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I often heard minimum wage discussions and typically a single figure is presented (where I live it is the gross monthly value, elsewhere I hear about the gross hourly rate).

However, there are great difference in regard to cost of living within a single country (or even region), so having a single value seems like a "one size fits all" solution.

This Pew Research Center article deals with a specific case from US and I will narrow my question to US to make it more answerable:

One factor complicating the minimum-wage discussion is that the cost
of living varies widely – not just from state to state but within
individual states, something that’s especially true in large, diverse
states such as California and New York.

The article dives into some financial figures but the bottom line is: while the cost of living can be quit different, there is a single value for the minimum wage.

Theoretically, the minimum wage could be somehow correlated with cost of living. I think could work similarly to different property tax based on where you live.

Question: Why is minimum wage not correlated with cost of living or similar factor?

Short answer - because that's what the proposers of the minimum wage legislation managed to push through.

USA had a long, long history of unsuccesful attempts to enforce a minimum wage limit, amongst other economic regulations, but Supreme Court (for a time) in defence of businesses and free market ruled all those regulations unconstitutional (so-called Lohner era). Of particular relevance to your question are two of them.

First was in 1933. Roosevelt administration attempted to include minimum wages in National Industrial Recovery Act. This case did differentiate not only on regional, but also on industry branch basis (i.e., for example, agriculture and textile industry would have different minimum wages). This was ruled unconstitutional in A.L.A. Schechter Poultry Corp. v. United States, on the grounds that federal government had no power to regulate intra-state matters (which, apparently, worker wages are).

Second was in 1938, in Fair Labor Standards Act - this time, at a fixed rate. This one was upheld by Supreme Court in 1941 in United States v. Darby Lumber Co., where it was ruled that Congress had the power under the Commerce Clause to regulate employment conditions.

I don't have enough knowledge on nuances of U.S. internal political games at the time, so I can't say what happened to cause one variant of the act to be declined, while another was upheld, but the end result was that fixed-rate minimum wages became a part of U.S. federal laws. Note that states still could have their own local laws regarding wages - for example, the state of Washington had a minimum wage legislation that was held legal in 1937 in West Coast Hotel Co. v. Parrish, a year before the Fair Labor Standarts Act was passed. By the way, as it is stated in the article you linked, the situation is changing - some states are passing laws to adjust minimum wages according to cost of living.

To sum up - the minimum wage being constant and not linked to cost of living in U.S. isn't an economically-based fact, it's just the historically established legal situation.

Danila Smirnov response covers the issue from a US point of view. Worldwide the answer is not different, though. The minimum wage is not tied to the cost of living because the laws which enacted it didn't tie the minimum wage to the cost of living, which is sort of a tautology.

There are, however reasons to not do it that way. First it's the cost of updating it. Employers need to know how much they are going to spend in wages with a certain margin of time - typically, at least a year. However, cost of living can go up quickly in cases of (hyper)inflation, housing bubbles, oil crisis, etc... If you tie the minimum wage to the cost of living you're forcing every employer in the country to update its financial state every time the cost of living is updated. If you update this value very frequently, it is quite a nightmare for everyone and a source of economical unstability, and it will surely scare away foreign (and probably local) investors. If you update it very sparingly, say, once per decade, then it's very loosely tied to cost of living, which will probably have diverged away.

The other problem is that cost of living varies greatly not just at the country level, but even at city level. Here in Spain cost of living of Madrid or Barcelona is twice the cost of living in nearby towns in the same province. If minimum wage is tied to actual cost of living then calculating and managing minimum wages at city level (or even neighborhood level) is perceived (for both governments and employers) as too complicated to handle, and in any case it could make companies to flee the most expensive places to live or distort the urban planning in several other ways. For example, retail workers in Poshtown are forced to live in the edge of Slumvillage so their employers can keep their salaries low. That wouldn't affect much qualified workers, who are paid much more than minimum wage, but it could render cities severely underserviced if menial workers weren't employed there - though, we have very much the opposite problem now where people paid minimum wages can't afford to live where they work due to cost of living being too high.

As other answers have said, this is about what the legislators have been able to pass. Some people are opposed to minimum wage laws and some are on the fence. Making them 'index linked' (i.e. tied to cost of living) would cause more people to oppose them.

Even proponents of minimum wage laws mostly admit that there would be economic conditions under which raising minimum wages in line with inflation would be a severe problem. In times of economic recession, when wages generally are not rising, it makes little sense to raise minimum wages; similarly in times of high inflation, when price rises are outstripping wage rises, or worse still when both are occurring together - the dreaded 'stagflation'.

Rather than have to pass legislation to specifically undo the index linking under these conditions, proponents consider it better to legislate each individual increase.

1. The cost of living is usually correlated with improved living conditions (otherwise, why pay more to live there?). So if you tie the minimum wage to the cost of living, you're basically rewarding low-income people for living in a good neighbourhood. It's unclear if that's the original intention.




2. It would be unclear at what organizational level one would calculate the cost of living: State, city, district, house? The more detailed you go, the more effort you have to put in.




3. People in low-income entities might very well object to a minimum wage from which they barely profit. This would risk the idea as a whole.

Well, in many ways, it is.

At least in my state, municipalities can set their own minimum wage on top of the state minimum wage, and that on top of federal, allowing them to adjust maybe a bit more finely than a federal system.

This also hews more closely to the idea of federalism, where many would argue that the massive disparity in cost of living is exactly why the federal government shouldn't be setting wages.

As you noted, the US has a single Federal minimum wage but wildly varying costs of living. CNN has this cost-of-living comparison calculator and if you compare just about anywhere to San Francisco or New York City, you'll find the cost of housing (and nearly everything else) is significantly higher in those two locations. For instance, making $50,000 in Atlanta, GA would need you getting a job making almost double that in SF ($97,500) to live there with the same standards (and, honestly, that number seems low). So it makes sense that Georgia has only the Federal minimum wage, while CA has $11/hr and San Francisco $15/hr.

The other idea has been to index it to inflation (which is what other things like Social Security use).

So why not do it that way? Well, it's a way to force votes on other issues, or make campaign promises. Consider this attempt from 2006

The House approved an increase in the federal minimum wage on Saturday, but its future was clouded because Republicans tied the pay change to an estate tax cut that had been blocked in the Senate.

In a prelude to a summer of campaigning in the battle for control of Congress, lawmakers clashed bitterly over the Republican decision to link the tax break for affluent Americans to a $2.10 increase in the minimum wage before the legislation was approved after 1 a.m. on a 230 to 180 vote.

The maneuver to couple the minimum wage increase long sought by Democrats and moderate Republicans and the estate tax change backed by conservatives left some Republicans uneasy and Democrats fuming. Opponents of the bill said the estate tax change and other tax breaks included in the $310 billion bill could kill it. They accused Republicans of a cynical ploy to make it look as though they were pushing an increase in the minimum wage when their real intent was to block it.

“It’s a political stunt designed to give vulnerable Republicans in tough elections the opportunity to say they voted to raise the minimum wage, even though they know this bill is going nowhere in the Senate,” said Representative Steny H. Hoyer of Maryland, the No. 2 Democrat in the House.

Democrats ran on a minimum wage increase in 2006 (amongst other issues) and won the majority in Congress. They then passed an increase in the minimum wage.