Resource productivity, measured as GDP output per resource input, is a widespread sustainability indicator combining economic and environmental information. Resource productivity is ubiquitous, from the IPAT identity to the analysis of dematerialization trends and policy goals. High resource productivity is interpreted as the sign of a resource-efficient, and hence more sustainable, economy. Its inverse, resource intensity (resource per GDP) has the reverse behavior, with higher values indicating environmentally inefficient economies. In this study, we investigate the global systematic relationship between material, energy and carbon productivities, and economic activity. We demonstrate that different types of materials and energy exhibit fundamentally different behaviors, depending on their international income elasticities of consumption. Biomass is completely inelastic, whereas fossil fuels tend to scale proportionally with income. Total materials or energy, as aggregates, have intermediate behavior, depending on the share of fossil fuels and other elastic resources. We show that a small inelastic share is sufficient for the total resource productivity to be significantly correlated with income. Our analysis calls into question the interpretation of resource productivity as a sustainability indicator. We conclude with suggestions for potential alternatives.