The main metrics are mean and median real income (i.e. inflation-adjusted). Baumol's only occurs if mean real income rises. Unless inequality rises simultaneously, then median real income (the metric most people care about) will rise as well.
How is this related to Baumol?
Baumol does not describe general inflation. It specifically describes when prices go up in some sectors because of an increase in productivity in another sector.
Baumol is also rooted in the concept of price elasticity, which in your contrived example seems not to exist.
> How is this related to Baumol?
Because people claim that higher costs are a result of Baumol and are hypothetically something good or normal when it's actually regulatory costs and government capture stealing from working people. "Don't worry, prices are only up because we got so much more productive, not because of artificial scarcity or because it now requires 10 people to do certain things that used to take one."
> Baumol is also rooted in the concept of price elasticity, which in your contrived example seems not to exist.
Because the example is housing, which is a necessity and therefore has fairly inelastic demand. If the price goes up, you pay it, because otherwise you're homeless. And then people buy flowers less because they can't afford it, so people lose their jobs at the flower shop, but new jobs open up in construction because it became more labor-intensive and has fairly inelastic demand.
> It specifically describes when prices go up in some sectors because of an increase in productivity in another sector.
Here's the less contrived example: Productivity improves in things like electronics or manufacturing, giving people more disposable income. But there is certain amount of disposable income people have to be left with before they'll revolt, and the increase in efficiency leaves them with more than that. Which allows the government to increase regulatory overhead or real dollars per capita collected in taxes or pass rules that artificially increase scarcity at the behest of campaign donors, without making people feel like they've lost ground.
But the efficiency improvements should have allowed them to gain ground, which is what has been taken from them.
Suppose that every single person in society receives the same compensation and has the same wealth, i.e. there is perfect equality.
Society produces housing and other necessities and people consume them in some amount and then have what's left as disposable income to spend on whatever they like, e.g. for going on dates.
Then a law is passed prohibiting the construction of housing with more than two stories. Building ten housing units on ten lots with ten foundations requires more labor than constructing ten units all on the same lot, so the price of housing increases, people have to spend more on housing and have less money left to buy flowers and some people quit their jobs at the flower shop to go pour concrete (while still getting paid exactly the same amount as before).
There is zero change in inequality but the cost of something has gone up and people have to eat it by getting less of something else.