Partial vs General equilibrium labor supply models

In the standard labor supply model, the individual's choice between income and leisure is mediated by the wage level. But in the analysis of labor demand, the presence of quasi-fixed, per-worker costs constrain the substitution of hours for workers. To an ignorant non-economist, the presence of these quasi-fixed costs raises questions about what economists mean when they refer to 'the wage' with regard to their labor supply model.

I'm sure my confusion could be easily cleared up with a few letters of the Greek alphabet, an indifference curve or two and a smattering of strategically-placed assumptions. But I want to try to do it the hard way, with examples drawn from real data that have a semblance of familiarity to the unlearned, such as myself.


According to the Bureau of Labor Statistics, the median hourly wage in the USA for all civilian workers in 2009 was $17.90 and the median weekly wage was $708. Imputing the median weekly hours from those two numbers gives us 39.6 hours. An earlier (2003) survey of total compensation costs reported wages and salaries as approximately 72% of total compensation costs. Benefit costs made up the rest. But a large portion of benefit costs are tied directly to hours worked. For the sake of convenience, we will assume that quasi-fixed, per employee costs comprise 10% of total compensation costs. On top of that, we will add a fixed 5% administrative cost to the compensation total, so that labor costs can be regarded as 105% of compensation.

The weekly cost to the employer for this median worker is calculated to be $1032.50, of which $147.50 are quasi-fixed costs. Now, if the worker 'chooses' to work 5% less or two fewer hours a week, this $147.50 fixed cost will act as a wedge of around 18 cents an hour between the given wage rate and the employer's cost. Either the employer would have to swallow this small differential or the employee would have to take a small wage cut in addition to a cut in weekly income proportionate to the reduction in hours.

Now it is arguable that our median worker will be just as productive in 37.6 hours as he or she previously was in 39.6 hours, so a loss of $42 in weekly income may seem unfair to the worker. In fact, considering long-term trends, the reduction from 39.6 hours to 37.6 hours might even make the worker more productive, not just on an hourly basis but in total. In 1958, BLS economist Joseph Zeisel called the long-term decline in the industrial workweek "one of the most persistent and significant trends in the American economy in the past century." That was, it had been persistent and significant up until around 1940.

A lot changed after the Second World War. One of the changes was the growing importance of per-employee benefits, which economists started to take serious note of in the 1960s. Another change was the institutionalization of government economic stabilization policy. Unions in the U.S. gradually ceased advocating shorter working time as a remedy for unemployment and started urging government spending instead. As political pressure for work time reduction receded, economic incentives for longer hours accumulated.

From 1850 to 1946, the industrial workweek declined from 66 hours a week to 40, a decline at the rate of about a half a percentage point a year. From August 1945 to March 2010, however, the average manufacturing workweek increased by six minutes. Let's imagine that the earlier trend reflected a sustained decline in the number of hours per week optimal for output. And let's assume that the same trend could have continued. Under such an assumption, the optimal full-time workweek today would be around 32 hours or about 18.5% shorter than it is. If that was the case, not only could we be producing as much in the shorter hours as we currently are in 40 but we could potentially produce more.

The theoretical basis for the above speculation has a remarkably prestigious pedigree: William Stanley Jevons, Alfred Marshall, Sydney J. Chapman, A.C. Pigou, Lionel Robbins, J.R. Hicks... Whereas the origins of the "labor-less labor supply model" are... ummm... somewhat murky.

(See also Lars Osberg's observations on a level playing field in hours from the Report of the Advisory Committee on the Changing Workplace, 1997.)

deja vu