The elasticity of derived demand, factor substitution and product demand: corrections to Hicks' formula and Marshall's four rules

Nearly 75 years ago, John Hicks introduced and formalized the concept of the elasticity of substitution between capital and labour and its relation to derived demand. The resulting formula has proven very useful in understanding the derived demand for productive factors, the distribution of factor incomes, and Marshall's Four Rules. This short paper notes that a slip occurred in the original derivation, presents a modified formula, and shows that Marshall's First Rule is no longer generally valid.