If all other factors remain equal, the higher the price of a good, the less people will demand it. That's the law of demand, a fundamental idea in economics. And yet there is no shortage of politicians, pundits, policy wonks, and members of the public who insist that raising the price of labor will not have the effect of lessening the demand for workers. In his 2014 State of the Union Address, for example, President Barack Obama called on Congress to raise the national minimum wage from $7.25 to $10.10 an hour. He argued that increasing the minimum wage would "grow the economy for everyone" by giving "businesses customers with more spending money."

A January 2015 working paper by two economists, Robert Pollin and Jeanette Wicks-Lim at the Political Economy Research Institute at the University of Massachusetts Amherst, claims that raising the minimum wage of fast food workers to $15 per hour over a four-year transition period would not necessarily result in "shedding jobs." The two acknowledge that the "raising the price of anything will reduce demand for that thing, all else equal." But they believe they've found a way to "relax" the all-else-being-equal part, at least as far as the wages of fast food workers go. Pollin and Wicks-Lim argue that "the fast-food industry could fully absorb these wage bill increases through a combination of turnover reductions; trend increases in sales growth; and modest annual price increases over the four-year period." They further claim that a $15/hour minimum wage would not result in lower profits or the reallocation of funds away from other operations, such as marketing. Amazing.

Pollin and Wicks-Lim calculate that doubling the minimum wage for 2.5 million fast food workers would cost the industry an additional $33 billion annually. They further calculate that reduced turnover will lower costs by $5.2 billion annually and that three years of sales growth at 2.5 percent per year and price hikes at 3 percent per year will yield $30 billion in extra revenues.

Let's consider turnover first. Pollin and Wicks-Lim claim that an increased minimum wage will substantially reduce the costs of employee turnover, saving money that can now go to pay higher wages. The two fail to grapple with, much less refute, a devastating response to this idea from no less a liberal than the Nobel-winning economist and New York Times columnist Paul Krugman. In his review of Pollin's 1998 book The Living Wage, Krugman wrote: "The obvious economist's reply is, if paying higher wages is such a good idea, why aren't companies doing it voluntarily?" (That question goes unaddressed in the current study.) Krugman continues, "But in any case there is a fundamental flaw in the argument: Surely the benefits of low turnover and high morale in your work force come not from paying a high wage, but from paying a high wage 'compared with other companies'—and that is precisely what mandating an increase in the minimum wage for all companies cannot accomplish." So scratch $5.2 billion.

What about Pollin and Wicks-Lim's sales growth projections? Well, sales don't always grow. McDonalds reported a sales decrease of one percent in 2014. Some analysts think that fast food sales may have peaked in the United States.

But there's a deeper problem. In the absence of the higher minimum wage, employers would generally hire more workers to meet any increased demand for fast food. Boosting the minimum wage means that the revenues that would have otherwise been used to hire new workers is not available. The end result: fewer jobs created and more folks unemployed.

Pollin and Wicks-Lim recognize that raising the price means that people will eat fewer hamburgers and fries. They calculate that a 3 percent per year price increase results in a 1.5 percent per year decline in what sales would have been, which means that revenues would increase by 1.5 percent. Then they assume that the price increases won't affect the underlying 2.5 percent annual sales growth rate. (Rising prices never slow sales, apparently.) Pollin and Wicks-Lim roughly generate the revenues they want to cover the higher wages by calculating that a three-year increase in prices and sales growth will net $10.6 billion and $19.8 billion, respectively. Adding these to the postulated turnover savings of $5.2 billion yields $35.6 billion, which handily covers the extra wage costs of $33 billion. Voila.

Since all companies would have to pay the new minimum wage, they argue that all fast food joints wouldn't have to fear that competitors would try to lure their customers away by lowering their prices. In this scenario, the restaurants get to sell fewer burgers than they would otherwise have done while making more money which they then fork over as higher wages. Aficionados of cheap tacos, hot dogs, and burgers are the big losers. But doesn't selling fewer burgers imply a need for fewer employees? Never mind.

Going through the artful assumptions in this scenario brings to mind the hoary old joke where a physicist, a chemist, and an economist are stranded on an island with just a can of soup to eat. The physicist says, "Let's smash the can open with a rock." The chemist says, "Let's build a fire and heat the can first." The economist says, "Let's assume that we have a can-opener…"

Meanwhile, two new studies by economists using actual wage and employment data have just been published. Both find that in the real world, the law of demand still applies to labor.

In the first paper, Andrew Hanson of Marquette University and Zack Hawley of Texas Christian University analyzed how low wage employment would be affected in each state by the imposition of a national $10.10 per hour minimum wage supported by President Obama. The Hanson/Hawley study takes into account how wages relate to the varying cost-of-living levels among the states. First they report the number of workers in a state that earn less $10.10 per hour. Next they apply the widely agreed upon formula that for every 10 percent increase in wages there is a corresponding 1 to 2 percent decrease in demand for labor. They then straightforwardly estimate that boosting the federal minimum wage from $7.25 per hour to $10.10 per hour would result the loss of between 550,000 and 1.5 million jobs. States with higher numbers of workers making less than $10.10 per hour would lose the most jobs. Georgia, for example, would lose 51,000; Illinois would lose 65,000; Texas would lose 31,000; and Wisconsin would lose 34,000.

The second study, published in December by Jeffrey Clemens and Michael Wither of the University of California, San Diego, parses how the actual increase of the federal minimum wage from $5.15 to $7.25 per hour between July 2007 and July 2009 affected the employment rates of low-skilled workers. Using U.S. Census employment data, they can focus specifically on how low-skilled workers fared when the minimum wage rose as the Great Recession proceeded. They compare what happened to the employment rates of low-skilled workers in states where they were generally earning below the new minimum wage versus those where low-skilled wages were already higher. They refer to the first set of 27 states as being "bound" by the increase and the second set as being "unbound" by it.

The minimum wage, they show, exacerbated unemployment. Their analysis starts in December 2006, when the employment-to-population ratio—defined as the portion of working-age Americans (ages to 16 to 64) in the labor market—stood at 63.4 percent and ends in December 2012 when it had dropped to 58.6 percent. They estimate that by the second year following the $7.25 minimum's implementation, the employment rates of low-skilled workers "had fallen by 6 percentage points more in bound than in unbound states." In other words, job losses were considerably higher in states where unskilled workers had been earning less than the new minimum. Overall, they estimate that the minimum wage increase "reduced the employment-to-population ratio of working age adults by 0.7 percentage points." That would have boosted the 2012 employment-to-population ratio from 58.6 to 59.3, which implies that there were 1.4 million fewer jobs than there would have been had the minimum not been increased.

The conclusion is clear. Defying the law of demand will end up harming lots of the people minimum wage proponents aim to help.