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204A-2010midterm - Econ 204A Midterm Exam Fall 2010 This...

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Econ 204A - Midterm Exam Fall 2010 This exam is closed book. Most points are given for the correct set-up of a problem and for economically insightful interpretations. Problem 1 (50p) Consider a Solow model with general production function Y = F ( K , AL ) . Notation is as in Romer unless noted. Population L grows at a rate n. The savings rate s is constant. The depreciation rate is δ = δ 0 >0. Productivity A grows at an exogenous rate g=g 0 >0. a. Derive an equation for the steady state capital-labor ratio k* =k 0 * (meaning: in efficiency units). [Derive means: Show your work. No credit for a memorized formula.] b. Suppose at time t=t 1 , a new way of organizing research is discovered that accelerates productivity growth but at the expense of making capital obsolete more quickly. Specifically, assume the economy after the discovery has the parameters g=g 1 >g 0 and δ = δ 1 > δ 0 . Derive the new steady state capital-labor ratio k*=k 1 *. Compare k 0 * and k 1 *. c.
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