  The existence of involuntary unemployment advocated by J. M. Keynes is a very
important problem of the modern economic theory. Using a three-generations
overlapping generations model, we show that the existence of involuntary
unemployment is due to the instability of the economy. Instability of the
economy is the instability of the difference equation about the equilibrium
price around the full-employment equilibrium, which means that a fall in the
nominal wage rate caused by the presence of involuntary unemployment further
reduces employment. This instability is due to the negative real balance effect
that occurs when consumers' net savings (the difference between savings and
pensions) are smaller than their debt multiplied by the marginal propensity to
consume from childhood consumption.
