A country is described by the Solow Model with a production function y = k1/2 wh
ID: 1239796 • Letter: A
Question
A country is described by the Solow Model with a production function y =k1/2 where y is output per worker and k is capital per worker. Now suppose that the fraction of output invested (or saved) is 50%. Assume that the depreciation rate is 5% and population growth is 0%.
A) Calculate the country's steady state level of output per worker.
B) Now suppose k is equal to 400. Is the country at its steady-state level of output per worker, above the steady-state or below the steady state? Show how you reached your conclusion.
Explanation / Answer
ANSWER (NO CALCULATOR NEEDED) To find the steady-state value of output in the country, werefer to Equation (3.3) on page 63???=?d?yA.-as?1s? Plugging in values: A = 1, a = 0.5, ? = 0.5, and d = 0.05, we get: ???=?-y?ss?0.051.0.510.510.50.5 =yss10. Simplifying the above equation, we get To find the current output per worker, we substitute in k = 400 into the production function to get:===yk40020.2211 That is, the level of current output is 20 whereas the steady-state output level is 10. Therefore, we>yyss conclude that so the country is above its steady-state level of output per worker.
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