Economic consequences of population decline

Population decline has many potential effects on individual and national economy. The single best gauge of economic success is growth in GDP per person, not total GDP. GDP per person is a rough proxy for average living standards, for individual prosperity.  Therefore, whether population decline has a positive or negative economic impact on a country’s citizens depends on the rate of growth of GDP per person, or alternatively, GDP growth relative to the rate of decline in the population.
Introduction.
The simplest expression for the size of a country’s economy isGDP = total population x GDP/personGDP/person is also known as GDP per capita or per capita GDP. This term is a simple definition of economic productivity as well as individual standard of living.
The real change in total GDP is defined as the change in population plus the real change in GDP/capita.  The table below shows that historically, for every major region of the world, both of these have been positive.  This explains the enormous economic growth around the world brought on by the industrial revolution.  However, the two columns on the right also show that, for every region, population growth in the future will decline and, in some regions, go negative.  The chart also shows that two major economies, Japan and Germany, may face the same conditions.
BecauseGDP = total population x GDP/person,as populations grow more slowly, assuming no changes in growth of GDP/person, GDP will also grow more slowly.
If per capita GDP increase is less than the decrease in total population..
The equation above shows that if the decline in total population is not matched by an equal or greater increase in productivity (GDP/capita), and if that condition continues from one calendar quarter to the next, it follows that a country would experience a decline in GDP, known as an economic recession.  If these conditions become permanent, the country could find itself in a permanent recession.
The possible impacts of a declining population that leads to permanent recession are:
If per capita GDP increase is greater than the decrease in total population..
The single best gauge of economic growth is growth in GDP per person, not total GDP. GDP/person is a rough proxy for average living standards, for individual prosperity. A country can increase its average living standard even though its population growth is low or even negative.
Consider for example Japan. During the period 2003–2007 Japan had a higher growth per capita than the United States, even though the U.S. GDP growth was higher than Japan's. In the United States, the relationship between population growth and growth per capita has been found to be empirically insignificant. Even when GDP growth is zero or negative, the GDP growth per capita can still be positive (by definition) if the population is shrinking faster than the GDP.
Updating this analysis (the table below) to a more recent time period, 2009–2017, finds the same result. Even though Japan’s population declined 0.9% over this time period, because its per capita GDP, a rough proxy for the standard of living of the average Japanese citizen, rose by about 13.8%, a much greater increase than the 0.9% decrease in its population, its GDP still grew by 12.7%.
Over the same period, US GDP grew 18.5%. Although this GDP growth rate is greater than Japan’s, mostly because the US population also grew 6.2%, US per capita GDP grew 11.6%, less than the Japanese rate. Therefore, during this period, even though its population declined, the standard of living of the average Japanese citizen grew a little faster than that of the average American.
The charts to the right show the comparison.
The projection for Japan’s population decline will accelerate to reach about -0.7% per year in the 2040–2045 time period. This means that for Japan’s GDP to grow during that period, per capita GDP growth must be at least greater than 0.7% per year.
This example of Japan during the period 2009–2017 shows that a nation can grow its economy and the standard of living of its citizens even though its population is declining. To do this it must grow its per capita GDP, its overall economic productivity, faster than its population declines.  Analysis of data for forty countries shows that while low fertility will indeed challenge government programs and very low fertility undermines living standards, moderately low fertility and population decline favor the broader material standard of living.