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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 India’s 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 δ and that savings is a constant proportion s of income. You may assume that δ > 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