Econ 100B: Macroeconomic Analysis Fall 2008 Problem Set #9 ANSWERS (Due September 29 - 30, 2008) A.Solow Growth Model: 1.Clearly and accurately draw and label a diagram of the Solow Growth Model. 2.Provide an economic explanation of the shape of the curve(s) in your diagram in #1. The per-worker production function shows a positive relationshipbetween income-per-worker, Y/N, and the capital-to-labor ratio, K/N, for a given level of productivity, A. The per-worker production function slopes upward because there are increasing returns to a higher capital-to-labor ratio, i.e., as the capital-to-labor ratio increases, income-per-worker also increases. The slope of the per-worker production function decreases as the capital-to-labor ratio increases because of the diminishing marginal product of capital, i.e., as the capital-to-labor ratio increases, income-per-worker also increase but by progressively smaller and smaller amounts. The per-worker saving function also shows a positive relationshipbetween saving-per-worker, S/N, and the capital-to-labor ratio, K/N. Because of the assumption of a constant saving rate, the per-worker saving function is simply proportional to the per-worker production function, the proportion dependent on the saving rate. K/N K/N Y/N, S/N, Ib/N Y/N S/N, Ib/N Y/N = A0 * f(K/N) Ib/N = (n + d) * K/N S/N = s * Y/N “A”
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