Optimal growth and the golden rule in a two-sector model of capital accumulation

We contribute to the literature on optimal growth in two-sector models by solving a Ram- sey problem with a concave utility function. The unique possible steady-state is independent of initial conditions and of the instantaneous utility function, but not of the discount rate, and is characterized by a wage-rental ratio depending solely on the technology of the capital sector. For an initially low-capital economy, we show that the wage-rental ratio increasingly converges to its balanced value during transition. If the consumption sector is relatively capital-intensive, the relative price of capital increases during transition. If the investment sector is relatively more capital-intensive, it decreases. We also prove that a negative shock on the subjective rate of impatience, that makes the social planner more patient, leads to an immediate positive jump in asset prices.capital accumulation ; optimal growth ; golden rule ; two-sector models

Optimal growth and the golden rule in a two-sector model of capital accumulation

We contribute to the literature on optimal growth in two-sector models by solving a Ram- sey problem with a concave utility function. The unique possible steady-state is independent of initial conditions and of the instantaneous utility function, but not of the discount rate, and is characterized by a wage-rental ratio depending solely on the technology of the capital sector. For an initially low-capital economy, we show that the wage-rental ratio increasingly converges to its balanced value during transition. If the consumption sector is relatively capital-intensive, the relative price of capital increases during transition. If the investment sector is relatively more capital-intensive, it decreases. We also prove that a negative shock on the subjective rate of impatience, that makes the social planner more patient, leads to an immediate positive jump in asset prices

Technical change in a neoclassical two-sector model of optimal growth

This paper investigates into the consequences of sector-speci c technological progress in a two-sector, optimal growth model. In accordance with existing theory, we find that consumption-specifi c Hicks-neutral technical shocks increase consumption but leave other parameters unchanged. Hicks-neutral, investment-specifi c technical shocks increase the wage-rental ratio, and increase steady-state consumption by a factor equal to the macroeconomic ratio of capital share to labor share. If the elasticity of substitution is equal to one in the long run, the growth regime with only investment-specifi c technical change is sustainable and asymptotically balanced

Technical change in a neoclassical two-sector model of optimal growth

This paper investigates into the consequences of sector-speci c technological progress in a two-sector, optimal growth model. In accordance with existing theory, we find that consumption-specifi c Hicks-neutral technical shocks increase consumption but leave other parameters unchanged. Hicks-neutral, investment-specifi c technical shocks increase the wage-rental ratio, and increase steady-state consumption by a factor equal to the macroeconomic ratio of capital share to labor share. If the elasticity of substitution is equal to one in the long run, the growth regime with only investment-specifi c technical change is sustainable and asymptotically balanced.Productivity ; optimal growth ; golden rule ; two-sector models

A note on 2-input neoclassical production functions

International audienceIn this short note, we show how the space of elasticity of substitution functions maps into the space of 2-input neoclassical production functions. In doing so we derive a general analytical formula for every 2-input neoclassical production function of class C2. We present a simple set of sufficient conditions for the Inada conditions to hold; and prove that the Solow model under capital-augmenting (or investment-specific) technical change is asymptotically balanced if and only if the capital share converges to a non-degenerated limit as the capital-labor ratio tends to infinity

The Habakkuk hypothesis in a neoclassical framework: (To make more with less or to make more with more: that is the question)

We present a new way to picture technological change in an otherwise standard Ramsey framework. Technological change takes the form of alterations of the production function itself, rather than changes in total factor productivity. These changes can take two directions that we dub respectively ‘complementation’ and ‘substitution’. Complementation results in a production function that is superior for lower values of capital, while substitution results in a production function that is superior for higher values of capital. Under the most general conditions, when the agent is initially at steady state, both options bring strictly positive utility gains to the agent.We analyze sequence of steady states with exogenous and endogenous direction of technological change.With exogenous growth, we prove that when the production functions are Cobb-Douglas or CES (with the same elasticity of substitution), output and consumption grow asymptotically at a common rate and the capital share tends to one under continual substitution; while continual complementation makes output and consumption converge to a common limit and the capital share tend to nil.With endogenous direction of technological change and under the most general conditions, the agent has a bias towards complementation which brings quicker gains than substitution. We assume that the production functions are Cobb-Douglas and that utility is logarithmic. Then, when the potential rate of complementation is strictly greater than the potential rate of substitution, the labor share oscillates around some endogenous long-run value, determined by the rates of complementation/substitution and by the impatience rate. This growth regime reproduces the Kaldor facts

The endogenous direction of technological change in a discrete-time Ramsey model

The relative price of capital (or equipment) goods with respect to consumption goods is strongly, negatively correlated with income per capita in cross-sections of countries. This stylized fact suggests that economic growth takeoffs are associated with changes in the direction of technical change. It also suggests that increases in productivity that are embodied in capital goods lead to relatively quicker growth.The goal of this paper is to explore the message of the discrete-time Ramsey model with logarithmic utility, augmented with endogenous direction of technical change. We suppose that the representative agent, while initially at steady state, is offered the possibility to increase either labor-augmenting productivity or investment-specific productivity. We derive the marginal increase in utility from each option. We find that when the elasticity of substitution, the capital share and the rate of impatience lie within the usual ranges, investment-specific technological change is relatively undervalued, because its fruits take relatively more time to materialize.This approach reflects some interesting ideas on the macroeconomics of structural change. However, its predictions stand at odds with cross-country evidence as well as with the early British growth experience (~1770–1913). We argue that the fixity of the production function constitutes a major obstacle for a consistent theory of the direction of technological changes on neoclassical bases