A tale of declining public provision and burgeoning private supplements

I study an economy, à la Epple and Romano (J Political Econ 104:57-87, 1996), where a private good (a necessity) is publicly provided (for free), while a supplement (close substitute) is sold in a competitive market. Majority voting determines the public provision level (and the associated tax rate), while unsatisfied private demand determines supplement purchases. I show that continual incremental decline in public-sector productivity (vis-à-vis private-sector productivity) initially keeps on reducing public provision by incremental amounts, but eventually causes a drastic scaling-down of public provision. Such changes lead to (1) a growth spurt in supplement purchases, (2) an increase in utility inequality among citizens, and (3) a discontinuous fall (respectively, rise) in the welfare of all below-median-income citizens (respectively, above-median-income citizens) when public provision is discretely scaled down. Specifically, utility of each below-median-income citizen is higher when the public provision regime is active, and when its scale is large. Both outcomes become less likely when public-sector productivity declines and/or private-sector productivity improves.