Macroeconomic Principles
Problem Set 4-Weeks 14 and 15
1. Assume a country has a generic production function: Y=AF(K,L), a generic marginal propensity to
save, mps and a generic depreciation rate, .
a. Show what country's steady state level of capital per worker and output per worker is.
b. Show what happens to the steady state level of capital and output per worker if the country is
hit by a natural disaster that severely decimates its capital stock.
c. After the country recovers from the disaster and is at a steady state level of capital and
output, the United Nations provides the country with even more capital. What is the steady
state level of capital and output after this increase in capital?
2. A country is at its steady state level of capital and output per worker.
a. Show what happens to the steady state level of capital and output per worker when the
savings rate increases.
b. Show what happens to the steady state level of capital an d output per worker when the
savings rate becomes 100%
c. Given your answer to part (b), does it make sense to save all of our income, have a high level
of steady state capital per worker, but have no consumption? If not, what would be the level of
savings that would maximize consumption?