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Economic Growth and The Solow Growth Model Looks at the overall economy in the longrun, i.e. Y* = YN. Focuses on a country’s standard of living, measured by real per-capita GDP (income per person). Model is commonly used to prescribe ways to maintain and improve a country’s longrun standard of living (economic growth), as opposed to getting Y* to a given YN (fluctuations). The Solow Growth Model: Simplifying Assumptions No Business Saving, all saving is Personal Saving (done by consumers). No government, i.e. G = T = 0 No international trade, i.e. Exports = Imports = NX = 0 The Solow Growth Model: Main Properties Full employment, so that labor employment = population Equilibrium is based upon constant per-capita levels of output and related variables Per-capita output = Y/N, where N is labor employment. Other per-capita variables are defined correspondingly. The Solow Growth Model: More Properties Even at equilibrium, the levels of output (Y) and capital stock (K) grow at a constant rate over time. Population (N) also grows at a constant rate over time, given by n. Since (Y/N)* and (K/N)* are constant, at equilibrium Y and K also grow over time at constant rate n. Incorporating Dynamics: Investment and the Capital Stock Important identity relationship between Investment (I) and the capital stock (K), not accounted for in static models: I = K + K, where is the rate of physical depreciation of the capital stock. The “Magic Equation” in The Solow Model The “Magic Equation” S + (T – G) + (-NX) = I. With G = T = NX = 0, it becomes: S = I. Note that the equation also holds in per-capita terms: (S/N) = (I/N). Determining the Per-Capita Saving Function (S/N) Consider the production function for the economy with positive and diminishing marginal product of labor and capital (from standard micro): Y = A[F(K,N)], where A is technological change. Assume the production function exhibits constant returns to scale (doubling all inputs results in a doubling of output). Determining the Per-Capita Saving Function, Continued Constant returns to scale the production function for the economy can be written (in per-capita terms) as: Y/N = A[f(K/N)], with f’ > 0. Determining the Per-Capita Saving Function, Finally Assume that consumers save a constant proportion (s) of their income S = (s)(Y), where s is the Average Propensity to Save or The Saving Rate. Multiply both sides of the per-capita production function by s (s)(Y)/N = S/N = (s)(A)[f(K/N)]. Determining the Per-Capita Investment Function (I/N) Recall that the capital stock grows at a constant rate n (the population growth) K/K = n. Use investment-capital stock identity to substitute for K. (I K)/K = n. Algebra I = (n + )K. Determining the Per-Capita Investment Function (I/N) Continue with this equation, I = (n + )K. Divide both sides by N, in order to form per-capita values: I/N = (n + )(K/N). Equilibrium in the Economy Equilibrium takes place where the percapita Saving and Investment functions intersect, gives a value of equilibrium per-capita capital stock (K/N)*. Equilibrium can change due to shifts in the per-capita Saving or per-capita Investment functions. Given changes in (K/N)* that occur, use the per-capita production function to infer how (Y/N)* will change as a result. The Effect of an Increase in Population Growth Consider an increase in the population growth rate (n). Described as shifting the Per-Capita Investment function upward (K/N)*. From the production function, this implies that (Y/N)* as well. Increased population growth lowers the average standard of living. The Effect of an Increase in the Saving Rate Consider an increase in the society’s saving rate (s). Described as shifting the Per-Capita Saving function upward (K/N)*. From the production function, this implies that (Y/N)* as well. An increased saving rate raises the average standard of living. Per-Capita Consumption and the Saving Rate What is the effect of an increase in the Saving Rate (s) on equilibrium Per-Capita Consumption (C/N)*? Not a trivial answer Per-Capita Consumption and the Saving Rate Two conflicting effects. -- An increase in the saving rate, ceteris paribus on (Y/N), decreases per-capita consumption. -- But an increase in the saving rate also increases (Y/N)*, which in turn increases per-capita consumption. There exists an optimal saving rate that maximizes (C/N)*. Technological Change and the Solow Model Technological Change is given by the variable A within the production function. An increase in A is referred to as neutral technological change, increases the efficiency of labor and capital stock equally, leading to higher output for given inputs. Effect of an increase in A similar to that of an increase in the saving rate. Multifactor Productivity and “The Solow Residual” The variable A is formally known as Multifactor Productivity, neutral technological change that increases output for given levels of labor and capital stock. The Solow Residual – seeking to come up with a data series for the estimated growth in A over time for a country, based upon the properties of the percapita production function. The Solow Model: Extensions Endogenous Growth Theory – policies seeking to induce continuous technological change over time Incorporating human capital in the production function Foreign Investment, technological change, and economic growth Infrastructure, technological change, and economic growth Political structures, legal determinants, and geography in economic growth