Consider an economy where output-per-worker, y(t), is produced according to the production function: y (t) =...

 

 

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Consider an economy where output-per-worker, y(t), is produced according to the production function: y (t) = Ak(t)a, where 0 < a < 1 and A > 0. Capital-per-worker, k(t), evolves over time according to the accumulation equation: k(t) = sy(t) - (n + 8) k(t), where 0 < s < 1,0 < d < 1, and n ≥ 0. 2.1. In your own words, explain what is meant by 'absolute convergence' and 'speed of convergence'. 2.2. Derive a relationship relating the growth rate of output-per-worker to the level of output-per-worker (and parameters) and use this relationship to find an expression for output-per-worker in steady state. Explain what it means for output-per-worker to be in steady state. Use a Solow-Swan diagram to illustrate the transition dynamics (20%) and the long-run effects of an increase in technology, A. Consider an economy where output-per-worker, y(t), is produced according to the production function: y (t) = Ak(t)a, where 0 < a < 1 and A > 0. Capital-per-worker, k(t), evolves over time according to the accumulation equation: k(t) = sy(t) - (n + 8) k(t), where 0 < s < 1,0 < d < 1, and n ≥ 0. 2.1. In your own words, explain what is meant by 'absolute convergence' and 'speed of convergence'. 2.2. Derive a relationship relating the growth rate of output-per-worker to the level of output-per-worker (and parameters) and use this relationship to find an expression for output-per-worker in steady state. Explain what it means for output-per-worker to be in steady state. Use a Solow-Swan diagram to illustrate the transition dynamics (20%) and the long-run effects of an increase in technology, A.

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21 Absolute convergence refers to the idea that poorer economies will grow faster than richer econom... View the full answer