xBookUtils.terms['fn_8_501'] = "The Solow growth model is named after economist Robert Solow and was developed in the 1950s and 1960s. In 1987 Solow won the Nobel Prize in economics for his work on economic growth. The model was introduced in Robert M. Solow, “A Contribution to the Theory of Economic Growth,” Quarterly Journal of Economics (February 1956): 65–94.";
xBookUtils.terms['fn_8_502'] = "Edmund Phelps, “The Golden Rule of Accumulation: A Fable for Growthmen,” American Economic Review 51 (September 1961): 638–643.";
xBookUtils.terms['fn_8_503'] = "Mathematical note: Another way to derive the condition for the Golden Rule uses a bit of calculus. Recall that c* = f(k*) − δk*. To find the k* that maximizes c*, differentiate to find dc*/dk* = f′(k*) − δ and set this derivative equal to zero. Noting that f′(k*) is the marginal product of capital, we obtain the Golden Rule condition in the text.";
xBookUtils.terms['fn_8_504'] = "Mathematical note: To derive this formula, note that the marginal product of capital is the derivative of the production function with respect to k.";
xBookUtils.terms['fn_8_505'] = "Mathematical note: Formally deriving the equation for the change in k requires a bit of calculus. Note that the change in k per unit of time is dk/dt = d(K/L)/dt. After applying the standard rules of calculus, we can write this as dk/dt = (1/L)(dK/dt) − (K/L2)(dL/dt). Now use the following facts to substitute in this equation: dK/dt = I − δk and (dL/dt)/L = n. After a bit of manipulation, this produces the equation in the text.";
xBookUtils.terms['fn_8_506'] = "For modern analyses of the Malthusian model, see Oded Galor and David N. Weil, “Population, Technology, and Growth: From Malthusian Stagnation to the Demographic Transition and Beyond,” American Economic Review 90 (September 2000): 806–828; and Gary D. Hansen and Edward C. Prescott, “Malthus to Solow,” American Economic Review 92 (September 2002): 1205–1217.";
xBookUtils.terms['fn_8_507'] = "Michael Kremer, “Population Growth and Technological Change: One Million B.C. to 1990,” Quarterly Journal of Economics 108 (August 1993): 681–716.";