I'm trolling Elizabeth Breunig. Because she said that "Human capital is one of the more odious terms in the capitalist lexicon". And I like the term "human capital", because I think it helps us think more clearly about investment in training and education.
Are new-born babies "human capital"? My first thought was that they possess no human capital, because they haven't invested in learning anything yet, so it was an abuse of the concept to say that babies are human capital.
Then I remembered "Lark Rise to Candleford", (HT Frances), a memoir of 19th century girlhood in a poor English village. Only one couple in the village had any savings. They were saving for their pension. They were the only childless couple in the village. All the other couples had children, who were costly to feed and clothe, but would support them when they were too old and sick to work. Their children were their pension plans.
At the individual level it might no longer be true that we expect our own children to support us in our retirement. But at the aggregate level it is still true. If nobody has any children, who will produce the goods and services we will consume when we are retired? Unless we can store consumption goods, or invest in building robots that don't need human labour to produce goods.
Think about a OverLapping Generations model with three generations: kids, parents, and grandparents. Only the parents work.
There is a Cobb-Douglas technology in which labour L and non-human capital K produce output, which can be either consumed C or invested I in creating more non-human capital.
C + I = La Kb where a+b=1 and dK/dt = I - dK where d is the depreciation rate, usual stuff.
A Barro-Ricardo version of the model assumes intergenerational altruism, where each individual maximises the sum of the utilities of all three generations. But dynasties are selfish, in the sense that individuals care only about themselves, their own kids, and their own parents.
If all dynasties are identical, the competitive equilibrium will duplicate the social planner's problem. You would not need to introduce Samuelsonian "money" into the model to ensure dynamic efficiency, because retired grandparents will support and be supported by their middle-aged children anyway, with gifts flowing in either direction, depending on the parameters in the model. There are no externalities between dynasties.
What happens if we relax the assumption of intergenerational altruism?
If the whole population stops having kids, because they don't care for their kids, and they know their kids won't care for them, they are in a collective pickle. They can still invest in non-human capital for their retirement, but there won't be any middle-aged workers to add their labour to that capital. So the rate of return on their investment will be minus the depreciation rate d. And that is the most favourable assumption, because I am assuming the investment process is fully reversible, so that machines can be converted back into consumption goods at zero cost.
That is an extreme case, of course, and a population like that will die out anyway. But it illustrates the point that there is an externality. My having kids will increase the labour supply when I am retired, which will increase the rate of return on my investment in non-human capital. But I can't force my kids to work with my machines; they will work with your machines too, and raise the rate of return on your investment. And if the population is large, almost none of the benefits will flow to me. Those who are selfish would agree to a social compact where they will all have more kids to work on each others' machines when they are retired, to raise each others' rate of return on their investment in non-human capital.
Are they treating their own kids as a means to an end? Yes. And in part, it was ever thus, in the age before pension plans. And it's still true today, in aggregate. My kids are part of your pension plan, and your kids are part of my pension plan.
But (I think this is true in the model) those who are Barro-Ricardian, and who want to have kids anyway, and can have kids anyway, might not care about them others who don't have kids. And they will die out anyway. But it's tough on the people who can't have kids, for whatever reason, if nobody else does.
I'm not 100% sure I've got my head fully around this idea yet. But don't say I'm odious for thinking about these things. They matter for human welfare, and they might matter a lot. And we need to think about them clearly.
[Update. If we add a fixed stock of land to the model, as perhaps we should, then the population level matters too. Without land, and with constant returns to scale, only the population growth rate matters.]