By manipulating the equations of the Solow model mathematically, it is possible to make more precise quantitative statements about the behavior of growth rates over time. For example, one way of quantifying the principle of transition dynamics is with the following equation:

g = 3 × (ln y* ˆ’ ln y₀) + 2,

where g denotes the growth rate of a country over the next 10 years (in percentage points), ln denotes the natural logarithm, y₀ is the per capita GDP of a country today (relative to the United States), and y* is the per capita GDP of a country in steady state (relative to the United States). For example, a country that is today at 10% of the U.S. level and is projected to have a per capita GDP relative to the United States of 20% in steady state would be predicted to grow at an average annual rate of

3 × [ln(20) €“ ln(10)] + 2 = 3 × 0.69 + 2 ‰ˆ 4.1.
That is, we€™d expect such a country to grow at 4.1% per year over the next decade.Of course, we don€™t usually know a country€™s steady-state position
vis-à-vis the United States. However, we do observe its growth rate. This question asks you to consider the facts from recent growth experiences in the table below.

Growth rates are rough, stylized estimates, excluding the impact of the financial crisis.

(a) Using those facts and the equation above, fill in the last column of the table. That is, offer a projection of where countries are headed in the long run.
(b) Provide a one-paragraph discussion of your results.

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Per capita GDP (U.S. = 100), steady state Growth rate during 2004-2014 (%) Per capita GDP (U.S. = 100), 2014 100 27 24 18 Country United States Argentina Mexico ?? ?? 2.0 4.0 2.5 ?? Brazil China India Uganda 5.0 ?? 12 8.0 ?? 5 ?? 8.0 3 ?? 4.0