Appendix

Proof of Result 1:

A comparison of fiscal policy (9) and (14) and structural reforms (8) and (13) shows that x_i^M > x_i^N
and s_i^N > s_i^M are both fulfilled if (bθ^G - dθ^B)>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 x_i .
Since y_i is falling in x_i (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 x_i^M - x_i^P > 0 is

[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 x_i^N - x_i^P > 0 is

[(λ² + c²)(λν₁² + c²ω₁ )]>λ(F_i + b(y* - y_i ))(λbν₁d + c²(bθG - dθB )).

s_i^P -s_i^N >0 is fulfilled if [dν₁ - b(bθ^G - dθ^B )]> 0 which could be positive if d is sufficiently
large.

Proof of Result 3:

The condition for xE - xN > 0 is (F_i + b(y* - y_i )λλbν₁ d + c² (bθG - dθB )]>0 which is fulfilled as
long as (bθ^G - dθ^B )>0. Because there is no seigniorage revenue, an increase in x_i implies a
decrease in s_i. Hence, s_i^N -s_i^E >0.

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