David F. Heathfield

Work Patterns and Capital Operating Hours: Micro Foundations

This paper investigates the microeconomic foundations of work patterns and capital utilisation. By work patterns we mean hours of work and shift rosters. Hours of work can be sub-divided into basic hours, overtime hours and short time working. Hours of work form a key dimension of labour utilisation, although a comprehensive measure would need to include issues of labour effort per hour (Bennett and Smith-Gavine (1976)). This paper focuses on length of day and time of day issues (in other words, those concerning work patterns), and how these relate to the firm’s utilisation of capital. Economic theory suggests that there will be some optimal type (or mix) of work pattern for each individual and each company. For the individual, this work pattern will be linked to the labour supply/hours of work decision. While the individual’s decision may be economically motivated, it is bound up with a variety of institutional features, including the role of trade unions and the public and social infrastructure available to those who work at unsocial times or hours. For the company, the optimal work pattern decision is linked to the optimal degree of capital utilisation or the timing of the supply of the product or service. The firm’s choice is associated with the achievement of the firm’s primary goal, such as cost minimisation or maximisation of profits.

The Translog Function

The CES was a natural extension of the Cobb-Douglas in that it permitted the elasticity of substitution to be something other than unity. The next obvious step is to generate a function which allows the elasticity of substitution to change with output and/or factor proportions.

Cost Functions and the Theory of the Firm

Having outlined the range of choices open to an entrepreneur (the production function), we shall now investigate the economic side of production, that is the choice of a technology and a level of output from among the many possible.

The CES Function

The first step in the development of the production function had been taken by Cobb and Douglas in the 1920s. The second step was to come some forty years later by a quartet of economists — Arrow, Chenery, Minhas and Solow (ACMS). They developed the Constant Elasticity of Substitution function.

Elasticity, Efficiency and the Theory of the Firm

In this chapter we shall ignore technological progress and focus attention on two quantitative aspects of a static production function. The first concerns some useful tools for investigating the relationship between prices and choice of technologies. The interface as it were between the technical and the economic aspects of production.

Empirical Work on Production Functions

Having a wide range of functional forms to choose among is obviously helpful when conducting qualitative investigations into questions of economic growth, income distribution, international trade and so on. However, it is often the case that some quantitative predictions are necessary. It is, for example, necessary to know the elasticity of substitution of the CES function before it will yield any information about the effect of wage increases on employment. This raises the question of how best to quantify the parameter values of the chosen functional form.

From Firms to Industry: the Johansen Production Model

As defined above, the production function refers to the micro decision making unit: for example the ‘firm’ or the ‘plant’. However, economists often use the notion of a production function to describe relationships between aggregates of some kind. These ‘aggregate production functions’ may refer to an ‘industry’ or a ‘sector’ or even to the whole economy and purport to represent the range of possible inputs of aggregate labour, and aggregate capital etc. capable of producing various levels of aggregate output.