رشد اقتصادی و انتقال بین منابع انرژی تجدید پذیر و تجدید ناپذیر

We study transitions between nonrenewable and renewable energy forms at different development stages of an economy. It is shown that in the historical context the emphasis on energy production may evolve from renewables to nonrenewables and back to renewables. Typically both energy forms are used simultaneously. Along the equilibrium path, nonrenewable resource consumption may increase and their price decrease. An inverted-U relation between carbon emissions and income level may follow even without environmental policy.

At the end of 1997, 160 nations reached an agreement in Kyoto, Japan to limit their production of carbon dioxide and other greenhouse gases. As a consequence, various industrialized countries now face the problem of determining how these emission reductions can be carried out and at what cost. The Kyoto agreement was strongly influenced by the scientific work coordinated by the International Panel of Climate Change (IPCC, 1995). Their predictions for future climate change rest on certain scenarios for emissions up till the year 2100. Recently, these predictions have been questioned in two economic studies. Schmalensee et al. (1998) use an econometric model to construct predictions of fossil fuel consumption through 2050. Although they use the same scenarios for population and GDP growth as the IPCC, their model predicts appreciably higher emissions. In another study, Chakravorty et al. (1997) construct a Hotelling (1931) type model with various fossil fuels and a noncarbon backstop like solar energy. The model is simulated using demand and supply estimates, including predictions of the costs of solar energy. According to this study the IPCC emission scenarios, by neglecting backstop technology, seriously overestimate the future development of carbon emissions after the year 2050. The authors compare the IPCC failure to the Club of Rome predictions of the 1970s that many of the earth's minerals would be depleted before the next century. Since predicting the future fossil fuels consumption has a clear economic dimension, there is no doubt that economists should continue this debate. However, it is worth keeping in mind that after Hotelling (1931) the main emphasis in the economics of nonrenewable resources has perhaps been put on physical resource depletion and on sustainability models that ‘should not be taken as literal descriptions of the economy’ (Krautkraemer, 1999).1 This is in contrast to the present need to understand the history and future development of fossil fuels consumption. It is in contrast also to the present growth theory where models are evaluated against their empirical implications (Temple, 1999). Backstop (or renewable, expendable) energy technology, which plays an important role in the study by Chakravorty et al. (1997), has been introduced into economic models by Nordhaus (1973). In Heal (1976) backstop technology refers to some future form of solar energy that is assumed to be available without limits but at high costs, which prevents its large scale commercial use. In typical models, the future switch to the backstop occurs when fossil fuels are physically depleted. In some models it is possible to speed up the introduction of a new energy technology (i.e. a discrete technological breakthrough) by investing in research and development (Dasgupta and Heal, 1974). More recently, a costly carbon-free future energy plays a vital role in a CGE model by Manne and Richels (1992). They predict that a switch to this technology may occur around the middle of the next century. A noncarbon backstop is included in a climate change differential game in Tahvonen (1994). In the Hotelling model that incorporates the optimally controlled accumulating carbon problem, energy policy typically evolves toward simultaneous use of fossil fuels and the noncarbon backstop (Tahvonen, 1996). This study questions whether the typical characterization of the backstop energy captures the key factors from the transition between nonrenewable and renewable energy forms. Renewable, nondepletable energy includes hydropower, wind energy, solar energy (both thermal and photovoltaic), biomass and geothermal energy. Many of these energy forms are presently in use and have been in use since before the industrial revolution. In fact the transition between renewable and nonrenewable energy forms may follow a pattern where at an early developmental stage economies use mainly renewable energy. Later the share of renewable energy declines as the share of fossil fuels increases. However, present development and future predictions suggest that developed economies may again move toward renewable energy. An example of this development is biomass, for which the present share is estimated to be about 15% of world energy. Its share is high in some developing countries (90–35%) but is decreasing, while the use of fossil fuels is increasing. In contrast, the share of biomass in the European Union is about 5% but steadily increasing. The future form of this energy is likely to be the biomass-to-fuel energy conversion technology that may be applied on a massive scale, because of the agricultural policy of setting aside millions of hectares of former agricultural land (United Nations, 1996; International Energy Agency (IEA), 1997). Wind and hydropower are other renewable energy forms that have a long history but also entail considerable potential for the future. Less than 10% of potential hydro resources have been exploited thus far (World Resources, 1994, p. 174). These examples suggest that specifying noncarbon energy sources as a future revolutionary backstop technology that will be adopted once fossil fuels are depleted may not fully characterize transitions between nonrenewable and renewable energy. An alternative is to develop models that describe the transition as a smooth process that may evolve in both directions at different developmental stages of the economy. Schmalensee et al. (1998) call for research that analyzes whether the reversal of the growth of carbon emissions in some high-income OECD countries is due to environmental policy, or whether there are fundamental economic trends that lead countries away from carbon-incentive energy sources. We aim to answer these questions by studying the transition between different energy forms using an economic growth model with nonrenewable and renewable energy. In addition, we explain empirically important findings such as declining prices and increasing consumption of nonrenewable resources. To specify a benchmark, we first assume constant technology. Nonrenewable extraction costs are stock-dependent, implying economic rather than physical resource depletion. The costs of renewable energy are given by a strictly convex cost function instead the usual constant marginal costs assumed in backstop specifications. Our economy starts its optimal growth using only renewable energy like biomass or hydropower, which on a small scale are postulated to be less costly than nonrenewable energy. After a period of growth the demand for energy increases and the use of nonrenewables starts smoothly from zero. This leads to a regime in which nonrenewables and renewables are used simultaneously but the share of fossil fuels increases. However, as the use of nonrenewables proceeds toward higher cost deposits, the economy moves back toward the use of renewable energy. Thus, although our economy does not have environmental policy (e.g. in terms of Pigouvian taxation), the use of fossil fuels (and carbon emissions) follow an inverse U relation (cf. Schmalensee et al., 1998). Next we add technical change following Arrow (1962) and Romer (1986). This leads to new description of nonrenewable resource markets since earlier models assume either constant or exogenously evolving technology (Krautkraemer, 1999). With endogenously evolving technology, the economy again starts its evolution using only renewable energy, but after a finite period there occurs a smooth switch to simultaneous use of both energy forms. This regime constitutes transitional dynamics toward a balanced growth path where again only renewable energy is used. Along the transitional regime, the use of nonrenewables starts from zero, reaches a maximum and then approaches zero. The price of the nonrenewables in terms of output has a U-shape form and the price in terms of current marginal utility may decrease monotonically. Thus the model is also able to explain both the historical decline in the real price of fossil fuels and their increasing consumption. These properties are in sharp contrast to the traditional economic growth–resource depletion model (Dasgupta and Heal, 1974) where nonrenewables and the backstop are never used simultaneously; the exogenously given resource stock is depleted physically; the extraction level is initially at a maximum and declines thereafter; and prices of nonrenewable resources increase monotonically (see reviews by Heal (1993) and Krautkraemer (1999)). Our models differs from Chakravorty et al. (1997) since their model specifies a partial equilibrium and takes economic growth as an exogenous trend. In their model, backstop technology refers to solar energy, while our specification refers to various kinds of noncarbon energy forms like biomass, which are typically used simultaneously with fossil fuels. Chakravorty et al. (1997) do not report results on resource prices whereas the essential feature of our model is that it explains the historical price decline for nonrenewables. Moreover, in their model technical change is exogenous. Endogenous growth literature with natural resources has mainly studied pollution while nonrenewable resources are typically omitted (e.g. Bovenberg and Smulders, 1996). However, Rebelo (1991) and Jones and Manuelli (1997) have included nonreproductive factors in endogenous growth models, but neglect backstop technology and extraction costs. In their specifications the price of nonreproductive factors increases monotonically, which is in contrast to numerous empirical studies (see Nordhaus, 1992; Berck, 1996). The survey by Krautkraemer (1999) does not report on studies in which technological development is endogenous in the context of nonrenewable resources. The paper is organized as follows. Section 2 presents the benchmark growth model with constant technology. Section 3 adds endogenous technical change and Section 4 concludes the paper.

The debate on climate change necessarily includes some predictions on the future development of fossil fuel consumption and carbon dioxide emissions. The economic understanding of these matters is usually based on some extension of the classical Hotelling (1931) model. Although the literature is extensive, models that explain the historical development of nonrenewable resource use and their prices are more or less absent. Our model is able to produce declining prices and increasing consumption of nonrenewable resources endogenously. It also describes the transition between energy forms as a smooth shift in the emphasis from renewables to nonrenewables and finally back to renewables. These features differ quite sharply from earlier economic studies. It may be asked why economic research on nonrenewable resources has put so much emphasis on the physical resource depletion since even geologists have pointed out that physical depletion is difficult to imagine (Goeller and Winberg, 1976). In the model of Chakravorty et al. (1997) market incentives to develop solar energy occur, since oil and natural gas are predicted to be totally used up during 50–70 years. Technical development is assumed to decrease the cost of solar energy but the costs of extracting the currently estimated fossil fuel reserves are postulated to remain constant or increasing. According to another hypothesis technical development may still increase the stock of economic reserves from those currently estimated. In this case the prediction of Chakravorty et al. (1997) may overestimate the role of market forces in developing commercial solar energy and underestimate the future carbon emissions.