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

AuthorZuleta, Hernando
PositionReport
Pages203(18)
  1. Introduction

    Natural resources have been an important source of wealth all through the history of the world. Every product we consume comes from at least one natural resource, either directly or indirectly. Scarce natural resources such as hydrocarbons have become one of the greatest concerns of our times as both scholars and journalists have foreseen the end of the oil age. In fact, analysts have forecasted the end of important energy sources such as gas and oil. The cries of oil scarcity heard some decades ago were certainly wrong: the world is not about to run out of hydrocarbons. Thanks to advances in exploration technology, there are more proven reserves of oil today than there were three decades ago (see Watkins, 2006). However, the question of what is going to happen as we approach the end of the oil age deserves attention.

    The classic supply side effect implies that when the supply of natural resources, especially energy sources, declines their prices raise. This price increase indicates the reduced availability of basic inputs in production, which motivates the use of new forms of energy. Using this logic, in 1932, John R. Hicks introduced the theory of induced innovation, according to which changes in relative factor prices lead to innovations that reduce the need for the relatively expensive factor. This theory has been tested. Kuper and Soest (2003), for example, who found through a panel of sectors of the Dutch economy that energy saving technical progress is particularly significant in periods preceded by high and rising energy prices, whereas the pace of this form of technical change happens to be much slower in periods of low energy prices (1). David Popp (2002) shows that there is a strong positive correlation between energy prices and innovations. With this evidence in mind, we extend the neoclassical growth models introducing the existence of capital goods that make use of energy and model in it, by a very simplified way, the production of energy.

    In the next section, we motivate the need of considering the finite supply of energy in traditional growth models. Then, we describe and solve the model. Finally we conclude.

  2. Machines, Energy and Growth

    Important episodes in the history of capitalism are related to the invention and use of machines. Capital accumulation is the only source of economic growth during the transition in a Solow-like type of model. In endogenous growth models a la Romer (2) technology is embodied in capital goods, so capital accumulation generates neutral technological change and, for this reason, long-run growth. Finally, in models of factor saving innovations' (3) capital abundance stimulates labor-saving innovations and savings are higher in economies where the technology is more capital-intensive. Therefore, also in this type of models the invention and use of machines is the main source of economic growth. Machines, however, need energy in order to be productive and energy sources today are predominantly finite. Thus, economic growth depends also on the supply of energy (4).

    We consider energy saving innovations and the existence of non-exhaustible sources of energy. Therefore, as exhaustible energetic resources become more expensive, the agents of the economy can adopt technologies that are more efficient in the use of energy or technologies that use non-exhaustible sources of energy.

    We assume that technology is embodied in capital goods and capital goods of better qualities are more costly. Also, as economies grow they consume more energy so the reserves of exhaustible sources of energy decrease and their price increases. Therefore, economic growth generates incentives to use non-exhaustible sources of energy in a more intensive way. This implies that in the long run, when oil has become exhausted, we will use only non-exhaustible sources of energy. Along the transition, the efficiency in the use of energy grows as exhaustible sources become more expensive. In the same way in which agents innovate in order to save labor and land when these factors become scarce they devote efforts to reduce the need of fossil combustibles.

    We do not model the invention of technologies. We assume that such technologies exist and are costly. Similarly we do not explain the beginning of the industrial era (5). We assume that the economy starts with a small amount of capital, a given technology, and big reserves of exhaustible sources of energy. Thus, during the first stage of industrialization, firms make use of exhaustible sources of energy and the efficiency in the use of energy is low. In a second stage, the reserves of exhaustible sources of energy are smaller so the price of energy is higher and firms start using more energy-efficient capital goods. Finally, in the third stage the stock of capital becomes big if compared with the reserves of exhaustible sources of energy, so the price of exhaustible sources is high and firms have incentives to use non-exhaustible sources of energy. In the long run, all the energy used in the production process comes from non-exhaustible sources.

    Finally, there is only progress in the efficiency with which energy is used, but not in the use of labour and capital. This assumption is made for simplicity. We want to focus on the technological changes related to the use of energy.

    The first studies that explicitly modelled the need of energy in the production process were presented by Stiglitz (1974) and Solow (1974). However they didn't consider the possibility of energy saving innovations or the existence of non-exhaustible sources of energy. Non-exhaustible sources of energy were introduced into economic models by Dasgupta and Heal (1974), Heal (1976) and Nordhaus (1979) and more recently by Manne and Richels (1992) and Tahvonen (1994). However, none of these models consider the possibility of energy saving innovations (Tahvonen and Salo, 2001). Finally, Groth and Schou (2002) and Smulders and Nooij (2003) consider the existence of exhaustible sources of energy but do not consider the existence of non-exhaustible sources of energy.

  3. The Model

    3.1. Consumers

    We assume that labor supply is inelastic, that population growth is zero and we normalize labor to one.

    The problem of the representative consumer-worker is the standard one,

    [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

    where a is the amount of assets at time t, [r.sub.t] is the interest rate, [w.sub.t] is the market wage, [c.sub.t] is the consumption of the representative agent and [beta] is the discount factor.

    From where,

    [[c.sub.t] + 1]/[c.sub.t] = [beta](1 + [r.sub.t+1]) (1)

    3.2. Producers of Final Goods

    The production function is a Cobb-Douglas that combines capital and labor. We assume, however, that an energy source ([e.sub.s]) is needed to operate capital goods. There are two sources of energy (s), non-exhaustible (N) and exhaustible (E) differentiated by their cost (s[epsilon][N,E]). Capital goods can be also of different qualities, they are differentiated by the source of energy they use, [e.sub.s], and by the efficiency in the use of energy ([gamma]S).

    Therefore, there is a production function for each quality of capital. Any production function is characterized by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the amount of capital of quality [[gamma].sub.s] designed to operate with energy, [e.sub.s], 1/([gamma]S) is the amount of energy [e.sub.s] needed to operate 1 unit of capital, for this reason we also refer to [[gamma].sub.S] as the efficiency rate in the use of energy type s. Finally, [L.sub.s] is the amount of labor working with capital goods of type [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] .

    The cost of the firms include the cost of labor w[L.sub.s], the cost of capital goods [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the cost of energy [p.sub.s][e.sub.s]. Where [p.sub.[gamma],s] and [p.sub.s] are the price of capital of quality [[gamma].sub.s], s and the price of energy of type s respectively.

    Firms are price takers and choose the amounts of capital and labor and the quality of capital ([[gamma].sub.s] and s)

    [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

    Since the production function is of the Leontief type, firms use capital and energy in such a way that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Thus, for analytical convenience we rewrite the problem in the following way:

    [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

    From the solution of the problem we find factor prices,

    [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

    [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

    [p.sub.s,t] = [[lambda].sub.t][[gamma].sub.s,t] (4)

    [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

    where [k.sub.t] is the capital labor ratio, [[lambda].sub.t] is the multiplier of the first restriction, [[mu].sub.t] is the multiplier of the second restriction and [[kappa].sub.t] is the multiplier of the third restriction.

    Equations 2 to 4 tell that the price of labor is equal to its marginal productivity; the price of a capital good (of any quality) is equal to its marginal...

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