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11S_Quiz2_Sol - Econ 204 Instructor J Li QUIZ 2 ANSWERS...

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Econ 204 Instructor: J. Li 1 QUIZ 2 ANSWERS, SPRING 2011 Given: production function: (a) Find: per worker production function. f ( k ) = F ( K , L ) / L (+0.25) = K α L 1- α / L = ( K / L ) α = k α +0.25 (b) Given: rate population growth = n . Find: The SS capital per worker, output per worker, and consumption per worker as a function of savings, depreciation and α. +0.25 The SS value of capital per worker k * is defined as the value of k at which capital per worker is constant; that is, Δ k = 0 sf ( k ) ( δ + n ) k = 0. +0.25 Or +0.25 Solving for we get: Or +0.25 Substituting k * into per-worker production function yields y *: y = k α +0.25 Similarly solve for c *: c = (1 s ) y * +0.25 (c) Demonstrate: The steady state solution in a diagram. +0.5 (d) (i) Define: The Golden Rule level of capital. The Golden Rule level of capital is the steady state value of k* that maximizes consumption. +0.25
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Econ 204 Instructor: J. Li 2 (ii) Find: The condition of Gold Rule: MPK = δ + n . +0.5 (iii) In a diagram: +0.25 for clear labeling; +0.25 for indicating at
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