Last week, Facebook COO Sheryl Sandberg made headlines for her Mother’s Day post calling for a minimum wage increase. “It’s long past time,” she claimed, “to raise the federal minimum wage.”That’s easy for Ms. Sandberg to say. Her company wouldn’t be affected by such a wage hike. Facebook made an astounding $10 billion in profit in 2016. Outside of Ms. Sandberg’s Silicon Valley bubble, things are dramatically different. Many businesses exist on razor-thin profit margins and would be severely impacted by drastic mandated increases to their labor costs.According to an Employment Policies Institute analysis, the annual profit per employee at an average grocery store is just $1,500. At full-service restaurants, it’s just $4,800. At retailers, it’s $7,400. At Facebook, it’s $544,000 per employee.Consider how the minimum wage hike Ms. Sandberg calls for would impact these businesses. Every dollar increase in the minimum wage would raise full-time starter employment costs by $2,000 annually. (Employment taxes would increase costs more.)Minimum wage increases to the $12 to $15 range mean employers would be losing money on many jobs they fill. Imagine Facebook faced this dilemma, with a required tech minimum wage that redistributed all the company profits to her employees. In that scenario, Ms. Sandberg would be singing a different tune.Then there is the “just raise your prices” strategy. That might work if consumers didn’t adjust. But service industries have found they are restrained by consumers who can elect to make fewer purchases during the year. Assume you normally eat out once a week. Imagine as a reaction to higher prices you drop one visit each month. If retailers broadly suffer that 25 percent drop in sales, most would go out of business. And the ripple effect on jobs would be enormous as those with few skills find themselves with less opportunity to work.Minimum wage proponents often respond to this pricing restraint reality by suggesting employers offset the cost of wage hikes by redirecting executive compensation. But as I explained in last week’s column, this argument doesn’t wash. Redistribute all of Wal-Mart and Starbucks CEO pay packages and their U.S. employees would run off with an additional average of roughly $1.50 a week. Ms. Sandberg doesn’t have to look far to see the real-world consequences to her rhetoric. In her Bay Area backyard, there has been what one local publication calls a “death march” of restaurant closures, with dozens of owners citing dramatic hikes in local minimum wage rates.What’s to blame for this massive difference in profit per employee between the tech and retail sectors? The answer comes down to productivity. Industries that produce or use intensive levels of technology have seen their productivity skyrocket in recent decades.Restaurants, grocery stores and other low-margin businesses haven’t benefited from this revolution. You can only restock shelves or prepare a fresh pizza so fast. While there have been small efficiency changes over the decades, including online ordering and self-checkouts, today’s restaurants and grocery stores look remarkably similar to those of decades past.As George Will recently noted, this productivity stagnation is known as “Baumol’s disease,” after late American economist William Baumol. His studies revealed how labor-intensive service industries like nursing, teaching and the performing arts see much smaller productivity gains than the overall economy. Playing Chopin’s one-minute waltz still takes a minute. And because wage gains are a function of productivity, a business can’t have the former without the latter and expect to stay viable.Big productivity gains have not been enjoyed by all business sectors. Sen. Elizabeth Warren claims the minimum wage today should be $22 if it had tracked general gains in productivity. It’s obvious that Ms. Warren was not teaching economics while at Harvard. According to the Bureau of Labor Statistics, there has been almost no productivity gain in the food service industry — the target of campaigns for a 100 percent increase in the federal minimum wage.Sen. George McGovern crashed into the realities of business math when in 1988 he opened a Connecticut bed and breakfast. He later wrote in The Wall Street Journal that he wished he knew as a senator what he had learned in business. He admitted it would have made him a more sensitive legislator attuned to the consequences of his votes.Those who work in the tech or political fields may be blinded to the realities of the service economy. Those like Ms. Sandberg who can’t see beyond their own education need the equivalent of a service dog. It would stop them from stepping off the curb into the intersection of business and economics.