# “I’m not sure I follow the arithmetic here.”

### “I’m not sure I follow the arithmetic here.”

“Unless productivity goes up by at least 25% to compensate, everyone will be worse off.”

“Dropping hours from 5 days a week to 4 means that the work that would have been done in 5 days now needs to be done in 4, which means each day needs a 25% increase in productivity. Where on earth do you think such an increase is going to come from?”

“OK, but to arrive at the same output in 4 days rather than 5 means that people have to become 25% more productive than they are today. That’s an awfully big jump in productivity. I’m not convinced that people today are that unproductive. Certainly when I think of my past workplaces, I don’t think my colleagues were that sub-optimal. A 10% increase in productivity seems more reasonable.”

Following up on yesterday’s post about comments in the Guardian, here are some thoughts about “where on earth” a productivity increase of 25 percent might come from:

Let’s start from a 40-hour week in which the rate of output declines somewhat toward the end of the day when workers are beginning to tire. Let\s assume the least productive eight hours of work produce only 75 percent of the output of the most productive 32 hours of work. Call the average output of the most productive 32 hours “one unit” of output. Total output for 40 hours work is 38 units.

Now, reduce the weekly hours to 32. Better rested, more motivated workers result in a “reasonable” 6.25 percent increase in average hourly productivity above and beyond the productivity gain from eliminating the least productive hours. Total output in 32 hours is now 34 units compared with 38 units previously produced in 40 hours.

Those are physical units of output not the monetary value of that output. Assume diminishing marginal utility of the total output. The last four units of output add less value per unit than the first 32 units. So let’s say in value terms 34 units = \$34 but 38 units = \$37. We are now producing 92 percent of the value previously produced in 80 percent of the time.

Instead of earning \$15 an hour for a 40-hour week, a worker now earns \$17.23 an hour for a 32 hour week. That’s a 15 percent increase in hourly wage coupled with a 20 percent decrease in weekly hours. Not too shabby! Considering that there are costs associated with commuting to work, etc., the 92 percent retention of weekly income might effectively be closer to full compensation.

All of the above, of course, is simply the fleshing out of assumptions. We assumed  diminishing productivity in the last hours, we assumed heightened productivity from a shorter working week and we assumed declining marginal utility of goods and services produced. Finally, we assumed a preference for free time over a vanishingly small increment of total income. The point is that each of these assumptions were relatively modest but when combined “add up” to a rather substantial cumulative result.