Quasilinear preferences on a public good and a numeraire good are limits of preferences where both goods are normal. The set of equilibria of the voluntary contribution (or private provision) game is easily characterized under quasilinearity by: top valuators aggregately contribute their common stand-alone contribution, whereas non-top valuators contribute nothing. Because, as long as preferences are randomly selected, there will typically be a single top valuator, it follows that, typically, the equilibrium is unique, with all players but one contributing nothing, hence free riding in the sense of the ordinary English usage of the expression. The upper-hemicontinuity of the Nash equilibrium correspondence implies that this is also the case when both goods are strictly normal, but the wealth effects on the public good are small.
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