Substitution And The Representation Of Alternative Methods Of Production

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Abstract
This note contrasts two different representations of the production process. The first representation is a differentiable microeconomic production function, and the second is a collection of discrete production processes. As is well known, in the first case small changes in factor prices lead to small changes in factor usage; in the second case, small changes in factor prices can lead to discontinuous jumps in factor usage. If alternative discrete processes are additive and divisible, then a degree of substitutability is available because different processes can be run side by side. The note shows, however, that this substitutability will not generally take the same form as that observed in the case of a differentiable production function, and indeed input use need not be inversely and monotonically related to input price.

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