It’s certainly true that workers’ wage gains have not kept up with the rising cost of living in recent years. Car prices have grown even faster than overall inflation, helping auto companies and their executives rake in eye-popping profits and pay packages, respectively.

Given these conditions, even employers agree that autoworkers deserve major pay increases. The Detroit automakers have offered raises of roughly 20 percent in hourly base pay. But the union’s president, Shawn Fain, says that offer is a “no go”; the union demands twice that.

Fain says his demand is based on the pay increases that automaker chief executives have received in recent years. These execs are “already millionaires,” he notes. If they got a 40 percent raise, the company can surely afford to give more modestly paid workers the same thing.

It’s a good line, but the math doesn’t quite work that way.

The compensation packages received by these CEOs are indeed enormous. But the millions they make are still dwarfed by the billions these companies spend in overall labor costs — which can’t be scaled up by 40 percent so easily. Put another way: Even if General Motors CEO Mary Barra gallantly forfeited her entire $29 million pay package and redistributed it to every rank-and-file worker, that comes out to … a few extra pennies per hour per employee.

This is nowhere close to the scale of the additional compensation the union is asking for.

The union wants not only that 40 percent base-pay hike, but a litany of other pricey changes, too. These include a restoration of defined-benefit pensions, which had been phased out for new workers in 2007; a 32-hour workweek, compensated at 40-hour pay; and a guarantee that workers will continue to be paid even if the plant employing them permanently closes. (That last item is similar to the “jobs bank” that contributed to the industry’s near-collapse 15 years ago.)

For context, right now, the Detroit Three automakers shoulder around $64 per hour per worker, including all wages and benefits. The UAW’s suite of compensation-related demands would roughly double that total hourly labor bill to about $130, according to calculations from Colin Langan, an analyst at Wells Fargo.

Now consider these firms’ competitors. Foreign automakers operating in the United States (Toyota, Hyundai, etc.) pay their workers around $55 per hour all in. Tesla is estimated to pay workers somewhere in the mid-$40s.

In other words, the legacy manufacturers are already at a significant cost disadvantage compared to their biggest competitors. Doubling employees’ total compensation costs would make them even less competitive.

The union counters that the companies have profits to spare. “Record profits mean record contracts,” repeats Fain, a slogan President Biden echoed in his own remarks supporting the workers. And it’s true that we’re coming off a period of unusually high demand for cars in the United States. But there’s good reason to believe that these record-high auto profits could soon, ahem, disappear in the rearview mirror.

These legacy car companies have proved notoriously dysfunctional in the past. And today, they seem to be struggling to adjust to the transition to electric vehicles. Despite huge government intervention, the Detroit automakers remain heavily reliant on selling big, gas-guzzling SUVs and pickup trucks. They have struggled to produce large numbers of EVs, even amid booming demand.

Meanwhile, competitors are eating their lunch.

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Tesla sells nearly 10 times as many EVs per month as General Motors, the next biggest U.S.-based competitor. More contenders are on the way, both American newcomers and upstarts from China and Vietnam, which have more competitive cost structures. In other words, the assumptions baked into the UAW’s list of demands — that established brands such as Ford and GM will remain dominant, with profits to spare, in perpetuity — might not hold. Ford CEO Jim Farley recently said accepting all the union’s demands might send his company into bankruptcy; it was clearly a self-serving claim, but given all the other challenges facing Detroit, it doesn’t seem so far-fetched.

Right now, labor and management are fighting over how to divide what looks like a huge and growing pie. The problem is that the pie might not grow very much, or even shrink, in the years ahead. And the unions would be wise to leave employers at least a little room to maneuver in this fast-changing market.