Hours of Work: Moving Beyond Gridlock

 Question: When does two plus two not equal four?

Answer: When one of the twos is fixed and the other is variable.

Arithmetic is easier to digest than algebra, so I'll state the employer's labour cost calculations here with numbers instead of letters. For one employee, assume an hourly wage rate of $16, an overtime premium of 50 percent (time and a half), a fixed-cost benefit package totaling $160 a week (independent of the number of hours worked), a standard workweek of 40 hours and an average workweek of 43 hours -- that is, an average of three hours of overtime per week. Then the average cost per hour worked equals ($16*43+$8*3+$4*40)/43, or $20.28. Note that the regular wage plus benefit package equals $20 an hour.

Now assume two alternative ways of structuring an"8 percent" increase in the basic package. The first calls for a 10 percent ($1.60) increase in the base wage rate. The second calls for a 5 percent($.80) increase in wages and a 20 percent ($.80) increase in fixed cost benefits. Both offers add up to nominal total of $1.60. However, the first package has a cost of $21.93 per hour worked, while the second package costs $21.85. The eight cent difference represents the savings from not having to pay an overtime premium on the benefits portion, or indeed any of the fixed cost benefits during the three hours of overtime (.80*1.5*3/43). Table 1, on the following page, shows how the cost per hour worked decreases as the component of fixed-cost benefits increases.

It should be emphasized that the differences illustrated in the above table are small. Indeed, subtlety may well be the key to their power because, although they are small, these differences are persistent and pervasive. Burning issues of the day come and go but the small cost slope in favour of fixed-cost fringe benefits is always there -- at least until the proportion of fixed costs exceeds the ratio of the overtime premium to total overtime pay.

In the above example, the cost advantage of the $.80 wages and $.80 benefits package amounts to only 1/3 of a percent of the total hourly cost. But imagine a roulette wheel with just a slight incline favouring one of the numbers. Imagine the slope is just enough to change the odds from the traditional one in 38 to one in 35. With a payoff of 36 to one, a player who consistently bets on the favoured number has an advantage on every spin of the wheel. The advantage is small, less than 1/10 of a percent, but over the course of a year, limiting himself to just 10 bets a day, the player could increase his stake 18 times. By increasing his limit to 20 bets a day, he could increase his stake more than 300 times. At 50 bets a day, his stake would increase by nearly 2 million times over the course of a year.