How does the redistribution of income that a regime prescribes for society and the amount of public-good social-overhead investment it provides depend on the nature of that regime? And how do these influence said society’s productive success? Connections among these phenomena informed much of Mancur Olson’s (1982, 1991) life-work now so foundational to the literature on redistributive politics, economic growth/prosperity, and the nature of regimes. Still a transparent simple account of how the nature of a regime determines trade-offs between transfers and public capital investment can improve the foundations and clarify anomalies present in the literature. Here we elaborate a model to address these questions and we prove, contrary to received wisdom, that redistribution can reduce or actually and unexpectedly increase supplies of public overhead capital. Redistributive taxation reduces capital productivity, which incentivizes governments to supply less. But, contrary to conventional wisdom, redistribution can also so deplete the tax base that to offset some of the loss government will actually invest more in the way of public-overhead factor inputs than would a less redistributive regime of an otherwise comparable society.