Canny Ca'canny

Under imperfect competition, according to a 1960s Samuelson textbook, "The canny seller contrives an artificial scarcity of his product so as not to spoil the price he can get on the earlier pre-marginal unit." The obvious corollary to this rule is that the canny employer of labor who has some monopsony power contrives an artificial surplus of labor inputs so as to restrain labor costs. The old textbook deftly manages to evade that implication and instead treats wages and hours of work as if they were determined by perfect competition and worker preferences for income or leisure, unless disturbed by the monopolistic practices of collective bargaining. I'm guessing the omission is sustained in current textbooks.

Something interesting happens, though, if we depart from the fairy tale about perfectly competitive setting of wages and hours of work and consider what might happen where the employer has considerable latitude in such matters. Keeping in mind the firm's objective is to maximize profits (not maximize output) a longer than optimal-for-output working day may offer attractive prospects.

Table 1, below, presents a hypothetical case in which an eight-hour day would be optimal for output. That is to say, over the long period in this scenario, working a longer day than eight hours would subtract from potential physical output due to fatigue or "systematic soldiering." The scenario assumes that workers are identically productive and work the same number of hours. Compensation is based on output per day. The hourly rate is thus arrived at by dividing the daily compensation by the number of hours in the workday.

As Table 1 shows, to achieve approximately the same output in a day, the fewest workers are required if an eight-hour day is worked. The number of workers required increases with either an increase or a decrease in the hours of work because daily output per worker declines in either direction.

Now compare the eight-hour day and the nine-hour day. Daily pay per worker for the nine-hour day is almost the same as for the eight-hour day. There are only two additional workers required to produce approximately the same output. But there is nearly a 15% increase in the number of hours supplied. That's 118 more hours per day to deal with such contingencies as late deliveries, equipment breakdowns, coverage of lunch and coffee breaks, shift changes and absenteeism.

Although, there is no overtime premium in the calculation, this could easily be accommodated by dividing the daily compensation by, for example, nine and a half hours instead of nine. Thus for a nine hour day, pay would be $15.08 for the first eight hours and $22.62, "time and a half for overtime" for the ninth hour.

In our example, those 118 hours cost the employer ten bucks -- or less than a dime an hour. Such a deal! Moments are indeed the elements of profit.

A ten-hour schedule would provide even more slack time but would result in a much reduced hourly rate and daily income in addition to increases in per-employee fixed costs. In the event of layoffs, there's also a 10% greater cost reduction per layoff for the nine-hour day than the ten-hour day. Remember, the employer's power to set wages and hours is not absolute.

The example in Table 1 makes it plain that although the maximum output per worker per day may be achieved in fewer hours, an extension of the working day beyond that output optimum offers greater flexibility to the employer to alter the rate and volume of output in response to external conditions, especially if the cost of providing that flexibility is borne by the workers, either through layoffs or through imposed, unpaid "on-the-job leisure."

This example can, of course, be extended to look at the revenue side of the profit maximizing problem for the firm, assuming imperfect or monopolistic competition. That would be a routine introductory textbook exercise.

The above demonstration is not routine, however. I have withheld discussion of the background analysis and literature for a later post because I think the example in Table 1 makes two crucial points: first, that the distinction between maximizing profits and maximizing output has consequences for the determination of wages and hours of work; second the standard "perfect competition" fairy tale ignores these consequences.