problem set #9

# problem set #9 - Econ 100B Macroeconomic Analysis Fall 2008...

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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 relationship between 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 relationship between 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 = A 0 * f(K/N) Ib/N = (n + d) * K/N S/N = s * Y/N “A”

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