Factors of production, or (in more modern terminology) ‘inputs’, are the things which are used in the process of producing goods or services. An early typology of inputs was provided by Jean-Baptiste Say, whose classification separately defined land, labour and capital as factors of production.
A distinction is often made between flow inputs (which are embodied in the final product and cannot therefore be used more than once in the act of production) and stock inputs (which can be used repeatedly). The distinction is somewhat artificial, however, because stock inputs characteristically depreciate in value over time, and this depreciation can itself usefully be regarded as a flow.
All factors of production can, in principle, be hired by the producer. In a non-slavery society, labour can be hired—at a per period cost defined by the wage—but not bought. Capital may, at the discretion of the producer, be bought rather than hired; it remains the case, however, that producers implicitly pay a rent (‘user cost’) on the capital under their ownership, because by using that capital they forgo the opportunity to hire it out to a third party. Land, likewise, may be bought or rented; in the former case producers implicitly pay a rent in order to use land as a factor of production, because they forgo the opportunity to earn a landlord’s income.
Labour will in general be hired by a profit-maximizing producer up to that point where the wage is just offset by the value of the marginal product of labour. In a similar fashion, long-run equilibrium requires that capital should be employed up to the point where the user cost equals the value of the marginal product of capital. A similar condition applies to land. A change in production technology which disturbs the productivity of any factor of production will generally alter the equilibrium employment of each input. Likewise a change in the price of any input (for example, the wage or the user cost of capital) will, so long as inputs are to some degree substitutable, cause a change in the mix of factors of production employed.
Simple models of the production process typically employ two factors of production, often labour and capital. The first of these is defined to be variable in the short run, while the second is assumed fixed. In effect, the minimum timescale within which the latter input can be varied defines the length of the short run. Given information about the producer’s objective function, this allows a distinction to be drawn between the behaviour of the producer which is optimal in the short run and that which is optimal in the long run.
The precise manner in which factors of production are converted into outputs is modelled by means of a production function. The simplest type of production function in common use postulates that the production of a single type of output is determined by a geometric weighted average of the various inputs employed. This is known as a Cobb-Douglas production function, the parameters of which may statistically be estimated by means of a regression which is linear in natural logarithms. The Cobb-Douglas function can be shown to produce downward sloping and convex isoquants—a characteristic which is conventionally deemed attractive because it establishes the existence of unique solutions to the constrained optimization problems characteristic of neo-classical economics.
The more general constant elasticity of substitution (CES) and transcendental logarithmic (or ‘translog’) production functions have become increasingly popular among applied economists. The Cobb-Douglas is a special case of both of these. The translog function adds to the list of explanatory variables used in a Cobb-Douglas type regression a full set of logged quadratic terms and interaction terms between the logged inputs.
An appealing property of all the production functions described above is their implication that the marginal product of variable inputs (eventually) falls as the employment of those inputs increases. This ensures the finiteness of the equilibrium level of output of the individual firm, regardless of demand conditions. The translog specification of the production function is particularly appealing because, depending upon the estimated parameters, it is consistent with the popular presumption that the long run average cost curve is U-shaped.
The production technology described by these functions is closely related to the way in which the producer’s costs are determined. Given the prices of the various factors of production, producers use their knowledge of the production technology to decide, for each level of output, what mix of inputs optimizes their objective function (usually profits). Once this input mix is chosen, the total cost of production at each output level is straightforwardly calculated as the product of the vectors of input prices and input quantities.
It is only recently that economists have begun rigorously to tackle the analytical problems posed by firms which produce many distinct types of output. Multi-product firms of this type might exist because of synergies which arise from the co-ordinated production of different goods and services. These synergies may in turn arise from characteristics possessed by inputs which can simultaneously be put to more than one use. In the case of firms which produce more than one type of output, output cannot be represented as a scalar, and so the technology of production is best understood by investigating the dual problem: that is by estimating a (quadratic or CES) multi-product cost function.
The simplistic view of labour as a variable input has been relaxed in recent work which views skilled labour as an investment in ‘human capital’. Such an investment takes time, and so in the short run skilled labour may be fixed. However, where more than two inputs are employed, the distinction between the short and long run becomes blurred. Indeed, an issue which has remained underdeveloped in the economics research programme concerns the application of methods commonly used in the literature on product differentiation to the case of heterogeneous factors of production.
Geraint Johnes
Lancaster University
Further reading
Heathfield, D.F. and Wibe, S. (1987) An Introduction to Cost and Production Functions, Basingstoke.
