Substitutability between dimensions varies with their values, not just fixed parameters.

Evidence

For each weakest link aggregation function we can ask the degree of substitutability across dimensions. With these highly nonlinear functions, substitutability varies not only with the size of the parameters but can change significantly as the values of Di change. Cobb–Douglas illustrates this nicely: there is no substitutability when either factor is 0; the degree of substitutability increases as Di increases. For those interested in the details of this, any economics or calculus textbook provides a mathematical analysis. Weakest link language occurs naturally in the discussion of production functions, notably in the Cobb–Douglas context (e.g., Chambers’s 1988 discussion of the “essentiality” of factors of production). — Gary Goertz, Social Science Concepts and Measurement, 972

Categorization

• XREF: Links conceptual aggregation to production-function economics; the ‘essentiality’ of inputs is the same math as necessary conditions.