In this paper, we first give a direct proof of the existence of Edgeworth equilibria for exchange economies with consumption sets which are (possibly) unbounded below. The key assumption is that the individually rational utility set is compact. It is worth noticing that the statement of this...

The warm-glow model (Andreoni in J Political Econ 97:1447–1458, <CitationRef CitationID="CR2">1989</CitationRef>; Econ J 100:464–477, <CitationRef CitationID="CR3">1990</CitationRef>) of public goods provision has received widespread interest, yet surprisingly most attention has focused on the voluntary contribution equilibrium of the model, and only very little attention has...</citationref></citationref>