Consider a version of the Solow growth model with a population growth rate of ππ = 0.02 (2%
population growth), a depreciation rate of πΏ = 0.06 (6% depreciation), a savings rate of π = 0.5 (50%
saving), TFP π΄ = 1, and a production function πΉ(πΎ, π) = πΎ0.5π0.5.
a.) Solve for the per worker production function π(π) where π is capital per worker. Show all of
your work.
b.) What is the equation that characterizes the steady state level of capital per worker in this Solow
growth model?
c.) Solve for the steady state level of capital per worker. Show all of your work.
d.) Solve for the steady state level of consumption per worker. Show all of your work.
e.) Is it possible to increase the steady state level of capital per worker you found in c.) by adjusting
the savings rate? Why or why not?
f.) Is it possible to increase the steady state level of consumption per worker you found in d.) by
adjusting the savings rate? Why or why not?
g.) Why do increases in TFP increase the long-run standard of living the Solow growth model but not
in the Malthusian growth model?