Energy saving innovations, non-exhaustible sources of energy and long-run: what would happen if we run out of oil?

We formulate and solve a model of factor saving technological improvement considering three factors of production: labor, capital and energy. The productive activities have three main characteristics: first, in order to use capital goods firms need energy; second, there are two sources of energy: non-exhaustible and exhaustible; third, capital goods can be of different qualities and the quality of these goods can be changed along two dimensions -reducing the need of energy or changing the source of energy used in the production process. The economy goes through three stages of development after industrialization. In the first, firms make use of exhaustible energy and the e¢ ciency in the use of energy is constant. In the second stage, as the price of energy grows the e¢ ciency in its use is increased. In the third stage, the price of exhaustible sources is so high that firms have incentives to use non-exhaustible sources of energy. During this stage the price of energy is constant. In this set up, the end of the oil age has level effects on consumption and output but it does not cause the collapse of the economic system.

Factor saving innovations and factor income shares

We present an endogenous growth model where innovations are factor saving. Technologies can be changed paying a cost and technological change takes place only if the benefits are larger than the costs. Since the gains derived from factor saving innovations depend on factor abundance, biased innovations respond to changes in factors supply. Therefore, as an economy becomes more capital abundant agents try to use capital more intensively. Consequently, (a) the elasticity of output with respect to reproducible factors depends on the capital abundance of the economy and (b) the income share of reproducible factors increases as the economy grows. Another insight of the model is that in some economies the production function converges to an AK in the long run, while in others long-run growth is zero

Energy Saving Innovations, Non-Exhaustible Sources of Energy and Long-Run: What Would Happen if we Run Out of Oil?

Se formula y resuelve un modelo de cambio tecnológico ahorrador de factores de producción que considera tres factores: capital, trabajo y energía. El modelo cuenta con características específicas con respecto a la interacción n entre la energía (la cual, de acuerdo a su fuente puede ser renovable y no renovable) y el capital. Una vez esta economía se ha definido, se supone que evoluciona en tres etapas luego de su industrialización, durante las cuales el carácter renovable o no renovable de la energía influye su precio relativo, eficiencia y afecta también el nivel agregado de consumo y producción de la economía, sin que esta evolución lleve al colapso del sistema económico.