Is the proof here about the existence of equilibria for "Linear Exchange" economies correct?
If so, it is much simpler than that of BC Eaves.
From my reading and understanding of the paper, it seems to me that what the author really wants to say in the first sentence of the first Remark in section 1, is that the strong assumptions about C and W are not required for the validity of the results that follow. The "perturbation" arguments that he refers to are often misleading, although they may be correct in the present context. I personally am very comfortable with his assumptions.
Would be helpful if someone answered my query.
Regards.