Suppose in a country with no population growth and no technological change, the parameters of the Solow growth model are

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Suppose In A Country With No Population Growth And No Technological Change The Parameters Of The Solow Growth Model Are 1 (415.39 KiB) Viewed 14 times

Suppose in a country with no population growth and no technological change, the parameters of the Solow growth model are given by s = 0.2 (saving rate) and 8 = 0.1 (depreciation rate). The output in the country with two inputs, K, capital, and N, labor, is determined by a constant- returns-to-scale Cobb-Douglas production function where productivity, A, is 1, and elasticity of output with respect to capital is 0.7. a. (3 points) Rewrite the production function in per-worker terms. Let k denote capital per worker (capital-labor ratio) and y output per worker. b. (5 points) Write the steady-state condition for the Solow model. Find the steady-state level of the capital-labor ratio, k* (enter your response rounded to two decimal places). c. (7 points) Find the Golden Rule capital-labor ratio, kg. d. (9 points) For the production function Y = KºL1-a and the depreciation rate is d, prove that the saving rate necessary to support the Golden Rule capital-labor ratio, Sq, is always equal to a. For the proof, follow the steps from part (a) through C) in parametric form, i.e, use a and 8 instead of their assumed values. e. (4 points) Based on the proof from part (d), do citizens need to save more or less than the assumed saving rate (if you could not prove the proposition, you can still use the outcome)? Discuss the effects of a policy that would promote a saving rate of sg on consumption per worker in the short run versus a long-run improvement in the standard of living.