ABSTRACT
Recalling that i = 1, ... , N, we see that in (1) and (3) there are n + n(m + t - 1) = n(m + t) eqNations in the same nNmber oj Nnknowns (nm c~:r and nt g}'s). If t = 1 we can reasonablY reqNire (1) and (3) to be uniqNeIY solvable. When t> 1 we cannot expect to solve Jor the g}'s, Jor to individNal cONntries the SONrce oj SNPPfy of a particNlar public good is a matter oj indifference; however, even when t> 1, we can reasonablY reqNire both the aggregate world SNPPfy oj individNal pNblic goods and the valNe oj all pNblic goods supplied I!J each particNlar cONntry to be NniqueIY determined, and that is all we need. Let the NniqNe solution be indicated I!J asterisks. From (3a),
From (5) and (3b), the latter with solution values inserted, g* = D(p, q,y). (6)
c* = Lc1* = LB1(p, q,y) == B(p, q,y). (8) Thus c;* and therefore c* depend on aggregate income onlY. The conclusions of the proposition
As already noted, the proposition does not rely on the assumption that country i purchases the whole range of private consumption goods; in fact it is not required that country i purchases any private consumption goods. Of much greater importance, it is not required that the intra-national publicness of public consumption goods be offset by corrective taxes. That assumption merely simplifies the proof by allowing one to treat each country as a single coherent maximizer.
