An optimal growth model in a declining population: Is a “smart contraction†of the Japanese economy possible?

We This study employs an optimal growth model to analyze an economy facing a declining birthrate, an aging population, and a shrinking population. In contrast with conventional models, the labor input variable in the production function is not the total population; rather, it is the working-age population, with the labor augmented technological progress. The construction of this model facilitates the derivation of an optimal steady-state solution that is saddle-point stable, thereby enabling the investigation of the conditions under which GDP per capita can exhibit growth in an economy confronted with population decline. Given that GDP per capita is widely regarded as a metric of a nation's well-being, an economy that experiences growth in GDP per capita despite population decline is designated as a "smart contraction" economy. The condition that enables such growth can be termed "smart contraction condition." The validity of this condition will be examined through an analysis of data from the Japanese economy. (154 words)