem in dynamic markets, especially after investment booms.  The latter may be characterized by an increased in spending on durable capital goods, where then entrepreneurs respond by setting aside funds to replace these when the time comes.  Thus, as these items depreciate income falls until the point where all these capital goods are finally replaced, elevating income once again.

Keynes believes that 1929 United States is a good example of this phenomenon.  He writes that the investment book of the mid-1920s had led to entrepreneurs to set up sinking funds and depreciation allowances for the expectation of future replacements.  This required a large volume of net investment, but without avenues of investment (no new investments to be had) it was impossible to maintain full employment income.  Thus, the economy slump; this latter event was elongated by an even greater hoarding of funds to protect against depreciation.

Contemporaneous Great Britain is another example.  A housing boom, and another increases in investment, spurred growth in sinking funds — money set aside to pay future debts or pay for capital replacement —, including by government agencies (at a growing rate).  This public control of investment, with growing sinking funds, contributed to increases in unemployment, since there was no new (net) investment maintaining income.  Another example, within the same history, is the fact that many new homeowners increased savings to remain debt-free by the time their new house depreciated completely.  Between pages 102–105 he goes over several statistical studies to show the relationship between net investment and fluctuations in employment.

What Keynes is trying to show is that these types of savings — prematurely deferring from present consumption to pay future depreciation — create a drag on consumption that needn’t occur.  This is especially paramount to understand within the context of Keynes’ belief that there is some limit to net investment.  Consumption is also important to Keynes because he understands that aggregate demand is imputed from present consumption.  This is doubly true when financing and physical production are two separate actions, such that deferred consumption may not necessarily lead to the physical provisioning for future consumption.  Finally, Keynes repeats the belief that there are only a limited number of investments that can be made.  As such, the problem of growing income and growing savings is a riddle that plagues the market economy.

Keynes also looks at the problem from the angle of disinvestment (past production?  surplus inventory?  is this consistent with his previous uses of the word “disinvestment?”), where any consumption satiated through past production leads to a reduction in aggregate demand.  L.A. Hahn, in The Economics of Illusion (pp.  207–208), makes it sound like an over-production argument.  Is this right?  Keynes writes, “New capital-investment can only take place in excess of current capital-disinvestment if future expenditure on consumption is expected to rise” (p. 105).  He notes, too, the lack of consistency on the part of those who argue the same thing when criticizing public investment (but, I think, misses the essence of these criticisms; it’s not about over-production, but failing to provide for what a dynamic consumer wants).

He seals the chapter with the crux of his argument: capital goods are not self-subsistent.  A fall in the marginal propensity to consume will lead to a fall in demand for capital.

Keynes, The General Theory: Chapter 7

John Maynard Keynes,The General Theory (BN Publishing, 2008), pp. 74–85.

[ed. This chapter includes a lot on Austrian capital theory and forced savings.  Questions of mine are peppered throughout.]

I.

Keynes restates his achievement in chapter 6: defining savings and investment such that they are always equal; i.e. S=I.

II.

Here we explore what Keynes means by investment: basically, the purchase of capital equipment, financial assets, housing, et cetera.  More specifically, the increase in the value of capital equipment.  Where his definition of investment from others’ is in the inclusion or exclusion of different individual items.  He gives the example of Ralph Hawtrey, who suggested that an “undesigned increment (or decrement) in the stock of unsold goods” should be excluded from a definition of investment (an unconvincing idea to Keynes).  Neither does Keynes agree with the Austrian definition, since he argues that the latter like to cite capital consumption “where there is quite clearly no net decrease in capital equipment as defined above.”  He also chastises the Austrians for not defining the terms, suggesting that the belief that “capital formation occurs when there is a lengthening of the period of production is ambiguous.”

This gives us some good grounds for discussion.  I will reproduce some questions I have asked elsewhere, concerning Keynes’ treatment of the Austrians here,

My first two questions deal directly with what Keynes means. First, when he chastises the Austrians for calling capital consumption what is not, is he referring to the theory of the business cycle? That is, capital consumption (malinvestment) occurs during periods of fiduciary expansion. Second, is the inability to find definitions merely a product of a lack of ‘required reading, so to speak? The last sentence is particularly interesting. My third question: what do you think Keynes is trying to say? In other words, what is his point?

III.

This is the dynamic part of the chapter: explaining the divergences between savings and income.

The volume of employment, N, is decided by the entrepreneur who is seeking to maximize “present and prospective” profits (φ(N)).  In turn, the volume of employment which will maximize profits is decided by the aggregate demand function (f(N)).  Therefore, an increased excess of investment over savings will induce entrepreneurs to increase N.  Basically, employment is decided by expectations of effective demand.

Keynes uses Dennis H.  Robertson’s explanation of pretty much the same phenomenon (according to Keynes) to clarify what he is attempting to get across.  Robertson defined today’s income as equal to yesterday’s consumption + investment; today’s saving = yesterday’s investment + (yesterday’s consumption – today’s consumption).  Saving can exceed investment if yesterday’s income > today’s income (yesterday’s income – today’s income = excess savings).  As such, excess savings = fall in income.  It describes the same phenomenon, but the two approaches (Keynes’ and Robertson’s) is different: the former is a future-oriented approach, while the latter is past-oriented.

IV.

This section is about forced savings.

At first, Keynes writes that he had mistakenly assumed some similarity between the concept of “forced savings” and the idea of “excess savings.” But, he notes, now he realizes this is not true.  He cites Friedrich Hayek and Lionel Robbins as users of the phrase, and argues that they have not clearly defined what they mean; but, he recognizes that it originates from changes in the quantity of money or credit.

Changes in volume of output (A) and employment (N) will cause changes in income, measured in wage-units.  This, in turn, will redistribute income between borrowers and lenders, and will change the amount of total income saved.  All the same, changes in the quantity of money may result in a change in the volume and distribution of income, which may affect the quantity of savings.  But, these cannot be called “forced saving.  Keynes promises to revisit the topic soon.

He decides to define forced saving by assuming a “standard rate of saving” equal to that which would exist in full employment.  Forced saving is therefore actual saving – standard rate of saving; but, Keynes points out that this would be rate and unstable (it would be a deficiency of savings).  Citing Hayek’s “Note on the Development of the Doctrine of Forced Saving,” Keynes notes that this was the original definition as employed by Jeremy Bentham.  An increase in the quantity of money cannot increase real income, therefore additional investment takes place by taking resources away from consumption.  However, writes Keynes, this concept is difficult to apply during periods of less than full employment.  This is because an increase in employment will be accompanied by an increase in capital equipment; i.e. there are idle resources.

V.

Keynes traces the origins of the idea that investment can differ from savings to an optical illusion.  Ultimately, writes Keynes,nobody can save without acquiring some kind of asset.  Aggregate savings must be equal to aggregate investment.

This, Keynes uses as an attack on the concept of forced savings.  Credit expansion will lead to greater current investment and incomes will be increased.  Except in conditions of full employment, this means that real incomes will rise with money incomes.  Then society will choose to divide its higher income between consumption and savings.  Keynes notes that it is impossible that the “intention of the entrepreneur… can become effective” without an increase in savings.  These savings are just as genuine as any other form of savings, because according to Keynes the decision to hold the new money comes at the expense of some of other form of wealth (despite the fact that new money will cause prices to rise).  He does concede that an increase in credit will lead to: (1) increased output, (2) an increase in the value of the marginal product in terms of wage-units, and (3) a rise in nominal wages.  But, he suggests that these three things occur with any rise in output.  Again, he will return to this topic in the near future.

So, while the idea that “saving always involves investment” is “incomplete and misleading,” it is better than the two alternatives: either “that there can be saving without investment” or that there can be forced saving.  Why? Because savings has two sides.  If everyone were to save simultaneously, incomes would fall: savings cannot exceed investment.  If investment were greater than savings, income would rise to where savings would equal investment.

He draws an analogy to the demand for money and its effect on money prices.  The demand for money is dependent on income and prices.  Thus, an increase in money will necessarily cause an increase in prices.  All the same, on aggregate, changes in aggregate demand cause changes in aggregate income.

Keynes, The General Theory: Chapter 6

John Maynard Keynes,The General Theory (BN Publishing, 2008), pp. 52–65 and 66–73.

[Anybody willing to help me and others interpret/understand what Keynes wants us to take away from this chapter would receive my eternal gratitude.  Many of the statements Keynes makes here are somewhat ambiguous and difficult to follow.  This is an incredibly complicated chapter.]

I. Income

Three assumptions,

  1. During some time, an entrepreneur will have sold finished output A;
  2. He will have also spent A1 on purchasing finished output from other entrepreneurs;
  3. He will end up with G, which is his end stock of unfinished goods/working capital and his stock of finished goods.

Call this relationship A + G – A1.  Some part of this is associated with the capital goods the entrepreneur had at the beginning of the time in question.  Thus, income is A + G – A1 minus the aforementioned sum.  How do we calculate this sum?  Keynes outlines two approaches, one related to production and the other to consumption.

(i)  G is derived from the maintenance and improvement of capital and its depreciation from use.  Had our entrepreneur not used this capital there would have still been some amount that he would have spent maintaining and improve it, which is denoted as B’.  At the end of the period, the resulting stock would have a value of G’, such that the net value would be B’ – G’.  (G’ – B’) – (G – A1) is user cost (U), or the opportunity cost of producing A.  Along with user cost, as already explained in chapter three, there is factor cost (F ≡ amount paid to other factors of production); F + U = the prime cost.  Income is therefore defined as the value of output sold minus the prime cost.  Aggregate (or social) income is equal to A (the value of output) minus U, since F is assimilated by the income of other entrepreneurs.  This quantity can be associated with the level of employment, because it is the entrepreneur’s expectations with regards to this quantity which decide how many factors of production are employed..

G – A1 will only be greater than G’ – B’ under two conditions,

  1. If inputs increase, but output isn’t finished and sold;
  2. If entrepreneurs are making the capital goods they use themselves.

“[I]n anticipation of the latter part of this chapter” (p. 54), aggregate consumption = Σ(A – A1); and aggregate investment = Σ(A1 – U).  That is, aggregate consumption is equal to the sum of all output minus the sum of all goods used for production and aggregate investment is equal to the sum of all goods used for production minus aggregate user cost.  In an “integrated system,” or considering the economy as a whole, where A1 is 0, consumption is equal to A and investment to -U.  Finally, effective demand is decided by the volume of employment where entrepreneurs expect maximized profits.

(ii)  First, Keynes wants to talk about non-prime costs, especially those which lay outside the control of the entrepreneur.  These are supplementary costs, V, which are involuntary, but not completely unexpected, losses.  These are things like changes in market values, capital obsolescence, natural disasters, et cetera.  Some of these are insurable risks.  This value is also the same as “the excess of the expected depreciation over the user cost.”  This value, V, should be subtracted from the income equation above (A minus prime costs) to come up with net income.  This is relevant to the entrepreneur’s role as a consumer, since it this net income that decides the relationship between spending and saving.

There is also windfall loss, which includes losses due to unexpected changes in market values and “exceptional obsolescence or destruction by catastrophe.”  The difference in windfall losses from supplementary costs is that the latter, since it is expected, more fundamentally enters into the entrepreneur’s calculations when deciding between saving and spending.  Keynes notes, however, that what these two types of costs include is largely arbitrary and dependent on the individual’s “psychology.”  The exact magnitude of V varies over time and is largely something that is considered at the time an entrepreneurial decision is made.  Thus, the exact magnitude of windfall losses varies as well, being only the difference between it and (U + V).  Keynes largely leaves the determination of these values to accounting.  But, they are relevant in that the entrepreneur or individual considers them when doing things like declaring a dividend, in the case of the former, and deciding the volume of present consumption, such as in the case of the latter.

Keynes refers to Hayek when discussing the ambiguity of definitions of “net income.” In the latter’s Economica article “The Maintenance of Capital,” he writes that an entrepreneur might prefer to keep the returns on his capital constant and set aside sufficient income to make sure that future income does not fall relative to today’s.  Keynes does not believe Hayek’s case here to hold any empirical weight, although logically sound, and further adds that the definitions of ‘saving’ and ‘investment’ are not vague and ambiguous, contra Hayek.  Keynes also refers to this previous Treatise on Money, explaining the re-definition of terms in The General Theory to avoid the confusions which the previous book brought when his terms were adopted for general use, without considering the “special sense” that Keynes originally used them in.

II.  Saving and Investment

To avoid any confusion, Keynes is determined to define these in terms agreeable to most.  ‘Saving’ is the difference between income and consumption.  Therefore, any ambiguity in the definition of ‘saving’ must be either with the definitions of income or consumption.  With income just defined (although still incredibly ambiguously), we are left with consumption — this is largely a debate over what a “consumer-purchase” is, or in more Austrian terms, what a consumption good is.  Keynes, though, avoids any drawn out discussion on this, given that as long as the definitions are consistently applied throughout the book there should be no issue with any definition.  He, in fact, states he has nothing really to add to whatever has already been discussed.

Within the framework of the variables and the income equations discussed above, consumption is Σ(A – A1).  Later in the book, Keynes drops the sigma and simply writes it (A – A1), intending to mean the same thing.  We know that income is A – U, consumption is A – A1, and therefore that saving is A1 – U.  Net saving is A1 – U – V.  Investment is equal to the same accounting function.  Indeed, given that at the end of any particular period of production entrepreneurs will have sold output A, ended with deterioration measures as U or -U (improvement in capital stock), after spending on A1.  Thus A – A1 is consumed, and the difference between (A – A1) – (A – U), or A1 – U, is the increase in capital equipment, or investment.  Net investment is A1 – U – V.

More concisely,

  • Income =  value of output = consumption + investment;
  • Saving = income – consumption;
  • Therefore saving = investment.

It therefore seems that these are backwards-looking definitions, or definitions of historical fact.

Keynes states that the “equivalence between the quantity of saving and the quantity of investment emerges from the bilateral character of the transactions between the producer on the one hand, and the other hand, the consumer or the purchaser of capital equipment.”  Income is value minus user cost, and investment is net of that paid out to other entrepreneurs for equipment.  Saving, determined by income, is a “residual” of the decision to consume and to invest.

Our author considers the possibility that individuals are “tete montéé” (excited?) in the decision on how much to save and investment, believing that such circumstances would lead to a lack of equilibrium prices at which “transactions could take place.”  In this scenario, these definitions just made no longer hold, since the value of output would be impossible to quantitatively define.  Keynes argues that there is some empirically-valid psychological trait that allows the “willingness to sell” to equal the “willingness to buy,” and therefore that equilibrium prices be established on the market.  The last paragraph of the chapter seems to confirm the idea that these are past-oriented definitions, since Keynes suggests looking at savings only after considering the decisions to consume and the decisions to invest.  This Keynes uses as his platform to re-introduce the term “propensity to consume,” stating that this will take the place of the “propensity to save.”

Appendix: Appendix on User Cost

I.  This is a digression from the main discussion, where Keynes attempts to make a comment on the relationship between user cost and the classical theory of value.  Again, user cost is defined as: A1 + (G’ – B’) – G.  G – (G’ – B’) = I, or the net current investment of the entrepreneur.  Therefore, U = A1 – I.  What this definition allows us to do is to avoid having to figure out exactly which goods are sold and which retained.  In other words, we avoid the problems of heterogeneous capital.  This relates to the decision to define output in terms of labor, or wage-units, as explained in chapter 4.

The “short-period supply price” is d(F + U), or equal to the prime cost.  This is in contradiction, according to Keynes, to equate the short-period supply price with dF.  While it may be okay to net user cost when computing aggregate supply price, like Keynes does in chapter three, it is misleading when using it to discuss the output of a single firm.  But, when determining the cost of the marginal unit of output, it seems sensible to consider both factor cost and user cost.  This is because the disinvestment which results from production cannot be neglected.

This allows us to establish a relationship between the “long-period supply price” and the “short-period supply price.”  Basically, this encompasses the life of the equipment being used, as thus must include both V (supplementary costs) and prime costs (F + U).  V + F + U is equal to the long-period supply costs, where to yield a “normal profit” the long-period supply price must be higher than the long-period supply costs, as to exceed the current rate of interest.  Keynes adds that we might even have to consider what he calls a “risk cost,” which is meant to cover uncertainty in actual yields.

Therefore,

  • Long-period supply price = (F + U) + V + risk cost + interest cost;
  • Short-period supply price = d(F + U).

Therefore, the entrepreneur must expect, at least, that V + risk cost + interest cost = d(F + U) – average value.  This is a long-period equilibrium.

What V is depends on the type of equipment. Take, for instance, the following two “extreme” cases,

  1. Maintenance that needs to occur while the equipment is being used: this is included in F.  Here dF = risk + interest costs, in the long-period;
  2. Deterioration of equipment while in use:  This is included in U, so that V here = 0.

Finally, entrepreneurs may prefer to user newer equipment first, because the lower U of older equipment is outweighed by relative productive inefficiency.  An entrepreneur prefers to use equipment where U + F is lowest.  This means that for every marginal unit of output there is a user cost that is not necessarily uniform.  In other words, U might increase with an increase in output.

II.  U is a link between present and future, since it represents an opportunity cost for using equipment for production.  More concretely, U is a sacrifice of future benefit for present benefit.  It is dU + dF + expectations of marginal proceeds that determine volume of output.  So, how is U determined by the entrepreneur?  It is the discounted value of what could be produced in a future use of the same equipment.  In order to postpone use, the user cost must be at least equal than expected present value.  If there is no idle equipment (no “surplus”), then dU is related to the decrease in life/efficiency if equipment is presently used + current replacement cost.  In the case of surplus equipment, however, then U is determined by the rate of interest and current V over the time this surplus equipment will approach redundancy.

III.  In the case of an industrial cycle, dU will depend on how long the entrepreneur expects it to last.  As the economy recovers, an increase in supply price might be a product of an increase in dU due to revisions of expectations.  Keynes argues that a policy which “scraps” half of the “redundant” equipment will cause an increase in supply price, since it will raise dU.  If V is high it follows that dU will be low.  Furthermore, during times of depressed economic activity dU and dF are not likely to be higher than average values.  Therefore, an entrepreneur with idle equipment is likely to be working at a (net) loss.

IV.  To finalize the appendix, Keynes criticizes Marshall and Pigou for assuming U to be irrelevant.  He states that it is true that the cost of maintenance of idle equipment may lead to a fall in dU, but this is a characteristic of the type of equipment and not of the short-period traits.

Keynes, The General Theory: Chapter 5

John Maynard Keynes,The General Theory (BN Publishing, 2008), pp. 46–51.

This is a short chapter that introduces us to Keynes’ use of expectations.  Here he describes a distinction between short-term and long-term (medium-term) expectations, and how these govern the rate of investment.  We will return to the latter in chapter twelve, which deals exclusively with long-term expectations.

Production takes place over time.  There is a period of time between the decision to  purchase inputs and the sale of outputs.  There is an implicit reference to uncertainty, since the entrepreneur does not know the exact demand function for his output.  Thus, the entrepreneur must form expectations, which can be divided into two categories: short-term and long-term.

Short-term expectations: The price an entrepreneur can expect, at the start of the investment, for finished output.  These are revised “daily” — “the shortest interval after which the firm is free to revise its decision as to how much employment to offer” —, which mean they influence short-term production decisions (although, short-term expectations may be influenced by long-term expectations).

Long-term expectations:  What an entrepreneur expects to earn in the future if he purchases finished output and uses it in conjunction with his capital equipment.

The level of employment depends on these expectations; likewise, realized returns will affect the level of employment only insofar as it will force changes to entrepreneur’s expectations.  Keynes’ point is that expectations are not past-oriented thoughts, but future-oriented thoughts.  As such, past expectations are largely irrelevant, except for the fact that current expectations will of course consider the present state of affairs, which is influenced by past expectations.  Also, changes in expectations will cause a change in the level of employment over after some amount of time.  This is true for short-term expectations, Keynes holds, because these expectations do not change frequently or violently enough to dramatically affect employment and output.  For the better, all changes in the level of employment require some time to elapse for “preparation,” or changing a firm’s equipment stock to allow for an increase in employment.

Long-term employment, therefore, is the level of employment which exists if a long-term expectation fully manifests itself in production.  However, given that expectations change on a frequent basis, Keynes questions whether any stable long-term employment is realizable.  For simplicity, let us assume that long-term employment is realizable.  How does this change take place?  Our author holds that inputs will be affected first, so that employment will rise in the earlier stages of production.  Over time, however, employment will rise throughout the production process (as the future unfolds).  It is also possible for employment to rise above its long-term trend, since Keynes holds that the “build up of capital” may lead to more employment and more consumption.  This means that employment over time will peak and then fall to its long-term equilibrium.

Two notes,

  1. This pattern of increasing employment (a negative parabolic function) is similar to the pattern of employment during a “cyclical movement;”
  2. The actual unfolding of events is more complicated, because there are overlapping expectations  (i.e. changes in expectations).

The present level of employment can be said to embody current expectations and the current stock of equipment.  The current stock of equipment, of course, embodies past expectations.  As such, the current level of employment is derived from a relationship between current and past expectations. (This is actually the opposite way Keynes describes it — emphasis should be on the fact that past expectations are embodied in present stock of equipment.)

Finally, it is long-term expectations which we will most consider during the course of reading The General Theory.  Short-term expectations are similar enough and gradual enough to not consider as much.  However, we must remember that in the case of durable goods, short-term expectations (of the producer) are governed by long-term expectations (of investors).  Long-term expectations cannot be checked in short-term intervals and they are liable to sudden revision.

Keynes, The General Theory: Chapter 4

John Maynard Keynes,The General Theory (BN Publishing, 2008), pp. 37–45.

This chapter, and some of the ones to follow, are meant to explain some of the concepts that Keynes tosses around the book.  Keynes suggests that none of these have really been treated elsewhere, so some type of introduction to them is in order.  This chapter, in particular, deals with Keynes’ choice of units; the units that we can assume his terms assume.

Keynes does not like the units which are already used.  He makes his point by referring to three concepts used in macroeconomics: the national dividend, the stock of real capital, and the general price level,

  1. National dividend: This a measurement of “the volume of current output or real income and not the value of output or money-income.”  More specifically, it refers to net output, or the quantity of output over that which is needed to make up for the use of capital to produce the measured output.  Keynes argues, however, that this measurement is flawed, because output is heterogeneous;
  2. Stock of real capital:  Taking a page out of Hayek (Keynes cites Hayek’s 1935 paper, “The Maintenance of Capital“), Keynes further suggests that measuring the net increase in output is difficult, because we cannot distinguish between what is needed to replace “capital wastages” (capital used during the process of production) and net output.  Here we also see the direction Keynes is driving at: he wants to look at value, not the physical make-up of the capital stock;
  3. General price level:  This term is too vague.  However, the idea of a “general price level” is never considered by business, and as such it is an economist’s problem.  Keynes suggests that there is something better.  Further, he argues that these concepts are better for statistical or historical analysis.  In their stead, Keynes wants more precise measurements.

The basis of the units Keynes suggests is in the fact that when we talk about increasing aggregate output, we are really talking about using a greater amount of aggregate labor in association with the given capital equipment used by firms.  Instead of measuring actual output, Keynes proposes to use labor as an imperfect — since labor and capital equipment do not increase/decrease in proportion — index.  This is the basis on which Keynes introduces us to two “fundamental units of quantity:” those of money-value and those of employment.

Keynes considers the first, money-value, to be homogenous (since national currency is a homogenous entity) and the second, employment, to be capable of being discussed in terms of homogeneity.  The latter is such because you can describe different qualities of work and varying salaries by comparing them to a standard hour of employment.  So, an hour of “special labor” that is rewarded at double the standard rate will count as two units.  Thus, the quantity of employment is measured in labor-units, and the money-wage of the labor-unit is the money-wage.  If E is total wages (wage bill), then E = N×W, where N is employment and W is the money-wage.

The author expands a little bit more on why there is no problem of heterogeneity.  As aforementioned, “special labor,” or labor that earns more of a money-wage per hour, can be interpreted in terms of multiple units of employment. When regarding diminishing marginal output per unit of labor, Keynes tells us to look at this as a falling efficiency in the capital equipment, not with as a different unit of employment.  Even when special labor cannot be substituted with each other, we can assume that the issue is with the capital equipment, which suffers from zero elasticity when special labor is at full employment.

Thus, Keynes proposes to measure total output on the basis of “the number of hours of labor paid for on the existing capital equipment.”  He does not see as relevant a comparison between the output produced by a given mixture of labor and capital with the output which could have been produced with another mixture of labor and capital (i.e. opportunity cost).  What is relevant is to “predict how entrepreneurs possessing a given equipment will respond to a shift in the aggregate demand function.”

Finally, the author wants to show us how he can use these two units he introduces to describe the aggregate supply function for any given firm,

Zr = φr(Nr)

Zr = proceeds (net of user cost) expectations which will induce employment Nr.  The relationship between employment and output, therefore, is where Nr results in output Or.  Or = ψr(Nr).  Such that,

[latex]p = \frac{{Z_r + U_r(N_r))}}{O_r} = \frac{\phi_r(N_r) + U_r(N_r)}{\psi_r(N_r)}[/latex]

UrNr is the user cost associated with employment Nr.

It follows that we can evaluate Or = ψr(Nr) in terms of Zr = φr(Nr), where we can aggregate all Nr‘s, but not all Or‘s, since O is heterogeneous.  We can also assume that Nr is a function of N (aggregate employment is distributed throughout industries in a unique way).