Solow_q - Solow Growth Sample Questions David Lagakos, May...

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David Lagakos, May 6, 2007 Question 1 - Setting up the Solow Model (a) Let the production function be Cobb-Douglas with capital share α and productiv- ity term A , where Y t is output, K t is capital, and L t is labor at time t . Let the savings rate be s , the population growth rate be n , and the depreciation rate be δ . Let con- sumption and investment be C t and I t . Write down the production function, the law of motion for labor, the law of motion for capital, the resource constraint, and the investment equation that describe the Solow Growth Model. Describe in plain English what each equation means. (b) Derive the per-capita resource constraint, the per-capita law of motion for capital, and the per-capita investment equation. Express per-capita variables in lower-case variables. (c) Derive the ’required investment’ curve using the per-capita law of motion in steady state. Provide an economic interpretation. (d) Plot this equation with k on the x -axis and i on the y -axis. What’s the slope of the line? Describe what happens to k for points on this graph (i.e. i , k pairs) above and below the line. (e) Plot the per-capita production function and actual investment equation. Demon- strate on a graph that for sufficiently low capital, the capital stock will rise. Explain why it will rise. 1
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Solow_q - Solow Growth Sample Questions David Lagakos, May...

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