You're saying that the value of a job isn't as important of the purchasing power created from its wages.
Ah ah no. "The value of a job" isn't a real thing. Things don't have value--even jobs.
You don't need to justify that point any further or defend it with an Economics 101 lesson.
Actually, if I brought this stuff into ECON101, the teacher would probably cry. A lot. I deal a lot in macroeconomics, and I'm using theories that are a lot more advanced than current in some places. One of my favorite economic tricks as of late is to demonstrate that scarcity does not imply that demand has exceeded supply--which has the metaphorical effect of sharpening a lot of the edges around fuzzy economic theories.
While I'm not an economist, I am a mathematician, who, as such, is inclined to tell you that "you and ten people" is eleven people total, though your math indicates a labor pool of ten. Try not to fail mathematics when you argue mathematics.
Hah, good catch; although I'm sure the point got across correctly.
Arguing about purchasing power being up when median income isn't is like a patient telling his doctor that he's not worried about his cholesterol levels because he exercises everyday and feels fit.
Actually, it's a bit like arguing that people in Japan eat a hell of a lot more salt than people in America, and yet they generally experience lower blood pressure. This happens to be true, and it's been leading us to identify that stable sodium intake does not raise blood pressure, but sudden increases in sodium intake do.
Purchasing power is income. If we doubled all of the money in circulation and doubled all the wages, median income would be up; yet people wouldn't be any richer. They'd still buy the same things they buy today, and they'd live the same lives; their savings accounts would be ransacked, although anyone holding a stock portfolio would recover quickly enough thanks to the run-up of stock prices in sudden inflation.
In other words: I can give you more dollars and change nothing about your financial situation by giving everyone more dollars. Raising the median income on its own is just inflation.
The existence of capital induces demand for products, which induces a demand for labor. Median income measures the strength salaries have to pay for products and services, which induces job creation.
There's your problem.
I told you: if I work an hour for $20/hr, I have 1 hour of labor for which I can induce someone with a $10/hr wage to work 2 hours.
What if we raised all the incomes by double?
Now instead of $20/hr or $40,000/year, I make $40/hr, or $80,000/year. The median income has doubled from $52,000 to $104,000. Salaries are up.
At the same time, that guy making $10/hr is making $20/hr. His salary doubled, too.
Well, to pay for 2 hours of his work, I was buying a $20 product. Now $20 only induces him to work 1 hour. That $20 product is now $40. I spend my 1 hour--the same amount of labor time--and induce him to work 2 hours. The same number of hours goes into products, and is bought by the same number of my working hours.
Where, pray tell, are these new jobs coming from, if a person working for 40 hours per week, for 52 weeks per year, is still only able to purchase the same products and induce the same labor and thus the same jobs as when the median income was half?
So when lower-wage jobs replace higher-pay jobs*, when existing jobs producing the same product pay less to laborers, and when jobs move to overseas markets where labor is cheaper, less demand for labor is induced. Less demand for labor creates less demand for work, restricting access to capital among laborers, which restricts their access to goods and services, decreasing quality of life.
Actually, when some but not all jobs have higher wages, the money goes into fewer hands, thus creating fewer jobs.
Income is paid out of revenue. In a given time frame, there is a limited amount of income. It's unchanging. Dollars aren't created by your employer chanting over a boiling cauldron to induce coins from the ether; they're taken from the money consumers spend on products.
New income is available in new time frames because of debt. A consumer's available income per month, for example, may not allow them to buy a house or a car; but stretch that purchase across five, ten, or thirty years and they can afford it. The Fractional Reserve System allows banks to loan more money than is on hand, and so issuing new money and getting it into banks (for example: by the government buying into bonds, then steadily recovering and circulating the new money by taxes on what the bond issuers spend that money on) allows consumers to spend large amounts of cash today, getting it into circulation. That cash becomes new income, which is then spent in the next time frame. This causes inflation.
As stated above: if all wages go up equivalently, then no change occurs. In that case, every individual consumer is able to buy the same amount of goods.
If, however, only some wages go up--for example: minimum wages--then the amount of total available wages are spent on fewer services. For example: a minimum wage increase from $8.50/hr to $15/hr would affect fast food prices in such a way that a McDonalds $8 value meal would become $8.17 (yeah, doubling minimum wage won't double the price of your hamburger). With the 268 billion customers served per year, that 17 cents represents $45.56 billion. At $8.50/hr, that's 2.68 million jobs.
What that means is those 17 cents are no longer available to spend on anything else when you buy a fast food value meal at the example $8 average. At each two-week pay period, consumers collectively receive a lot of money; then they spend that money, and two weeks later receive another increment. When you raise a subset of wages, there's the same amount of money to be spent, yet someone is getting a bigger chunk of that money. That someone is undoubtedly in a better position to buy, and thus richer; and someone else isn't receiving those dollars, because new dollars aren't created by the act of raising someone's wage, but rather have to already exist as income to be spent, or be brought into existence by issuance of money and by debt.
In the most-extreme case, we simply buy what was previously $45.56 billion dollars's worth less fast food. 2.68 million fast food jobs go away, and we continue to spend those 17 cents on other things. That math works out perfectly because it assumes we allocate the same amount of money to fast food and spend until we run out. We still spend that $45.56 billion dollars on fast food; just we buy less total fast food because it costs 2.125% more.
In a less-extreme case, we buy the same amount of fast food, but less of something else. That tends to mean that shippers, retailers, and other people in the supply chain lose their jobs (the same is actually true of fast food: it's not all burger flippers). The higher the mean wage of jobs lost, the fewer jobs we lose in this turn-over.
The ugly truth is we create more jobs by pushing people into poverty, and we destroy jobs by elevating them out of poverty with higher wages. There are alternate strategies that can reduce poverty more-effectively; and the labor force essentially adjusts (via everything from early/late retirement to more people going to grad school or exiting college to work) to buff away any permanent losses and gains, which is why raising minimum wages to keep up with inflation hasn't been an absolutely-catastrophic strategy for the past hundred years (and also why trade can't permanently-destroy jobs or permanently-create jobs, even though it can create and destroy jobs). Welfare is an important part of a functioning economic system.
The biggest take-away that people miss is time and source. Wages and consumer spending are roughly the same thing, and so people can only spend as quickly as they get paid; and they have to spend enough to make sure the person doing the work gets paid, which means higher labor costs bring higher prices. Money isn't instantiated when you pay someone; it's taken from consumers. Put these together and you get stuck with any subset rise of wages creating unemployment.
Median nominal wages have gone up, yet median "real" wages (inflation-adjusted) hasn't. In a sense, that's a good thing: an increase in median inflation-adjusted wages would mean higher unemployment, by rough mechanism. In another sense, I hate these economic measurements, because a flat "real" wage coupled with an increase in "real" GDP-per-capita (productivity) in general means your actual buying-power income has increased by the GDP-per-capita increase--your wages have gone up, for real, somehow, even though "your real wages" haven't gone up. These measurements are... annoying... because they don't do what they say on the tin.
which restricts their access to goods and services, decreasing quality of life. All this happens, even if our purchasing power has risen relative to median income.
The problem is "our purchasing power has risen" means that our purchasing power has risen. That is the definition of increasing quality of life: the median purchasing power has risen, the purchasing power of every class of income has risen, and thus they can more-easily get food, more-readily access health care, and live in larger and more-comfortable houses with more luxuries. That median income that hasn't gone up? It buys more shit. That's what an increase in quality-of-life is. That's the only measure of quality-of-life.
Also, I found your labor force statistics fascinating. Honestly. Though I'd like to know their source.
Bureau of Labor Statistics. For example, number of employed. We don't count farm workers. I computed the total labor force aged population by dividing the labor force size by the labor force participation rate (e.g. if you have 170 million labor force at 62.9% participation, 170M / .629 tells you how many people are in the age range of 16 to retirement and, ostensibly, could be put to work).