Tuesday, July 22, 2008


by the Sandwichman,

"This crime called blasphemy was invented by priests for the purpose of defending doctrines not able to take care of themselves." - Robert Green Ingersoll.

"To compel an employer to hire men for only eight hours and to compel the employe [sic] to work no longer than eight hours is certainly un-American." - David McLean Parry.

Consider a single individual with a utility function U (y, ℓ ) where y is income and ℓ is leisure. Both y and ℓ are 'goods', i.e. the consumer prefers more of each.

Suppose this person has non-labor income of G, and can work as many hours, h, as she wishes at a wage of w per hour. Total time available for the only two possible activities, work (h) and leisure (ℓ) is T.

If she allocates her time between work and leisure to maximize her utility, what can we say about her decisions, and about how these decisions will respond to changes in the exogenous parameters, w and G?

Three questions:

1. In what sense can w and G be said to be "exogenous"?

2. Defend the proposition that an individual "can work as many hours as she wishes at a wage of w per hour."

3. In what way does the supposition of the static labor supply model that individuals are free to work as many (or few) hours as they wish differ from the Parry doctrine that regulation of the hours of work by law is "un-American"?

To assume that wages are "exogenous" to the number of hours worked is to assume either that there is no effect on productivity from variation in hours or that there is no effect on wages from variation in productivity. Those assumption are not mere convenient simplifications but rather egregiously violate core principles of marginalist analysis.

"Suppose that supply has no effect on price and that price has no effect on demand." What kind of "economic model" could one construct based on that statement? That is the level of incoherence exhibited by the static labor supply model.

The blasphemy committed by advocates of shorter working time is not -- as claimed by economists -- an assumption that there is a fixed amount of work to be done regardless of the cost of labor. The blasphemous assumption of shorter work time advocates is that individuals are not free to work as many or as few hours as they wish at a given wage. Their crime is thus not committing a fallacy but refusing to be conned by one.


Unknown said...

"In what sense can w and G be said to be "exogenous"?"

Well, this one's easy. It's not that w and G are exogenous. It's just that they're determined by BOTH labor supply and labor demand. So when analyzing only one of them - here labor supply - they are "exogenous" (i.e. taken as given) from the point of view of an individual worker. In other words, the worker expects the same wage to prevail in the market, regardless of whether she herself decides to work or not (or how many hours, within a reasonable range). Of course the SUM of all these little individual choices does determine the wage, endogenizing it.

#2 is more problematic and is essentially the assumption of a smooth, frictionless, competitive labor market. If you're going to hang your critic's hat then this is probably the peg where it goes.

I believe that in Chapman's formulation the individual workers also take the wages as given. Rather its the disutility of labor that varies with the hours. A similar situation holds for the point of view of an individual firm who take wages as given but for whom the labor productivity varies with labor hours (due to exhaustion, etc.) - I don't have the article handy atm (I'll look it up later) but I can look it up in a bit.

Where Chapman departs from what I guess could be called the 'standard' view is in assuming that workers and firms do not come to optimal decisions in regard to working hours because the former (and maybe the latter) are myopic (this part of Chapman's article, as I remember it, is more speculative and less clear. It is also does not comprise the majority of the article).

As Hick's noted, if you drop this assumption and let workers and firms come to an optimal outcome you basically get the pure 'standard' model. Of course this may not happen in the real world - though even than it's hard to see why there should be a uniform, rather than an industry or even occupation specific, limit on number of hours.

Anyways. To use Chapman's theory to argue that restrictions on hours can reduce unemployment, you'd need a model with actual unemployment in it - another friction which prevents some vacancies from being filled. As I understand it, Chapman's baseline is basically still a model of full employment, just with work shift length chosen (possibly) sub optimally.

Sandwichman said...


Thank you for some very helpful comments.

You're right about Chapman using the term 'myopia'. But wrong about it being a minor aspect of the paper. It's the crux of the matter, which is clear from Pigou's recapitulation and Robbins's and Hicks's comments on it.

It would be presumptuous of me to say ''that isn't what he means" by myopia but I do think he means something other than what the term normally connotes -- an unfortunate choice of words. The employer and the worker are indeed "short sighted" but they are compelled to their short-sightedness by competition.

In other words, if an employer, acting alone, did take the long view, it wouldn't do her any good because a competing firm could poach away her well-rested workers with the offer of a higher wage. Similarly an individual worker who refuses to work overly long hours will have to accept a lower wage rate for working his preferred hours. So the 'myopia' is not an intellectual deficit but a circumstantial necessity.

Ironically, myopia also come into play when workers do "take the long view". Employers tend to reward eagerness to "go the extra mile" (by putting in extra hours) with promotions. A worker who wanted to get ahead presumably would respond to those incentives rather than to an unreinforced notion of what might hypothetically be optimal for physical and psychological welfare, when such optimum is not an option actually offered by employers.

The sub-optimal outcome is thus not an "assumption" for Chapman but the result of a quite conventional neoclassical analysis. Hicks wasn't talking about dropping an assumption but "setting aside" the logical outcome of an analysis that he accepted as definitive. His reason for doing so is important to the whole setting aside notion. Hicks was assuming that "in the real world" as opposed to the theoretical model, trade unions were so strong and ubiquitous as to be able to force employers to yield to any demand for shorter hours that didn't actually impair productivity. My guess is that such an estimate of union strength was far-fetched as a description of Britain in the 1930s -- but the USA in the 2000s? Really.

Again, you're right that Chapman's model didn't address the question of unemployment. In my view, however, Chapman's analysis does lend credence to Ira Steward's shorter hours theory, which does indeed address unemployment. I would love to produce a synthesis of Steward's and Chapman's analyses, particularly in the light of Keynes's analysis. Not being a professional academic, though, I have to proceed one step at a time. I've done my debunking of the lump of labor fallacy. I've done my extended discussion of Chapman's theory and its fate. Now I have to turn my attention to Ira Steward and George Gunton and tie it all together.

I have to confess I remain perplexed by "exogenous parameters" that get endongenized the moment they're viewed from a total labor force perspective -- although I suppose that's why they call it a "static" labor supply model. It's not so much that I object to unrealistic assumptions as that I'm curious as to what is supposed to be revealed analytically by making this particular assumption. If the SUM of all those individuals expecting a given wage changes the wage, won't they ever learn? Well, no they can't because then those 'individuals' wouldn't be of any use to economists. They all have to somehow be both stupid and rational at the same time!

Unknown said...

I found Chapman's article. As an aside I'm sympathetic to the view that modern day economics doesn't really say much about the optimality or determinants of work shift length. An exception here would be a fairly recent article by Prescott and somebody (horrible of me not to remember the coauthor) which has a theory similar to Chapman's but where the hours are optimal and the whole thing is embedded in a real business cycle model, making it unpalatable to those with heterodox tendencies. So, for completely unrelated reasons I spend some time awhile ago thinking about this issue. Anyways.

"But wrong about it being a minor aspect of the paper."

Well, it's actually sort of hard to say. The Economic Journal article is from 1909 which means it's written in a completely different style and with different rhetoric. It's a 20 page article (353-373). Of those the first 5 or 6 are purely devoted to convincing the reader that the topic is important and are essentially "literary" in character. The actual analysis begins at bottom of page 358 but up until page 364 it's pretty much defining "leisure", laying out how productivity and utility vary with hours and how competition works (per my comments in previous comment).

In fact there's a bit of "literary" aspects here and the whole actual model is essentially contained in footnote 1 on page 363-365.

The stuff about the hours being suboptimal begins on page 364 in the main text and in that lengthy footnote. Here Chapman refers first to the "wise" "far-sighted" "operative" (employee):

'Apart from satisfaction or dissatisfaction of working, therefore, the far-sighted operative who took into account the value of leisure would choose...'


'Then the working day which perfectly wise operatives would choose would be...'

In the following paragraph he contrasts this with the choices made by the non-wise operative:

'the operative who lives for the day ...'

Anyway. The crux of the matter seems to be contained further in the paragraph:

'less the loss occasioned by the reduction which will ULTIMATELY (emphasis in the original) take place in the productivity of the operative's earlier hours in consequence of the addition of the O nth increment of time to the working day.'

As far as I can make out from the "literary" main text some confusion arises from the way that the word "exhaustion" is used and how leisure is described.

As to the first, what Chapman seems to be saying is that there's two kinds of exhaustion. The first is on-the-job kind of exhaustion. If I turn a crank for many hours, eventually my arm will get tired and I can't turn the crank as fast and so my productivity (measured say by number of turns per unit of time) suffers. This kind of exhaustion is accounted for by the firm and is not the source of the sub-optimality.

The other kind of exhaustion, on my reading, occurs when a worker works long day after long day and is essentially a form of mental exhaustion which erodes what these days would be called the "human capital" of the worker (in one or two places Chapman suggests that long shifts lead to increased drunkenness and that's the major source of the productivity decrease. This was written in 1909 after all)

Presumably the firm doesn't care about this kind of long-term exhaustion since, this being a competitive labor market on both sides of the bargain, it can always replace a drunken exhausted operative by a fresh one and set him on his road to ruin anew. What's not clear is why the workers would accept this - without demanding higher wages in order to compensate them for this erosion of human capital. In fact, in Chapman's model (myopic) workers are happy with this situation.

And that's where the (true) myopia seems to come in. So you're partly right. On the part of the firm the "myopia" isn't really myopia. But to get it to work Chapman does assume that the workers REALLY are myopic:

'Hence we must conclude that operatives who are NOT ALIVE (i.e. not aware, myopic, etc. my emphasis) to the reactions of long hours on efficiency and capacity to enjoy life and work (this is the leisure side of things) will tend to choose a longer working day than is wise from their point of view'

Some other things to note;
1) Here it is the workers who make the wrong choices and employers are only happy to accommodate them. It's not that the firms are FORCING the workers into these choices.
2) At the end of the footnote (pg 365) Chapman seems to indicate that essentially technological (productivity) progress and increased education will eventually solve the problem: 'The general conclusion is manifest that progress may be expected to be accompanied by a progressive curtailment of the working day'. Since this was written 99 years ago, a snarky cynic might observe that the problem HAS been solved.
3) Relatedly, in the last portion of the article - another 5 pages - Chapman throws out some opinions and options. At one point he actually says that he thinks that rather than a government restriction on hours 'it might not be better to suffer for a time present ills in the hope that there would grow up in the community an adequate power of self-regulation". In other words, remind the workers that hard daily toil will have an adverse effect on their long run productivity.

So the main problem here arises because Chapman's describing dynamic effects and slapping them on top of a static model. The only way he can sort of reconcile these two dimensions (understandably given the techniques available to him at the time) was to make workers completely myopic.

And so

"individual worker who refuses to work overly long hours will have to accept a lower wage rate for working his preferred hours"

does not imply that this - or its reverse, accepting a higher wage rate for longer hours - are suboptimal.

My actual sense of this is that with the extra variable of shift length there is actually an indeterminacy which cannot be got rid off without some extra behavioral/economic structure. That's sort of where I got stuck when I was thinking about this some way back and all I could get is an upward sloping wage-hours curve but no way of knowing where you'd wind up on that curve.

Ok. Too long already.

Unknown said...

Also, I don't know Ira Steward's theory. Got a reference?

Sandwichman said...


Excellent summary of Chapman's article. Thank you. It really is a pleasure to be able to do a comparative reading.

With regard to the Chapman's notion of the workers' myopia, there is a long tradition of paternalism toward workers by economists and Chapman didn't escape it. One only has to read Marshall, Chapman's mentor, or Pigou to see reservations about whether workers would know how to use their leisure appropriately. Even Ira Steward -- and he was a mechanic, not an economist.

Chapman's literary style was quaint, to say the least. Had he tried his hand at Gothic novels, he could have given Bulwer-Lytton stiff competition. The long footnote and diagram on page 363 almost says it all -- except that he should have used four diagrams and explained the steps both technically and colloquially. My editorial advice would have been to turn the article inside out. The footnote should outline the main structure of the article and the literary chaff should be trimmed substantially and what is left put into footnotes!

Pigou presented a more concise version in the Economics of Welfare. I haven't read it in a while, so I'm reluctant to say whether it was clearer or complete. Nevertheless, I found reading the two together helpful.

Ira Steward also poses a challenge of isolating and reconstructing the usable kernel of his argument. He wrote propaganda. George Gunton, his 'disciple', also wrote propaganda. That was fair enough considering that most of the reputable political economists of the day essentially wrote propaganda from the employers' side.

I would recommend reading Steward with some context. A good place to start is Dorothy W. Douglas's "Ira Steward on consumption and unemployment" in the Journal of Political Economy, August 1932. Henry Mussey's 1927 essay, "Eight-hour theory in the American Federation of Labor" (in Economic Essays, edited by Jacob Hollander) is sympathetic but critical. Reading Mussey's essay in juxtaposition to Douglas's is instructive because they fall on opposite sides of the stock market crash and start of the depression. Different "consensuses" are evidently in play.

Steward's tract, "A reduction of hours an increase of wages" is available through the Internet Archive in John R. Commons' Documentary History of American Industrial Society. George Gunton produced a more systematic exposition of Steward's theory in his 1889 pamphlet, "The economic and social importance of the eight-hour movement", which can be found in the anthology, Wages, hours and strikes: L
labor panaceas in the 20th century, (edted by Leon Stein and Phillip Taft).

A couple of more contemporary discussions of Steward are Lawrence Glickman's "Workers of the world, consume" in International labor and working class history Fall, 1997, and David Roediger's "Ira Steward and the anti-slavery origins of the American eight-hour theory, Labour History, 1986.

A couple of points I would like to make about Steward, Gunton and their interpretors. First, Steward's theory appeared without a frame or, more accurately, outside of and in opposition to the frame of classical political economy and its wages-fund theory. There are loose ends in it that I suggest could be resolved within a Keynesian frame. Keynes himself alluded to the possibility of such a reconciliation in his war time remarks on the reduction of working time as the "ultimate solution" to unemployment. Second, no one has ever re-evaluated Steward's theory in the light of Chapman's theory of the hours of labor. I strongly believe that a reconciliation of Steward, Chapman and Keynes (throwing in Luigi Pasinetti for good measure) is feasible and would be extremely invigorating for heterodox economic thought.

YouNotSneaky! said...

Thanks for the references on Steward. I found some mention of him here:


which is also a good overview of both the work-length movement, and actual times.

Steward appears to be a sort of a pre-Keynesian Keynesian. The effect of reducing work hours on unemployment is here as there demand driven (unlike in Chapman where there's an effect on productivity). As such, if one thinks that demand only matters for short term fluctuations, and long run trends are determined by productivity, this remedy (shortening the work day) would be a short term solution. This might also be how Keynes - depending on one's reading of him - saw this policy. Of course a 'synthesis' of Chapman and Steward might work differently.

I apologize for delay in response - had some personal matters to attend to - and note that I've switched to my original blogger account.

Sandwichman said...

Steward appears to be a sort of a pre-Keynesian Keynesian

Yes, that's pretty much Dorothy Douglas's point. My sense is that there is more than one thing going on contributing to productivity gains and employment gains and losses and that finding the right balance is a crucial factor in determining whether there is a net gain or loss of jobs. I will repost the bibliography to a new entry. Including the Whaples article you mention. Thanks for that.