Clothing retailer Gap Inc. has won praise from the White House in announcing its decision to raise entry-level wages to $9 an hour this year, and $10 next year. President Obama applauded Gap and argued that Congress should follow suit by passing a bill to increase the federal minimum wage from $7.25 an hour to $10.10 by 2016.

But there’s a big difference between a voluntary increase in a market-determined wage rate and a government-mandated minimum wage.

Gap must report to shareholders and make a profit to stay in business; politicians report to voters and must win elections to stay in office. Polls show that the American public strongly support a higher federal minimum wage — but only if it appears to be costless.

President Obama, in promoting a higher minimum wage, argues that it would “lift wages for more than 16 million workers—all without requiring a single dollar in new taxes or spending.” This is the free lunch that politicians love to promise—and it is an illusion.

When the government arbitrarily pushes up wage rates above the competitive level, two things happen: some jobs are lost; and more workers look for jobs but can’t find them, so unemployment of lower-skilled workers increases. These effects are greater in the long run as employers switch to labor-saving technology.

When firms make adjustments in expectation of higher minimum wages (both federal and state), there will be a decrease in the number of jobs for lower-skilled workers (mostly younger, inexperienced, less-educated workers) but an increase in the demand for higher-productivity, skilled workers who complement the new technology.

Gap has already made significant investments in labor-saving technology and recently implemented a “reserve-in-store” computer program that relies on higher-skilled workers whom Gap invests in to enhance their human capital. Gone are the days when high-school dropouts could easily get a job with retailers. As Gap raises its starting wage, there will be more competition for a dwindling number of jobs. More workers will want a job, but fewer workers will be hired, and those that are will be of higher quality.

Glenn K. Murphy, Gap’s CEO, told the company’s employers upon announcing the change in policy, “To us, this is not a political issue. Our decision to invest in front-line employees will directly support our business, and is one that we expect to deliver a return many times over.”

This is free-market, Randian thinking: self-interest is the motivating factor, not altruism.

When President Obama says, “It’s time to pass [the minimum wage] bill and give America a raise,” he is making a promise that can’t be kept: some workers will gain (those who have higher productivity) but others (the least productive workers who most need a job to gain experience and move up the income ladder) will lose.

Indeed, the Congressional Budget Office now tells us that an increase in the federal minimum wage to $10.10 an hour could cost a loss of 500,000 jobs. Those most affected would be low-productivity workers in low-income families—making them poorer, not richer. (If the government promises a wage of $10.10 an hour but a worker loses her job or can’t find one, then her income is zero.) There is no free lunch!

People do what is in their own best interest. Gap may win some friends by increasing entry-level wages and saying this is in tune with company “values,” but unless that business decision is profitable Gap will lose sales, and its shares will drop in value. There is thus a market test of the decision to raise wages.

The government has no business telling private employers what to pay or telling workers they cannot offer their labor services at less than the legal minimum wage, even if they are willing to do so to retain or get a job. The President’s minimum wage is anti-economic freedom and violates personal freedom; Gap’s higher entry wage does neither. This is a case of “the emperor has no clothes!”