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Handout 5

Handout 5 - k max(d What is the value of consumption at k...

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Econ 3140 Fall 2009 Handout #5 1. Consider an economy with a production function of the form Y t = AK 1 = 3 t N 2 = 3 t , where Y t is output produced in year t , A is the total factor productivity, K t is the available capital stock at the beginning of year t , and N t is the number of workers available at year t . The depreciation rate of capital is 12% per year and the population growth rate is 3% . Households consume 75% of income and save the remaining. (Saving function is then S t = 0 : 25 ° Y t where S t is the total national saving in year t ). (a) If total factor productivity is °xed at A = 15 , Calculate y t = f ( k t ) ,where is y t is output per worker, and k t is the capital-labor ratio. (b) What is the maximum possible value of capital, k max ? (c) What is the value of output at
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Unformatted text preview: k max ? (d) What is the value of consumption at k max ? (e) What is the steady-state value of the capital-labor ratio, k & ? (f) What is the steady-state value of output per worker, y & ? (g) What is the steady-state value of consumption per worker, c & ? (h) What is the Golden rule value of the capital-labor ratio, k G ? (i) What is the Golden rule value of output per worker, y G ? (j) What is the Golden rule value of consumption per worker, c G ? (k) Describe what happens if the initial level of capital-labor ratio is k = 100 . (l) Describe what happens if the initial level of capital-labor ratio is k = 200 . 1...
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