Consider again the Solow model with population growth. Suppose
the government decides that the
saving rate s of the individuals is too low and decides to
collect a fraction t of total output every period
and direct it fully towards investment. The individuals will
save and consume out of the remaining income
(1 ? t)Y at a savings rate of s.
(a) Obviously the law of motion for capital will be di?erent.
Not only do we have the investment coming
from private savings, we also have the contribution of the
government. Write the new equation of capital
accumulation taking this into account.
(b) Find the steady state capital per worker and output per
worker in this situation. How does it compare
to before the tax?
(c) Are individuals better o?? Discuss the possibilities by
looking at per capita consumption in steady
state before the tax and after the tax.