On the Invariance of the Rate of Return to Convex Adjustment Costs, Issue 8635
The Modified Golden Rule, which relates the rate of return on capital and the growth rate of the capital stock along long-run growth paths that maximize the utility of a representative infinitely-lived consumer, is invariant to the introduction of convex capital adjustment costs. Therefore, along balanced growth paths in neoclassical optimal growth models with an exogenous long-run growth rate of capital, the rate of return is invariant to the introduction of convex adjustment costs, though the capital-labor ratio is reduced along such paths. In AK models, convex adjustment costs reduce the growth rate and rate of return on capital.
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Abel and Blanchard absence of convex additively separable adjustment cost function adjustment costs reduces AtNt balanced growth paths Baxter and Crucini Blanchard 1983 capital-labor ratio competitive economy Condition 1 Finite Condition 2 Permissible constant growth paths convex adjustment costs convex costs costs of adjustment Equation 16 equilibrium Finite Utility function in equation Golden Rule rate Golden Rule relationship gross investment homogeneous in Kt instructions inside intertemporal optimization introduction of convex investment is zero ip Gk Kt and Kt+i Kt+i,AtNt labor Lemma Leonid Kogan linearly homogeneous long-run growth rate marginal adjustment cost Market maximize the social Modified Golden Rule neoclassical balanced growth neoclassical growth models on.line papers in hard paths that maximize paths with J3 Permissible Values presence of convex product of capital production function production possibilities frontier Proposition rate of capital rate of return return on capital social discount rate social marginal product social planner social welfare function z2 Gk