How Energy and Work Drive Material Prosperity
6. 6.1 The production function approach INTRODUCTION In this chapter we seek to explain economic activity and growth in terms of a ‘production function’. A production function hereafter can be thought of as a model to explain output (GDP) consisting of a function of two or three independent variables. The traditional two-variable scheme involves only capital stock – or capital services – (K) and labor supply (L). For reasons explained at length in previous chapters, we do not consider the one-sector two-factor model hereafter, except as a point of departure. The threefactor scheme involves energy or natural resource use – call it X for the moment. In most studies, the factors of production (K, L, X) are regarded as independent variables. The assumption is that some combination of these variables can explain changes in a fourth dependent variable, namely the gross domestic product (Y) over a long period of time. We also assume (in common with most practitioners) that the production function exhibits constant returns to scale. Mathematically this implies that it is linear and homogeneous, of degree one (the Euler condition), which implies that the individual variables are subject to declining returns. The usual formulation is deterministic, with output treated as a dependent variable. In our model, the four variables (including output) are regarded as mutually dependent (and cointegrated) in the long run. Each is determined (over time) by the others. Statistical evidence in support of this conjecture is provided in Chapter 7. On the other hand, we do not suppose that...
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