Wage unit
The wage unit is a unit of measurement for monetary quantities introduced by Keynes.[1] A value expressed in wage units is equal to its price in money units divided by the wage (in money units) of a man-hour of labour.
Other units of value
Labour theory of value
The classical economists believed that the value of a product could be identified with the number of man-hours of labour which went into its production. This value was inherently real.
Monetary (nominal) values
Economic values can always be expressed in monetary terms except in a barter economy. There are two reasons to avoid doing so. The first is in order to make comparisons of wealth between different periods or currencies. The second is that in many simple models all prices will move together – for instance in perfect competition the effect of a change in money supply may be a proportional change in all prices. In the latter case it is easier to work with a single variable denoting price level than with a vector of prices; and real values are then automatically available as money values divided by the common price level.
Real values
The use of real values beyond the confines of simple models relies on price indexes derived from baskets of goods. A complication arises if values defined this way are used in an economic model, which is that the model may treat wages differently from prices. If services (which may sometimes amount to direct payment for labour) are included in the index, care needs to be taken to avoid confusion.
Wheat values
Pigou, in his paper on the value of money,[2] used wheat values, which he claimed to have taken from Marshall. The value of money is represented by “the number of bushels of wheat which a unit of it will purchase”.
Properties of wage units
If prices and wages move together, then values in wage units will be unchanged; hence the use of wage units is equivalent to expressing values in real terms. But if prices move while wages are fixed, then values in wage units will move in parallel with prices, and the use of wage units is equivalent to expressing values in money terms. However there is unbounded scope for simultaneous movement of wages and prices, whereas prices have only limited freedom to move while wages are fixed, so values in wage units resemble real values more than they resemble money values.
Keynes’s reasons for eschewing ‘real’ values
Keynes’s decision not to work in real terms was in tune with the intellectual fashion in his day. Schumpeter observes that:
most of the leading Austrians took a critical, not to say hostile, attitude toward the idea of ‘measuring’ variations in the purchasing power of money (reciprocal of price level) by index numbers. They were inclined to refuse citizenship to the concept of price level and, in any case, to deny its measurability on principle [he supplies a reference to von Mises]. In view of the fact that so many economists placed and place an uncritical trust in index figures without troubling themselves about their meaning [he supplies a footnote referring to Keynes], this attitude provided a much needed antidote.[3]
and the footnote reads:
In the last ten years or so a reaction has set in of which the most important symptom is that Lord Keynes, who in the Treatise on Money (1930) evidently attached much importance to price indices as tools of theoretical analysis, entirely avoided their use in his General Theory (1936).
Keynes viewed real values as introducing unnecessary imprecision rather than as being meaningless. He comments that...
...the well-known, but unavoidable, element of vagueness which admittedly attends the concept of the general price-level makes this term very unsatisfactory for the purposes of a causal analysis, which ought to be exact.
Nevertheless these difficulties are rightly regarded as ‘conundrums’. They are ‘purely theoretical’ in the sense that they never perplex, or indeed enter in any way into, business decisions and have no relevance to the causal sequence of economic events, which are clear-cut and determinate in spite of the quantitative indeterminacy of these concepts. It is natural, therefore, to conclude that they not only lack precision but are unnecessary. Obviously our quantitative analysis must be expressed without using any quantitatively vague expressions. And, indeed, as soon as one makes the attempt, it becomes clear, as I hope to show, that one can get on much better without them.[4]
The units of the General Theory
Keynes used a subscript w to indicate values in wage units,[5] but was imprecise and inconsistent. In the words of Bradford and Harcourt:
On balance, it appears that for all the ingenuity and subtlety of Keynes’s reasoning on the question of units, he ultimately failed to apply it consistently in The General Theory. Given the importance attached to these concerns in Chapter 4, this is a serious defect...[6]
We will briefly set out the main equations of his system taking care to make units and dependencies explicit. The values we shall discuss, and the units in which we express them, are as follows:
| Meaning | in real terms | in wage units | in money terms | pure number |
|---|---|---|---|---|
| wage rate (per man-hour) | W | |||
| pricel level (per unit of real output) | p | |||
| consumption | c | C | ||
| saving | s | S | ||
| income | y | Y | ||
| investment schedule | is | Is | ||
| liquidity preference | L () | |||
| money supply | M̂ | |||
| interest rate | r | |||
| proportion of income consumed | λ() |
We make no use of subscript w ’s. The conversion factor between wage units and real terms is p / W , so C = (p / W )·c. W is assumed given but p is an unknown which needs to be determined.
The propensity to consume
The propensity to consume is introduced in Chapter 8 as the desired level of expenditure on consumption (for an individual or aggregated over an economy) as a function of income. Let us assume that the proportion λ of income consumed is a function of real income, so
- c = y ·λ(y ) C = Y · λ(Y / (p / W ))
Keynes assumes that λ(y ) varies relatively slowly with y, and that p / W moves only within a narrow compass, and thus concludes that changes in p / W have only a weak effect on C, allowing us to adopt the approximation C = C (Y ), i.e. to treat the propensity to consume as independent of the price level. In the same way we can write S = S (Y ). Keynes shows that he is conscious that he is making an approximation in Point 1 of §II of Chapter 8.
The schedule of the marginal efficiency of capital
Chapter 11 of the General Theory is disconcertingly free from any mention of units, but the argument is evidently real. The schedule specifies “by how much investment... will have to increase within the period, in order that its marginal efficiency should fall to any given level” (p136): in other words, how much new equipment will give a return above that level. We can write is (r ) for the amount of real investment whose return will be at least r, and write Is (r, p / W ) = (p / W ) ·is (r ).
In Chapter 14 Keynes derives an equation in Y and r by looking for the point at which the curve which ‘relates the amounts saved out of an income Y1’ to a given ‘investment demand-schedule’, which is to say to a given schedule of the marginal efficiency of capital. He gives no indication what units he is working in, although he refers to I and S with no subscript w. When he recapitulates the argument in Chapter 18 he assigns wage units to increments of ‘investment’ and ‘aggregate income’ (p248), and we assume that this applies equally to the units of the earlier statement. We can therefore write the equation as S (Y ) = Is (r, p / W ). The dependence of the right-hand side on p is not acknowledged by Keynes.
Liquidity preference
Keynes’s initial (Chapter 13) model of liquidity preference considers the demand for money to depend solely on the interest rate. This is purely monetary: the liquidity preference can be written L (r ). His more elaborate theory (Chapter 15) makes liquidity preference depend on Y as well as on r . He provides no w subscript for income, implying that it is specified in money terms, in which case L should also be in money terms; but this is contradicted later (p246) when Keynes says that L is in wage units.
It is impossible to be sure which he meant: the units of liquidity preference should also be the units of money supply M̂, given that the two quantities are set equal to each other, and the money supply is usually considered to be externally determined in money units (but Keynes allows for the effect of a change in the wage unit on p266). On the other hand it is slightly more accurate to say that liquidity preference in wage units depends on income in wage units than to state a similar dependency in money terms. Taking Keynes’s later statement as authoritative we shall write liquidity preference as L (Y , r ) in wage units.
Classical and Keynesian equations
Classical and Keynesian economics can both be expressed by sets of three equations. The differences go beyond the differences in the equations since the interpretations differ more than the mathematical form: Keynes’s causal connections are almost the reverse of those in classical economics. N is the number of workers employed, V (r ) the velocity of money, and M̂ the money supply. The unknowns are N, r, and p : Y is a known function of N in the classical equations and of N and p in the Keynesian ones.
| Classical | Keynesian | ||
|---|---|---|---|
| Y' (N ) = W / p | The first postulate | ∂Y / ∂N = 1 / p | |
| Is (r ) = S (Y (N ),r ) | Determination of the interest rate | Is (r, p / W ) = S (Y ) | Determination of income |
| M̂ = p ·Y (N ) / V (r ) | Quantity theory of money | M̂ = L (Y ,r ) | Liquidity preference |
| Y, Is , S in real terms; M̂ in money terms | Y, Is , S , M̂, L in wage units | ||
Keynes believed that the last two of his equations could be solved in isolation, but this is due to his not having a conversion factor in the ‘income’ equation.
If he had stuck with his Chapter 13 account of liquidity preference, he would have been free to write the income equation in real terms with no conversion factor and the liquidity preference equation in money terms. Under his Chapter 15 theory income is present in both and this makes it impossible to adopt a consistent set of units in which the two equations can be solved on their own.
Keynes fully accepts the first equation – the ‘first postulate of classical economics’, as he calls it (Chapter 2) – and eventually makes reference to it himself (in Chapter 20), so it was open to him to fall back on it earlier to solve for all three unknowns together.
Interpretation of income in wage units
Although Keynes needs the first equation in order to get a solution, he presents his system as complete except for details as soon as he has the last two equations,[7] which he interprets as being in Y and r alone.
This creates the possibility of falling into a certain misunderstanding. Assuming that income is indeed determined in wage units by these equations, it might be supposed that – income being a quantity in man-hours – the level of employment is likewise determined. But the expression of income in man-hours is purely artificial. In particular, although the level of income has been determined, its division between wages and profits has not, so the level of employment is indeterminate.
Units for IS-LM curves
John Hicks presented Keynesian arguments in money terms in “Mr Keynes and the Classics”. He supplies income as an argument to both propensity to save and liquidity preference, implying that the proportion of income saved is a function of income in money rather than real terms. Keynes himself complained that Hicks made ‘saving a function of money income'.[8] He also followed Keynes in ignoring the fact that the schedule of the marginal efficiency of capital is defined in the first place in real terms – his expression should correctly be Is (r, p ) = p ·is (r ).
He was aware that there were difficulties and at one point had smoothed his path by assuming that wages were constant. The following observation is by Richard Kahn:
I was surprised by Hicks’ statement that:
All expositors of Keynes (including myself) have found this procedure [working in terms of wage-units] a difficulty [...] We had to find some way of breaking the circle. The obvious way of doing so was to begin by setting out the rest (multiplier, liquidity preference and so on) on the assumptions of fixed money wages.[9]The result, as Hicks points out, is the false impression that Keynes assumed wages to be constant at any level of employment short of full employment.
Hicks’ procedure is completely unnecessary. Keynes, in many contexts, emphasised the ‘stickiness’ of wages. But that was not the reason for his use of the money-wage as a unit.[10]
References
- ↑ “The general theory of employment, interest and money”, 1936.
- ↑ “The value of money”, Quarterly Journal of Economics, 1917.
- ↑ “History of economic analysis” (1954), Part IV, Chapter 8, §4 (c).
- ↑ Chapter 4, §2 (iii)
- ↑ p41, footnote.
- ↑ “Units and definitions“ in G. C. Harcourt and P. A. Riach (eds.) “A second edition of the General Theory, vol 1”, 1997.
- ↑ He describes the national income as ‘almost the same thing’ as the level of employment near the end of §I of Chapter 18.
- ↑ Collected writings XIV, p80, cited by G. M. Ambrosi, “Keynes, Pigou and Cambridge Keynesians” (2003).
- ↑ John R. Hicks, The crisis in Keynesian Economics. Yriö Jahnsson Lectures. Oxford: Basil Blackwell, 1974, p60.
- ↑ “The making of Keynes’ General Theory ” (1984). Raffaele Mattioli lectures.