## 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 three-factor 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 all of the short-term fluctuations, whether attributable to business cycles or other causes, are fully accounted for by the above set of four variables. Any or all of them can be subject to external influences, whether natural disasters, conflicts, shortages or government fiscal or monetary policy changes. For instance, the labor supply may be decimated quite suddenly by epidemics, as happened during the various episodes of the 'black death' in Europe, or by wars. Wars, floods, storms or fires can destroy capital goods. Energy supplies (and prices) can be affected by political events, such as the oil embargo of 1973-4 or the Iranian revolution of 1979-80. We postulate, however, that most of these influences lead to short-term effects that are smoothed out over time. The exceptions might be major wars, like World War II, revolutionary changes of regime such as the downfall of the Soviet system, or major policy changes, such as the end of the gold standard.

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