Consider the Solow Model where technology is assumed to be given by Y = A K/4L3/4...

   

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Consider the Solow Model where technology is assumed to be given by Y = A K¹/4L3/4 In addition, capital is assumed to depreciate at rate 0 < < 1, every period. Savings are assumed to be a fixed fraction of Income Y. And L is assumed to grow at a constant rate n. Y a) Derive the production function for output per worker y = Show all your work b) Derive the law of motion for capital per worker k = ? Show all your work. d) c) Derive the steady state value of capital per worker and output per worker. Show all your work. Show your answer in a diagram, with capital per worker on the horizontal axis and output on the vertical axis. Make sure you mark on your diagram what the steady state values for capital, output and consumption per worker are. e) Assume that Labor is constant over time (n = 0). Use a diagram with k on the horizontal axis and kt+1 on the vertical axis to show that the economy will converge over time to the steady state, no matter what the initial level of capital per worker is. Make sure to clearly label your axis and curves. Consider the Solow Model where technology is assumed to be given by Y = A K¹/4L3/4 In addition, capital is assumed to depreciate at rate 0 < < 1, every period. Savings are assumed to be a fixed fraction of Income Y. And L is assumed to grow at a constant rate n. Y a) Derive the production function for output per worker y = Show all your work b) Derive the law of motion for capital per worker k = ? Show all your work. d) c) Derive the steady state value of capital per worker and output per worker. Show all your work. Show your answer in a diagram, with capital per worker on the horizontal axis and output on the vertical axis. Make sure you mark on your diagram what the steady state values for capital, output and consumption per worker are. e) Assume that Labor is constant over time (n = 0). Use a diagram with k on the horizontal axis and kt+1 on the vertical axis to show that the economy will converge over time to the steady state, no matter what the initial level of capital per worker is. Make sure to clearly label your axis and curves.

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a Derivation of the production function for output per worker The production function is given by Y ... View the full answer