The relationship between the main production factors in an economy is, along with their levels, one of the determinants of economic growth. Currently there are still few empirical studies which have examined how these factors relate to each other and how that relationship affects the productivity growth in different territories. This paper considers a production function obtained by the product of the total factor productivity and the total factor input. The total factor input is given by a translog function of four factors of production, allowing greater flexibility to the estimated function. The parameters of the estimated function allows an interpretation in terms of the possible complementarity or substitutability between factors as well as the existence of increasing or decreasing returns to the factors considered. Also, the elasticity of the marginal product of each factor relative to other factors, and compared to the same factor, is calculated in order to analyze the relationships between these factors. How these relationships affect productivity growth in the Spanish provinces is estimated at the period from 1985 to 2008.

Keywords: Elasticity of marginal product; translog function; complementarity among factors; economic growth.