Wage unit

The wage unit is a unit of measurement for monetary quantities introduced by Keynes. 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

Main article: Real versus nominal value (economics)

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, 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.

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.

The units of the General Theory

Keynes used a subscript w  to indicate values in wage units (see Keynesian economics), but was imprecise and inconsistent. 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 ()
interest rate				r
proportion of income consumed				λ()

We make no use of subscript w ’s. The conversion factor between wage and money units 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 shows “by how much investment... will have to increase within the period, in order that its marginal efficiency should fall to any given level”. We can write i_s (r ) for the amount of real investment whose return will be at least r, and write I_s (r, P / W ) = (P / W ) ·i_s (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 shows that the multiplier has a role in it, and the multiplier had earlier been defined in wage units (Chapter 10), so we can assume that these are the units of Chapter 14. We can therefore write S (Y ) = I_s (r ); but this conceals a dependence on P / W. Since P is unknown the equation cannot easily be used as it stands.

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 ; and here, correctly, he provides no w  subscript for income, which needs to be specified in money terms; so in our notation liquidity preference would be L (W ·Y , r ).

Classical and Keynesian equations

Classical and Keynesian economics can both expressed by sets of 3 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 externally determined 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 (W ·Y ,r )	Liquidity preference
Y, Is , S  in real terms		Y, Is , S  in wage units

Keynes believed that the last two of his equations could be solved in isolation, but had failed to take account of the conversion factor between real terms and wage units in the ‘income’ equation. It might be possible, by means of a sufficiently drastic approximation, to eliminate the dependence on P, but it doesn’t seem worth while to do so. Keynes fully accepts the first equation – the ‘first postulate of classical economics’, as he calls it (Chapter 2) – and eventually has to make reference to it himself (in the very difficult Chapter 20), so it was open to him to fall back on it earlier to solve for all 3 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, 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 was not entirely explicit about the units he used in “Mr Keynes and the classics”. He supplies income (which he denotes I ) as an argument to both propensity to save and liquidity preference, presumably intending it to have the same units in each case. Since he is speaking “on behalf of the ordinary classical economist“ who “would have preferred to investigate many of those problems in money terms”, these units are probably nominal. This is the right decision for liquidity preference but hard to defend for the propensity to save. Hicks 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.

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.