A country has the following per-worker production function Yt = 5kt.5 Where yt is output per worker and k, is the capital-labor ratio. The depreciation rate is 0.2 and the population growth rate is 0.05. The saving function is St = 0.2Yt Where St it the total national saving and Yt is total output. 1.1 Derive the steady-state values of the capital-labor ratio, output per worker, consumption per worker, and investment per worker?

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Chapter1: Making Economics Decisions
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Question 2
A country has the following per-worker production function
Yt = 5k0.5
Where yt is output per worker and kɩ is the capital-labor ratio. The depreciation rate is 0.2 and the
population growth rate is 0.05. The saving function is
St = 0.2Yt
Where S, it the total national saving and Y, is total output.
1.1 Derive the steady-state values of the capital-labor ratio, output per worker, consumption per
worker, and investment per worker?
1.2 Show your results on the Solow diagram.
1.3 What is the long-run balanced growth in total output and capital?
1.4 What is the long-run balanced growth in output per worker and capital per worker?
1.5 Explain the difference between capital deepening and capital widening.
1.6 Suppose the economy begins with a level of k less than k*. As k moves toward k*, is w (a wage
for each unit of labor) growing at a rate greater than, less than, or equal to its growth rate on the
balanced growth path?
1.7 Can this model generate sustained economic growth in per capita income? Explain.
Transcribed Image Text:Question 2 A country has the following per-worker production function Yt = 5k0.5 Where yt is output per worker and kɩ is the capital-labor ratio. The depreciation rate is 0.2 and the population growth rate is 0.05. The saving function is St = 0.2Yt Where S, it the total national saving and Y, is total output. 1.1 Derive the steady-state values of the capital-labor ratio, output per worker, consumption per worker, and investment per worker? 1.2 Show your results on the Solow diagram. 1.3 What is the long-run balanced growth in total output and capital? 1.4 What is the long-run balanced growth in output per worker and capital per worker? 1.5 Explain the difference between capital deepening and capital widening. 1.6 Suppose the economy begins with a level of k less than k*. As k moves toward k*, is w (a wage for each unit of labor) growing at a rate greater than, less than, or equal to its growth rate on the balanced growth path? 1.7 Can this model generate sustained economic growth in per capita income? Explain.
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