The view of labor as household’s product is suggestive in that labor is a remunerated
input used in the creation of other goods. But this view is contra-indicated in commonplace historical
observations: the higher a population’s real wage, the less will it work. Economists have long
had an intuitively satisfying narrative for this phenomenon. It is usually given in terms of the
economic system’s response to generally improving manufacturing technique:
1. Sensing an opportunity for gain, an economic sector raises the capital investment
needed to implement an improved technology. This increases the profits with which to reward its new
investors, while making the sector a more efficient user of its inputs.
2. Increased efficiency means that more of this sector's output can be produced at a lower unit
cost. Thus the sector can reduce the price of its output in order to sell more, yet still attain
the additional profits needed to justify its expanded investment.
3. This increased efficiency lessens the sector's general use of its inputs, including some
demobilization of labor.
4. But, as the real wealth of the economic system has expanded, fewer hours of work should
nonetheless suffice to buy even more than was purchased prior to the implementation of the new
technique.
5. Efficient labor markets should then operate to redistribute unemployment to the end of
maximizing everyone's utility, i.e.: marginally better lives are provided with marginally less
labor.
Thus labor is fundamentally unlike other economic goods that are produced in greater abundance when
their prices rise. A sector in need of more workers can generally find them by raising its wage;
but, cet. par., only by taking these workers away from other sectors to the general effect of reducing
overall labor availability. In conventional analysis this would be to say that both the supply and
demand schedules for labor are downward sloping when viewed from the standpoint of the macro economy.
In continuation of ideas that have not changed much since Jevons, our essential premise for describing households is that they arrange their affairs for the maximization of leisure. More precisely, we proceed from the notion that time exhausted in the acquisition of things is limited by a need to allocate the time needed for the enjoyment of things. People generally labor in order to rest; and to earn that which provides comfort, amusement, and security in their leisure time. Stated formally, this means that one stops working when the enjoyment of a prospective hour of leisure is equal in value to what is earned by the last hour worked.
Time’s inherent unity enables further analysis by relating labor to leisure in a simple and systematic way. Time always flows at t = 8766 hours per year — which is, perforce, all the time experienced by any single worker. If this worker is typical, he is at his job for 2000 hours per year, leaving him with -Y = 6766 hours per year of leisure.
Taking leisure -Y as the product created by households’ intake of consumables does not remove labor availability from the analysis: final consumption simultaneously specifies both labor and leisure because both are residuals of one another with the unity of time t, which is a constant of nature. Retaining focus on a single, typical worker, we can bring the parameter t into the following picture of labor/leisure/wage tradeoffs:
The figure above consolidates all household consumption into a single good. E = 480 physical units per year of this good therefore represents the real wage. An ‘input’ of 480 units of the universal consumable per year ‘produces’ -Y = 6766 hours per year of leisure. Reference to the unity of time’s flow allows us to infer labor availability from this same ‘household production function’: t(=8766) + Y(=-6766) = 2000 hours of labor per year. Essentially, we view households as working up to a point where they can support the consumption needed for contentment within the leisure segment -Y of their continuing experience of time t.
(SFEcon’s sign convention has things going into the economy presented as positive quanta to suggest increasing distance from the observer; things coming out of the economy are signed in the negative to suggest decreasing distance from the observer. In this interpretation, labor and consumption are positive quanta because they are ‘inputs’ that go into the economy for the sake of producing other things that come back out of the economy. Leisure is negative because it is among the economy’s products.)
When improving economic conditions are manifested in a rising real wage E, SFEcon’s portrait of household utility would have more leisure ‘produced’, which compresses the amount of labor going to market. Our structure is therefore expressive of the observed historical trend by which real wages rise while labor availability falls.
Having treated household utility in close analogy to production theory, we can continue on to a marginalist explanation as to why a given [Y,E] relation should be preferred over all others and therefore remain stable. These analyses always presume exterior specification of a price environment [p,P], i.e.: the money wage, p $ per hour, and the universal consumable’s price P $ per physical unit. Noting that every hour at leisure is exactly one less hour at work, we can infer the price of our household product as minus the wage p. Household consumption’s value of marginal product VMP is then imputed as -p• ¶Y/¶E. Finally, we arrive at a specification of the household optimum by equating the consumable’s VMP (or marginal revenues) with its price P (or marginal cost):
Had we pursued the more obvious formulation of labor as the household product, consumption’s value of marginal product VMP would have been imputed as p•¶(t+Y)/¶E. Noting that t does not vary with E, the above equation of marginal revenues with marginal costs would have changed only with respect to its leading minus sign. This comparison formalizes the initial premise of our analysis by requiring that the first hour of a household’s leisure must equal the value of its last hour of labor for the economy to be at stasis. Thus our household premise is seen to function just as the premise of maximal profit functions in the standard analysis of a generic industrial production function.
The analysis here will of course require elaboration in several directions if it is to be of use in empirically meaningful economic models. The most obvious improvement will be to disaggregate our single consumable E into EJ, viz.: all the separate inputs J to household leisure. Each input J will have its distinct price PJ; but our formulation’s close analogies to standard production theory are such that standard theory will encompass this extension.
Usage of the parameter t will require more in the way of creative development if it is to serve more realistic purposes than those of Model 0. A household sector’s limit of labor availability is most sensibly computed as t multiplied by the number of workers in that sector; and the questions of ‘who is or is not a worker?’ or, ‘when does someone voluntarily unemployed become a job-seeker?’ must be conjured without references in pure theory. And matters of demographic shifts within a sector would seem to owe more to forces that are beyond economics than to forces originating within economics.