Appendix
Proof of Result 1:
A comparison of fiscal policy (9) and (14) and structural reforms (8) and (13) shows that xiM > xiN
and siN > siM are both fulfilled if (bθG - dθB)>0 . Given symmetry, this increase in fiscal burden
will result in an increase in the rate of inflation, because inflation is a function of the average xi .
Since yi is falling in xi (eq. 1) monetary union implies that the expected output (disregarding any
positive output shock) in country i falls.
Proof of Result 2:
The condition for xiM - xiP > 0 is
d1У (xN + (y * - y .))
n j j yj y j
bθB
[λb2 + c2 )(λVιV2 + c ω,λ )]> λ(Fi + b (y* - yi ))(λbν 2d + c2 ⅛ (bθG - dθB )).
sP - sM > 0 is fulfilled if [d-ν1 + b(dθB -⅛bθG )]> 0. Although, by assumption,
(bθG - dθB )>0, (dθB - ⅛bθG )>0 can be fulfilled if d and/or n are large.
The condition for xiN - xiP > 0 is
d1У (xN + (y * - y ))
n j j y j y j
bθB
[(λ2 + c2)(λν12 + c2ω1 )]>λ(Fi + b(y* - yi ))(λbν1d + c2(bθG - dθB )).
siP -siN >0 is fulfilled if [dν1 - b(bθG - dθB )]> 0 which could be positive if d is sufficiently
large.
Proof of Result 3:
The condition for xE - xN > 0 is (Fi + b(y* - yi )λλbν1 d + c2 (bθG - dθB )]>0 which is fulfilled as
long as (bθG - dθB )>0. Because there is no seigniorage revenue, an increase in xi implies a
decrease in si. Hence, siN -siE >0.
23
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