1 Savings and Growth
Many households have been forced to reduce savings in response to the COVID-19 crisis. Using the
growth model from class, consider the impacts on long-run growth from a reduction in the savings
rate. Provide a graph that clearly illustrates the effects along with a brief discussion. Be sure to
mention the effects on the long-run growth rate.
2 Growth Discrepencies
Both China and India have averaged around 7% GDP growth rates over the last 5 years while the
US and Japan have averaged around 2%. The population growth rates for the US and China and
Japan are all under 1% (.5% for China, .8% for the US, and ?.1% for Japan) while Indias is 1.2%
(also relatively modest). Discuss these facts in the context of a Solow-Swan growth model, clearly
explaining your reasoning.
3 Growth Model
Suppose that output (Y ) in an economy is given by the following aggregate production function:
Yt = Kt + Nt
where Kt
is capital and Nt
is the population. Furthermore, assume that capital depreciates at rate
? and that savings is a constant proportion s of income. You may assume that ? > s.
1. Suppose that the population remains constant. Solve for the steady-state level of capital per
worker.
2. Now suppose that the population grows at rate n. Solve for the steady-state level of capital
per worker.
3. Based on your answer to part 2) above, solve for the steady-state growth rates (in terms of
n) of the following:
(a) capital per worker
(b) output per worker
(c) capital
(d) output