The Nested Binary CES Composite Production Function: CRTS with different (but constant) pair-wise elasticities of substitution among three factors

The policy debate on global warming has raised the prospect of large taxes on Greenhouse pollutants leading to a very substantial rise in the price of energy. Models in which output is produced according to a technology in which capital (K), labour (L) and energy (E) are substitutable run into the difficulty of how to allow parsimoniously for the higher likely substitutability between K and E than between L and E. Nesting all three factors in a single CES aggregator function is unsatisfactory because of the constancy over pairs of factors of partial substitution elasticities. This paper is a variation on the CES theme. It presents a new composite three-input production function (based on CES and Leontief components) which allows the partial substitution elasticities between capital and labour, capital and energy, and between labour and energy, to differ but to remain individually constant.