Question 1:
Consider an economy with the production function
Y=AK*2/5N*3/5.
a.) Suppose the economy is growing at an average rate of 3.5% per year, K growing at 4%, and N growing at 2%, what is the growth rate of total factor productivity (A) for the economy?
b.) Demonstrate that the per capita production function for this economy is y=Ak*2/5
(Note: To "demonstrate", you need to perform the mathematical steps to derive y=Ak2/5 from Y=AK*2/5N*3/5.)
c.) For n=0.05, d=0.2, s=0.4, A=5, what are the Steady State values for y, i, c, and k?
d.) Draw the per capita production function and supporting curves to capture the economy at its steady state.
e.) Suppose the re-emergence of Cold War-type geopolitics (starting with the events in Ukraine) decreases the savings rate to s=0.32 as former investment is diverted to fund a larger military. Compute the new steady state values and include the impact of this change on your figure for (d).
f.) Include a plot of the evolution of y, i, c, and k over time as the economy adjusts from the old pre-Cold War steady state to the post-Cold War steady state.
g.) Provide a brief economic explanation of the consequence of lower savings for per capita consumption and why. An economic explanation should be devoid of math and should not reference the figure
h.) Provide a brief economic explanation of the consequence of lower savings on long- term growth rates.
i.) Demonstrate mathematically that the Golden Rule savings rate for this economy is sg=2/5.
(Note: The starting-point formula can be found online or in your lecture slides. You need to show the mathematical steps to obtain the objective, sg=2/5)
j.) Starting from the original steady state, if there had instead been an increase in savings, what direction would consumption have changed? Explain your answer
Question 2:
Consider the sources of growth and the models related. Build your answer using these tools..You should be able to answer in short concise responses.
Please read the linked article in The Economist. Published in Dec 2011, it makes the case that Africa is poised to enjoy high economic growth. The article includes numerous
facts and analysis to support this theory. Identify those that are consistent with the Solow and endogenous growth models. Briefly explain how each fact or notion that you identify fits into the models of Solow and endogenous growth.
a.) List all the sources of growth developed in the article. For example, the article discusses the expansion of the middle class and how this is good for the economy, so your list should include "rise of middle class".
b.) For each item in your list, indicate those that are captured by the growth models developed in class (the Solow growth model and the extensions, including endogenous growth).
c.) For each item on your list that is captured by one of the developed growth models, explain how the feature contributes to growth consistent with the model.
d.) For each item that is not directly explained by one of the developed models, see if you can link the item to something that is captured by one of the models developed. You might, for example, link the rise of a middle class with more schooling and thus human capital growth.