In a recent paper Andrieu [l] derived the rules of derived demand for a factor in a perfectly competitive industry when the industry’s production function was homogeneous but not necessarily of degree one. In order to achieve compatibility with competitive behaviour economies of scale were assumed to be external to each firm but internal to the industry. Within this framework he showed that Marshall’s third rule concerning relative shares was modified and, further, proposed a ‘ fifth law ’ with respect to the returns to scale parameter :
‘ Other things being equal, an increase in the returns to scale will make the derived demand for a factor more (less) elastic if the demand for output is elastic (inelastic).
The purpose of this note is to examine a model which is the polar opposite to that considered by Andrieu. Here the firm is assumed to be the industry i.e. a monopolist. Non-constant returns to scale are introduced by assuming that the production function is homogeneous of an arbitrary degree. The analysis is not completely general since both the price elasticity of demand and the elasticity of supply of the second factor are assumed to be constant. However within this model it is shown that not only are Marshall’s second and third laws modified but also Andrieu’s fifth law.
