Zero-Sum Foolery 4 of 4: Wage Prisoner’s Dilemma
by Sandwichman
Zero-Sum Foolery 4 of 4: Wage Prisoner’s Dilemma
Soon after the wages-fund doctrine fell out of favor with economists, it was immediately attributed to trade unionists under the label of the “fixed work-fund fallacy” and then the “Theory of the lump of labour.” In denunciations of the lump-of-labor fallacy, it has become fashionable recently to appeal to the notion of the “zero-sum game” in addition to the customary allegation of a “fixed amount of work to be done.”
What follows is a brief sketch of the wage prisoner’s dilemma that I modified from one posted last June. The outline can be elaborated by thinking of the dilemma in terms of Garrett Hardin’s “Tragedy of the Commons” and Elinor Ostrom’s analysis of common-pool resources. I have previously presented the perspective of labor power as a common-pool resource and a full treatment of wage prisoner’s dilemma would incorporate those arguments. I’ve added a pay-off matrix at the end.
The principle of labor as private property is enshrined in the chapter, “Of Property,” in John Locke’s Second Treatise of Civil Government:
…every man has a property in his own person: this no body has any right to but himself. The labour of his body, and the work of his hands, we may say, are properly his.
Except for the most part we are not talking about just “the labour of his body, and the work of his hands.” We are referring to a complex division of labor, co-operation and means of production that dwarfs the manual labor of a person. Regarding this augmented labor power as a common-pool resource recognizes the greatly-enhanced social productivity of labor. The wages system is calculated to siphon off the lion’s share of that social productivity and award it to the owners of capital.
How does that happen?
Consider the wage prisoner’s dilemma: given a choice between working long hours for more money and working short hours for less money, many will chose to work longer hours. But if a preponderance of workers choose (or are compelled) to work long hours, they will oversupply the labor market, depressing wages. They may end up working longer hours for less money.
This is not rocket science. It is elementary supply and demand: an observed regularity. And, no, it does not imply or assume “a fixed amount of work to be done.” If I flood the market with bananas, it is likely the price of bananas will fall even if the demand for bananas increases in response to the lower price. It is conceivable that the temporarily lower price could instigate a banana craze that subsequently overwhelms the initial price decline. But as a rule…
Imagine the following scenario:
One hundred workers are fully employed for 40 hours a week. The current wage is $10 an hour. Due to some inscrutable technical feature of the production process, it is determined that optimal scheduling requires workweeks of either 36 hours or 44 hours. However, weekly output per worker is the same for a 36-hour worker and a 44-hour worker. Hourly output is correspondingly higher for the 36-hour worker. Pay is determined by averaging total output and aggregate hours of the workforce as a whole.
After adjustment to the new schedules, the uniform wage rate will be somewhere between $9.09 and $11.11 an hour, depending on the proportion of workers who choose each schedule. Weekly pay will thus range between $328 and $400 for those working a 36-hour week and between $400 and $488 for those working a 44-hour week.
If half the workers choose a 36-hour week and half choose a 44-hour week, hourly wage will remain at $10 and thus the weekly pay will be $360 and $440 respectively.
One payoff matrix – out of 99 – for each worker would look something like the following, with the worker’s choice occupying the rows:
Assuming an individual was indifferent about the loss of leisure time, that individual would be “better off” choosing a 44-hour workweek whether all the other workers chose 36 hours or 44 hours. Aside from that assumption, the best option would depend on the relative strengths of the worker’s preference for leisure, risk aversion and assumptions about other workers’ preferences.
This is, of course, an extremely simple-minded example. It is meant only to suggest that “zero-sum thinking” is not the sole possible explanation for people’s anxieties about unemployment – it is unlikely to be the most plausible.
Despite all the arrogant rhetoric about zero-sum fallacies committed by advocates of shorter working time, early retirement, trade protectionism or limiting immigration, there doesn’t appear to have been any research to substantiate the claims empirically. There has, however, been empirical research on prisoner’s dilemmas or social traps, as the tragedy of the commons model is also known. Elinor Ostrom was one of the authors of “Cooperation in PD games: Fear, greed and history of play” that references Rapoport’s earlier studies. “Take-Some Games: The Commons Dilemma and a Land of Cockaigne,” by Peter Mitter is included in Paradoxical Effects of Social Behavior: Essays in Honor of Anatol Rapoport.
Another kind of game has evolved with a primarily didactic rather than investigative purpose. Julian Edney’s nuts game and Linda Booth Sweeney’s harvest game exemplify the commons dilemma or social trap learning game. In principle, there is no obstacle (other than time and money) to incorporating a harvest-type game into a research design similar to the prisoner’s dilemma research conducted by Rapoport, Ostrom and their respective colleagues.
cross posted with <a href=”http://econospeak.blogspot.com/”>Econospeak</a>
“[For] the most part we are not talking about just ‘the labour of his body, and the work of his hands.’ We are referring to a complex division of labor, co-operation and means of production that dwarfs the manual labor of a person. Regarding this augmented labor power as a common-pool resource recognizes the greatly-enhanced social productivity of labor. The wages system is calculated to siphon off the lion’s share of that social productivity and award it to the owners of capital.
“How does that happen?”
IF it happens, it happens because without capital, men have nothing to which to apply their labor. To build, one must have the materials to build. To build large, complex things, someone must organize the production and provide for the maintenance of the laborers until the product can be sold. The owners of that capital must be compensated for the time that they cannot use that capital elsewhere, and for the risk that they will not get it back at all.
But does what you say actually happen? According to Federal Reserve data going back 50 years, labor share has not dropped below 60% of GDP in that time. So the lion’s share is NOT going to capital. Other measures indicate that labor share is not declining at all.
http://blogs.wsj.com/economics/2015/03/26/thomas-piketty-says-labors-share-of-income-is-declining-but-is-it/
Your sample scenario, BTW, is fatally flawed by this: “However, weekly output per worker is the same for a 36-hour worker and a 44-hour worker.”
If that were the case, the employer would reduce everyone to a 36-hour week, and not pay anyone to work the extra eight hours.
Well, no, Warren. My scenario is not “fatally flawed” because it is not meant to be an image of reality. It is a fable used to illustrate a a type of decision structure. “Imagine an economy that produces two kinds of goods: hot dogs and hot dog buns.” There is, of course, no such thing. An economy that produces only hot dogs and hot dog buns could not exist. But that kind of fable is used by Paul Krugman to illustrate the concept of complementarity. Whether or not a hot dog and bun economy could exist doesn’t mean its use as an illustration of complementarity is fatally flawed. Sigh.
If we are talking about fables, it helps to remember that the lion’s share is all of it, not some larger fraction. That was the whole point of the fable.
The impossibility of hot-dogs-and-buns economy does not affect the point of his example. The same-output-in-36-hours-as-in-44-hours fallacy does affect the point of yours.
Warren,
In 1929 Lionel Robbins wrote, “The days are gone when it was necessary to combat the naïve assumption that the connection between hours and output is one of direct variation, that it is necessarily true that a lengthening of the working day increases output and a curtailment diminishes it.”
Obviously he was wrong. Those days are not gone. The “fallacy” you speak of was the insight that contributed to the demise of classical political economy and the rise of marginalism. Thomas Brassey, Francis Amasa Walker, Alfred Marshall, Sydney J. Chapman and Philip Sargant Florence — along with Robbins, Pigou and Hicks — would all be surprised to learn that output varies in direct proportion to hours worked and that there is no length of the day beyond which additional hours of labor do not, if they are maintained over time, lead to a decrease rather than a decrease of output.
Output, Warren, is a function of time and of effort. Effort is a function of motivation and fatigue. Whether or not there actually exists a production process in which the same output is produced in a workweek of 36 hours as in a workweek of 44 hours, there is no “fallacy” or “impossibility” inherent is specifying such a process for the sake of argument.
This may seem counter-intuitive to you. That is fine. What I would like to encourage you to do, though, is to IMAGINE a situation in which the conditions I specified existed. IF such a situation existed, workers would be faced with a decision problem, etc. What you seem to be telling me is that you KNOW something that makes imagining that situation impossible.
You don’t.
“Whether or not there actually exists a production process in which the same output is produced in a workweek of 36 hours as in a workweek of 44 hours, there is no ‘fallacy’ or ‘impossibility’ inherent is specifying such a process for the sake of argument.”
The impossibility is not that the same output can be achieved in 36 hours as in 44, but in assuming that the employer will continue to pay for the extra eight hours when there is no attendant increase in productivity.
Warren,
The employer’s total payroll cost is the same, whether workers work 36 hours 44 hours or some combination of the two. Same output, same cost, employer is indifferent. Your objection come from you adding something to the model that isn’t there and then objecting to the thing that you have added. I have tried to explain the model to you but it is clear that you don’t want to understand, you just want to object. You are therefore objecting to what you refuse to understand. There is no point in me continuing to try to explain.
Sandwichman:
Sometimes it is better to just ignore. His initial objection brought about a well written response from you, one I would whole heartedly agree with after reading it. That was the one good thing to come out of this. How much is the course?
“The employer’s total payroll cost is the same, whether workers work 36 hours 44 hours or some combination of the two. Same output, same cost, employer is indifferent.”
Yet the original post has this:
“Weekly pay will thus range between $328 and $400 for those working a 36-hour week and between $400 and $488 for those working a 44-hour week.”
The “reasoning” behind this is that, “Pay is determined by averaging total output and aggregate hours of the workforce as a whole.”
What employer would do that? It simply does not make any sense at all. He would just cut everyone’s hours to 36 per week, pay them the same hourly, and pocket the profits or lower prices to gain market share.