Econ 333 Homework Set 3 Solutions

Econ 333 Homework Set 3 Solutions - Homework Set 3 Economic...

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Homework Set 3 Economic Development 333 Solutions 1. Give an interpretation of the following equation, which is derived from equation A3.3, p. 136. Δ y = AΔ k y The right-hand side is growth rate in output The left-hand side is the growth rate of inputs, k = K/L or capital per worker 2. What does the term sf ( k ) of equation A3.5 (p. 137) mean and why is it plotted below the production function f ( k ) in Figure A3.1 (p. 137)? y = f ( k ) is the total output, or GDP, or total income s = S/Y savings rate or the proportion of the GDP available for investment Note: s cannot be greater than 1; you cannot save more than your total income When you multiply s x f ( k ) = sf ( k ) will necessarily be less than f ( k ) sf ( k ) is the savings amount that is available for new investment in capital 3. What does the term ( δ + n ) k mean and why is it plotted as a straight line in Figure A3.1 δk is the capital depreciation nk is the amount of capital per worker to net worker joining the labor force ( δ + n ) k is the net depreciation in capital per worker It’s a straight line with slope ( δ + n ); when k = 0, the capital stock K in the economy is zero and the entire term is zero 4. The Solow Growth Model achieves steady-state when Δ k = 0 in equation A3.4, p. 137. Identify the steady-state in Figure A3.1, p. 137. Δ k = sf ( k ) - ( δ + n ) k This equation says: The change in capital per worker equals the savings amount available fore new capital investment less capital depreciation per worker When Δ k = 0 sf ( k ) = ( δ + n ) k Which means the economy saving available for investment in new capital is just enough to replace the depreciation in capital per worker
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5. Why does growth in output, y tend to increase when sf ( k ) > ( δ + n ) k ? When sf ( k ) > ( δ + n ) k The savings amount available for new capital investment exceeds the depreciation of exiting capital Mathematically, Δ k will necessarily be positive since the right-hand side of Δ k = sf ( k ) - ( δ + n ) k is positive. Since Δ
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Econ 333 Homework Set 3 Solutions - Homework Set 3 Economic...

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