Robby Soave writes for the libertarian magazine Reason . Follow him on Twitter @robbysoave . The opinions expressed in this commentary are solely those of the author.

(CNN) What happened late last week to Talia Jane -- who became suddenly Internet famous after being fired from her job at Yelp -- fits an all-too-easy narrative: underpaid 20-something writes desperate complaint about low wages and greedy corporate employer suppresses dissent by firing her.

But millennials working for starvation pay should learn something from Jane's fate: Things could be worse, and will be, when minimum-wage laws price them out of their jobs.

For many, Jane -- who wrote an open letter to her CEO about her situation -- is a sympathetic figure. She claimed she was making just $8.15 an hour after taxes working a boring job in customer relations for Yelp/Eat24. That's not a lot of money -- especially in San Francisco, and especially for an unfulfilled college graduate with an English degree and journalism aspirations.

Jane claimed her situation was so hopeless that she often went to sleep hungry, and many of her co-workers found themselves in similar situations. (Hours after publishing the letter, Jane was fired. Yelp denies her public statements had anything to do with it).

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Critics pointed out that Jane did herself no favors by whining, and was in far-from-desperate straits.

"The issue is that this girl doesn't think working a second job or getting roommates should be something she has to do in order to get ahead after three months of an entry level job in the most expensive city in the country," wrote Stefanie Williams , a fellow millennial who started out waiting tables and worked her way up to the New York City lifestyle and job she wanted.

For others, Jane's circumstances present a compelling argument for the government to raise the minimum wage. Indeed, union activists would like the state of California to raise its minimum wage from $10 to $15. Numerous cities are gradually doing so -- San Francisco will have a $15-per-hour minimum by 2018.

Younger workers might cheer this news. They shouldn't. That's because a company like Yelp wouldn't pay an employee like Jane any more money, even if forced to do so. Instead, it would never have hired her in the first place.

It may sound harsh, but the reality is that a person's labor is only worth so much. Markets are far from perfect, but competition (not always, but usually) prevents companies from getting away with drastically undervaluing their employees -- if Yelp did that, a rival could poach all its workers by offering them slightly more money.

On the other hand, if Yelp had a policy of paying workers exactly what they needed to get by, rather than exactly what their labor was worth, the company would go out of business.

That's why high-minimum-wage laws are actually bad for the very people who think they need them most: millennials. Companies that are forced to pay workers a minimum of $15 an hour won't hire from the young, inexperienced, fresh-out-of-college crowd. They can't spend that much money on an unproven, untested investment.

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Millennials may not realize it, but working for low pay is a competitive advantage (and a temporary one). Older workers have more obligations -- families to provide for, house payments to make, kids' tuition costs to pay -- and can't afford to work for less. Recent graduates can't beat them on raw talent, but they can beat them on price. For hardworking young people who just need to get a foot in the door and gain some experience, the minimum wage is, as Forbes editor John Tamny put it, "a cruel barrier."

The science bears this out. Studies often find that higher minimum wages correspond with decreased youth employment In fact, if the government's explicit goal were to make it harder for young people to compete for jobs, they could scarcely design a more perfect policy.

Writing on behalf of aging workers everywhere, the Foundation for Economic Education's Isaac Morehouse satirically observed:

"The obvious solution is to make it illegal to work for low wages. Working for free is absolutely out of the question. If young and poor people could simply offer to work for little or no pay, they'd soon be gaining valuable skills and competing with us for jobs!"

The recently fired Jane may need more money, but first she needs to find a new job, period. Raising the minimum wage would only make that harder for her.