The NYT featured yet another piece on a country, in this case Japan, facing a future with a lower population. The piece warns that it will be difficult to maintain economic growth with a declining population and that Japan's labor shortage would get more severe.
This doesn't sound like too bad of a story to people familiar with economics. Thus far the labor shortage has not been serious enough to cause wages to rise in Japan. If it eventually does get more severe and wages do rise then it just would mean that some of the least productive jobs would go unfilled. For example, perhaps Tokyo would no longer pay workers to shove people into overcrowded subway cars.
As far as GDP growth, economists usually care about GDP per capita as a measure of living standards, not total GDP. This is why Denmark is a richer country than India, even though India has a much larger GDP. (The piece does note this point in passing in the second to the last paragraph.)
It is worth reminding readers that growth in productivity swamps the impact of demographics. If Japan can sustain a 1.5 percent pace of productivity growth, then output per worker hour would be 80 percent higher in forty years. Even in a very extreme demographic change, say going from three workers per retiree to 1.8 workers per retiree, this would still allow for a 17 percent rise in average living standards over this period. (This assumes retirees consume 80 percent as much as workers on average.) And this does not account for the benefits from less strain on the infrastructure and the natural environment. Nor does it take account of the lower ratio of dependent children to workers.
If Japan can sustain productivity growth of 2.0 percent annually (well below the 3.0 percent Golden Age pace in the United States from 1947 to 1973 and again from 1995 to 2005), then the living standards of workers and retirees could rise by 42 percent over this period, in spite of the rising ratio of retirees to workers. Presumably the folks who are concerned about the job-killing robots expect that productivity growth will be considerably more rapid.