María Pilar Martínez-García

The general instability of balanced paths in endogenous growth models: the role of transversality conditions

Abstract We prove the instability of optimal balanced paths in endogenous growth models, as long as transversality conditions are satisfied. Moreover, we prove the complete instability of models with one state variable, whereas, in models with two and three state variables, we offer necessary and sufficient conditions for the saddle point property to occur. Our results generalize some classical stability results of steady states in neoclassical growth models, to balanced paths in the new endogenous growth models.

TECHNOLOGICAL LEADERSHIP AND SUSTAINABLE GROWTH IN A BILATERAL TRADE MODEL

This paper develops a trade model for a technologically leading country and a developing country that exploits a renewable natural resource. Technology diffuses from the technological leader to the developing country through foreign direct investment (FDI). Alternatively, innovative activities can also be carried out in the developing economy. We prove the existence and uniqueness of an equilibrium path along which both countries grow at the same rate, maintaining the natural-resource stock at a constant level. The saddle-point property for this equilibrium is proved and a sensitivity analysis is carried out. The steady-state growth rate and consumption under both scenarios are compared and the effect of resource abundance analyzed.

North — South Trade and the Sustainability of Economic Growth: A Model with Environmental Constraints

We present a model of trade between two different regions, North and South. The South specializes in a natural resource intensive good which is sold to and used as an input in the North. Assuming an environmental R&D sector in the North, which increases the efficiency of the traded good, the North-South trade and the natural resource management are modeled in a dynamic way. The existence of a sustained growth in the North, which allows a permanent growth of consumption in the South without exhausting natural resource, is proved. Transitional dynamics is also studied.

An R&D-Based Endogenous Growth Model of International Tourism

According to the tourism area life cycle (TALC) model of Butler (1980), the evolution of a touristic destination follows an S-shaped curve which is upper-bounded by its carrying capacity, usually assumed to be a fixed constant. This forecast prevents a tourism-based economy from maintaining positive growth rates in the long run. However, infrastructures, transportation networks, accommodation facilities and the variety of attractions can be broadened to increase the tourism carrying capacity. In this paper, innovation is the motor of carrying capacity growth. The model follows the tradition of R&D-based endogenous growth models and allows the long-run sustainability of economic growth in a tourism-specialized economy. Along a balanced growth path, the income from tourism grows at the same rate as the innovation, and the carrying capacity will grow as the rate of innovation surpasses the foreign economic growth rate. The long-term growth of the economy depends on the real exchange rate.

The poststagnation stage for mature tourism areas: A mathematical modeling process

The tourism area life cycle (TALC) model of Butler explains the temporal evolution of a tourism resort. Lundtorp and Wanhill find that the logistic growth model represents the first phases of the TALC model. However, since the logistic model assumes a fixed tourism market ceiling, it fails to explain the poststagnation stage, where rejuvenation, decline, or any other intermediate possibility may arise. Taking into account the data of passenger flows to Bornholm from 1912 to 2001 collected by Lundtorp and Wanhill, the authors find that the superposition of several logistic growth models fits better with these data. Then they propose a multilogistic growth model, where investment or innovation in the tourism sector boosts the addition of new logistic curves which superpose the old ones. The continuous birth and superposition of these new life cycles is not free; it requires the purposive effort of entrepreneurs and governments seeking new markets and the improvement of infrastructures.

Unbounded growth in the Neoclassical growth model with non-constant discounting

For a Neoclassical growth model, the literature highlights that exponential discounting is observationally equivalent to quasi-hyperbolic discounting, if the instantaneous discount rate decreases asymptotically towards a positive value. Conversely, in this paper a zero long-run value allows a solution without stagnation. We prove that a less than exponential but unbounded growth can be attained, even without technological progress. The growth rate of consumption decreases asymptotically towards zero, although so slowly that consumption grows unboundedly. The asymptotic convergence towards a non-hyperbolic steady-state which saving rate matches the intertemporal elasticity of substitution and the speed of convergence towards this equilibrium are analyzed.

On the Effect of Resource Exploitation on Growth: Domestic Innovation vs. Technological Diffusion Through Trade

The economic growth in a developing country endowed with a natural resource and with a resource-dependent economy can be based on its own investments in new technology. Conversely, it can rely on trade as a channel for technology diffusion from a technologically advanced country. The existence, uniqueness and stability of a sustainable growth path are proved under both assumptions. Our second concern is on the resource curse hypothesis. When the developing country does not export the natural resource but uses it as an essential input in the production of a final good, resource bounty is not a curse. Resource abundance increases long-run growth in the closed-economy scenario, and it is growth-neutral but consumption-enhancing when technology is transmitted from abroad through international trade.

Sustainable Growth in a North-South Trade Model

Abstract A model with two different regions that trade with each other is presented. The South specializes in a resource intensive good while the North specializes in a capital intensive good. The North-South trade and the management of natural resources are modelled in a dynamic way so that sustainable economic growth can be analyzed. The existence of balanced paths that allow sustained growth in the North and permanent growth of consumption in the South without exhausting Southern natural resources is proved. The transitional dynamics to a balanced path is also studied.

A NOTE ON THE STABILITY OF FULLY ENDOGENOUS GROWTH WITH INCREASING RETURNS AND EXHAUSTIBLE RESOURCES

We analyze a general R&D-based endogenous growth model with a growth-essential natural resource. The economy comprises two separate sectors, final output and R&D, both directly or indirectly dependent on the natural resource. Because the resource is exhaustible and it is an essential productive input, increasing returns to scale to manmade inputs are compatible with nonexplosive sustained growth. The instability problem usually associated with increasing returns is overcome thanks to the existence of imperfect markets in a decentralized economy. We find an admissible range of values for the elasticity of capital in the R&D sector under which growth is fully endogenous and saddlepath stable, with no need of exogenous population growth.

Can sustained growth be attained through trading exhaustible resources for foreign research

We analyze the existence and the stability of a sustained balanced growth equilibrium (SBE) in a model of two non-homogeneous trading economies. A technological leader country which sells patents of new intermediate products in exchange for an exhaustible resource extracted by a technological follower trade partner. Considering a growth-essential resource, the ‘knife-edge’ assumption of exactly constant returns to scale (CRS) to manmade inputs can be alleviated, and the scale effects associated with R&D-based growth models overcome. A fully endogenous SBE is proven to exist, although its stability turns out to be a ‘knife-edge’ possibility. The long-run equilibrium is saddle-path stable assuming CRS in manmade inputs. Conversely, considering increasing returns to scale together with a completely specialized two-country trade, the equilibrium could be reached only if the two economies initially guard a particular relation, described by a particular subset of the state space.