A large portion of country wealth is often tied up in land and infrastructure. Wealth generally creates more wealth (through interest and similar), so the same wealth spread across a smaller number of people will push GDP per capita upwards.
Higher incomes are also closely associated with better education. If you keep the number of universities and schools constant while decreasing the population, you give a larger percentage of the population access to better education.
If a family has two children, the wealth of the family must be divided between both children and each child has less individual wealth. As you need wealth to start a business, a higher base wealth across the population means more chance of new successful businesses being started by these children.
If a family has no children, the estate will move into public control, effectively increasing GDP per capita for the surviving population.
A reason for a low birthrate in Japan is lack of financial security. This means that people who have low wealth are self-selecting out of reproduction, effectively moving their wealth into public ownership when they pass away and moving the average up as the proportion of low wealth to high wealth families is shifted.
So yes, practically, GDP per capita will go up in Japan as the population shrinks. The global economy is more complex than just 'producing shiny widgets', or China would be far more well off than it is. Capitalism in action.
EDIT: As pointed out by others correctly, increased welfare burdens from too large a proportion of retired citizens will have an effect. This can swing two ways: increased taxes, or reduced welfare payments.
If reduced welfare payments is chosen, it will cancel out the problem. Japan will hopefully choose this route out of self preservation.
If increased taxes is chosen, it will effectively tunnel income into the housing sector (old age homes, etc) and medical sector (medicine, life support, etc). The housing sector increase will be offset by a smaller housing demand from lower population. The medical sector is the big issue: if this wealth can be tunneled into Japanese medicine and health care, then it will simply be a transfer from taxpayers to Japanese in the medical sector. This would probably cause all kinds of distortions and should be avoided. However, it's not guaranteed to be a bad thing, I think anyway. You'll just have more Japanese going to medical school.
There's no interest genie either. If no one can invest and earn returns on borrowed money, there's nothing to sustain interest.
Inherited wealth isn't enough to sustain anyone but the rich. GDP only measures new wealth anyway, not preexisting wealth. You have to continue producing goods and services. In fact, most forms of accumulated wealth (currency, securities, real estate) are really just shares of these goods and services as they're produced, but you need at least some actual labor for that to work.
If you selectively culled unproductive people, per capita GDP would go up. It's not clear that low birth rates accomplish this.
I guess I wasn't clear enough. Lets break down the working population into categories:
[unique skills - ceos, etc]
X people
[highly demanded skills - top class engineers, specialty surgeons, etc]
Y people
[regular required jobs - doctors, pharmacists, designers, etc]
Z people
[unskilled jobs]
A people
[unemployed]
As the population decreases, the demand for each of the sets should decrease in proportion if per capita GDP would remain the same (ignoring wealth effects). However, this isn't the case. If Sony needs 10,000 engineers to create their phones for export to USA, they will still need 10,000 engineers regardless of decreasing population. In addition, a medical school that takes 50 students per year will continue to take 50 students per year even if populations fall, as the number of applicants is far in excess of 50.
This is just a few examples, but you could easily find far more. The root cause of this is the existing wealth of the country will enable more people to succeed as the population decreases. A further indication of this effect is that GDP per capita is strongly related to wealth.
There actually are limits to physicians per capita. You wouldn't have a functioning economy where everyone was a physician. If the population drops by 10%, demand for physicians drops as well.
For engineers it's a supply side issue--we could productively employ many more engineers than we do, but it would take immense breakthroughs to have a population where everyone could be an engineer. That's what I meant when I said you'd have to selectively cull the unproductive. If you reduce the population, the remaining workers have to be more productive for per capita GDP to rise, and you still haven't shown that this would happen. It doesn't help if you only need 10,000 engineers when you can only produce 0.01 engineers per capita. You'd need this proportion to rise. How does lowering birth rates do this?
In other words--sure, you could probably have a very per-capita rich Galt's Gulch with only 1000 people. But reducing the population arbitrarily to 1000 people will not accomplish this.
"If a family has no children, the estate will move into public control, effectively increasing GDP per capita for the surviving population."
I'd think that families that have significant wealth are the ones that are the most likely to have children, since they'd have no problems affording them.
Higher incomes are also closely associated with better education. If you keep the number of universities and schools constant while decreasing the population, you give a larger percentage of the population access to better education.
If a family has two children, the wealth of the family must be divided between both children and each child has less individual wealth. As you need wealth to start a business, a higher base wealth across the population means more chance of new successful businesses being started by these children.
If a family has no children, the estate will move into public control, effectively increasing GDP per capita for the surviving population.
A reason for a low birthrate in Japan is lack of financial security. This means that people who have low wealth are self-selecting out of reproduction, effectively moving their wealth into public ownership when they pass away and moving the average up as the proportion of low wealth to high wealth families is shifted.
So yes, practically, GDP per capita will go up in Japan as the population shrinks. The global economy is more complex than just 'producing shiny widgets', or China would be far more well off than it is. Capitalism in action.
EDIT: As pointed out by others correctly, increased welfare burdens from too large a proportion of retired citizens will have an effect. This can swing two ways: increased taxes, or reduced welfare payments.
If reduced welfare payments is chosen, it will cancel out the problem. Japan will hopefully choose this route out of self preservation.
If increased taxes is chosen, it will effectively tunnel income into the housing sector (old age homes, etc) and medical sector (medicine, life support, etc). The housing sector increase will be offset by a smaller housing demand from lower population. The medical sector is the big issue: if this wealth can be tunneled into Japanese medicine and health care, then it will simply be a transfer from taxpayers to Japanese in the medical sector. This would probably cause all kinds of distortions and should be avoided. However, it's not guaranteed to be a bad thing, I think anyway. You'll just have more Japanese going to medical school.