Take the auto industry. Automobile production in the United States fell 50 percent from 2007 to 2009, meaning the sector had tremendous excess production capacity in the ensuing years even as the sector recovered. “Companies could fulfill a lot higher demand without having to make any new investments,” said Jaana Remes, a McKinsey partner and a co-author. “Typically the newest technology is implemented in the latest factories. People don’t upgrade a factory that can fulfill demand perfectly well.”

Or consider how this dynamic might apply in the restaurant industry (or retail, or tourism).

The basic technology for self-serve kiosks has been around for years. But when the unemployment rate was at its post-crisis highs, employers could have their pick of good workers at relatively low prices. Now, with the jobless rate at 4.1 percent, good workers are harder to find. And, perhaps unsurprisingly, companies have been more open to installing technology that may have a significant upfront cost and require reworking how a restaurant is organized, but allow more sales without hiring more workers.

“A consequence of a really tight labor market is a higher turnover rate,” said Liah Luther, marketing manager at Nextep Systems, a Michigan company that sells self-ordering kiosks to restaurants, casinos and corporate facilities. “Once you eliminate the need for extensive training on a point of sale system, you can focus on soft skills like customer service, and reduce the cost of turnover.”

The optimistic case for both productivity and overall economic growth goes like this: For the last several years, a lack of demand and plenty of spare capacity of both workers and equipment made businesses complacent and unwilling to invest in new equipment, software or new ways of doing things that might allow more output per hour of labor.

Now, with companies having a harder time finding qualified workers and with demand for their products rising, they’ll have no choice but to re-engineer how they work to try to increase productivity. Higher productivity will in turn make it easier to justify higher wages, creating a self-reinforcing cycle of higher economic growth.

There are some risks to that rosy forecast, which Ms. Remes and Mr. Manyika warn about.

They see a great deal of potential from digitization of businesses that have been slow to embrace the lessons of the cutting-edge companies in their industry. But this might be slow to generate the kinds of big productivity gains that are possible.

Even as more retailers adapt to an age of digital commerce and learn from Amazon, for example, they may in the near term end up simply doubling up traditional retail and e-commerce-focused workers, making such companies less productive rather than more.