Abstract Most human complex traits are enormously polygenic, with thousands of contributing variants with small effects, spread across much of the genome. These observations raise questions about why so many variants–and so many genes–impact any given phenotype. Here we consider a possible model in which variant effects are due to competition among genes for pools of shared intracellular resources such as RNA polymerases. To this end, we describe a simple theoretical model of resource competition for polymerases during transcription. We show that as long as a gene uses only a small fraction of the overall supply of polymerases, competition with other genes for this supply will only have a negligible effect on variation in the gene’s expression. In particular, although resource competition increases the proportion of heritability explained by trans-eQTLs, this effect is far too small to account for the roughly 70% of expression heritability thought to be due to trans-regulation. Similarly, we find that competition will only have an appreciable effect on complex traits under very limited conditions: that core genes collectively use a large fraction of the cellular pool of polymerases and their overall expression level is strongly correlated (or anti-correlated) with trait values. Our qualitative results should hold for a wide family of models relating to cellular resource limitations. We conclude that, for most traits, resource competition is not a major source of complex trait heritability.