The paradox of value, directed technical change, and the relative abundance of the chemical elements

•The “paradox of value” argues that mineral prices are due to relative abundance.•We show that prices decrease, and output and R&D increase, in crustal abundance.•The causal link from relative abundance to R&D runs through total industry revenues.•More abundant resources have larger revenues, causing R&D to be biased towards them.•This is why the value of water versus diamonds has remained constant for millennia. Classical economists used the “paradox of value” that water is essential to life yet cheap, while diamonds were inessential to life yet dear, to explain how long-run supply is affected by relative abundance. This paper expands upon this theory by developing and estimating a directed technological change (DTC) model to analyze the relative abundance correlations of relative prices, world production, and R&D, as well as their growth rates, for the 87 chemical elements present in the Earth's crust. We show that these imply that the elasticity of substitution between resources and the elasticity of R&D with respect to industry revenues are such that more abundant resources have had larger markets, causing R&D to be biased towards more abundant resources. This explains why the paradox that water has been cheap while diamonds dear has held for centuries, and possibly even for millenia, even though prices have been falling relative to per capita income and per capita production has been rising for nearly all resources.