The increasing returns to scale CES production function and the law of diminishing marginal returns

Abstract

This article analyzes the constant elasticity of substitution (CES) production function when there are increasing returns to scale and the elasticity of substitution exceeds 1, which I refer to as the explosive case of the CES. For this explosive case of the CES, the article demonstrates a new and surprising result: marginal and average products of labor and capital approach infinity as either labor or capital approach infinity. Obviously, in this explosive case of the CES, the law of diminishing marginal returns is eventually violated in a dramatic way. Some implications of this result for growth theory are discussed. The article concludes by deriving, for this explosive case of the CES, lower and upper bounds for the capital labor ratio which are consistent with the law of diminishing marginal returns.