FE 312Q
Professor Smith
Fall 2012
Growth Problem Set
1.
Let’s consider the U.S., France and Germany after WWII. Suppose that all three countries had
been at their steady state capital levels before the war. Suppose that the production function for all
three countries is Cobb-Douglas, with constant returns to scale:
Y=zKαN1-α, where Y is output, K is the capital stock, N is the number of
workers, and z is a technology parameter.
i. Write an expression for output per worker in all three countries.
ii. Find an expression for the growth rate of capital in the three countries (assuming
each is a closed economy). Show your derivation of this expression
iii. Assume the savings rate is constant and equal to .40, the technology
parameter=.1, depreciation=.01, capital share in production=0.5, and population
growth=.03 in all three countries. What is the steady state per capita capital
stock?
iv. Since the war took place on another continent (for the most part), if the U.S.
population had been cut in half but no change to the capital stock occurred, what
would be the post-war growth rate in the U.S.? If half of the German capital
stock had been destroyed but little change in population, what would be the
post-war growth rate in Germany? In France, if the capital stock and population
were cut in half, what would be the post-war growth rate? Give numerical
answers.
v. How would the growth rates of all three countries evolve over time after WWII
according to this (the Neoclassical Growth) model?
vi. Russia, like the U.S., lost many lives but relatively less capital stock destruction.
Suppose, however, Russia’s savings rate is much higher. Would their post-war
growth rates resemble the U.S.? Will they converge to the same steady state
growth rate and income per capita?
2.
The fearless leader of Ghana has decided to choose an advisor to help him find ways to raise
steady state per capita income (and capital stock). If chosen, using your Solow Growth model,
what policies would you implement? Mention at least three, remembering however what is
realistically influenced by the government. What would you do if you wanted to increase long run
growth in Ghana? Explain using graphs.