Strategic monetary policy in a monetary union with non-atomistic wage setters

The goods-market-clearing condition implies that total output demands equal supplies,

7 [7PC + (1 - 7)PC^,] = PhYh                     (8)

(1 - 7) [7P5 +(1 - 7)PC*] = PfYf                    (9)

where Yh ≡ ʃɪ Yh(z)dz and Y_f ≡ ʃɪ Yf(z)dz. From equation (8) and (9) we can derive
the following expression:

Ph Y h = Pf Yf                        (IO)

where Yh ≡ ɪ ʃɪ Yh(z~)dz and Yf ≡ ɪɪr ʃɪ Yf(z~)dz. Relation (IO), together with the
assumption that agents do not hold international assets, implies that current accounts
always are zero (Obstfeld and Rogoff, 1998) and that

C_w = C = C *.⁶

Let Mh ≡ ʃj Mjdj and Mp ≡ ʃɪ Mjdj be the total money supply in the Home and
Foreign country, respectively. We assume that total money supply in the monetary union
is distributed across the two regions according to the country size as follows

M_u = m ɔʃ m ɪ^.
h Hr

Normalizing the previous period nominal money supply, the current nominal money sup-
plies can be expressed as

Mu = 1 + mu

where mu ≈ log Mu stands for percentage increases.

Finally, using equation (11), (8) and the cash in advance hypothesis, the aggregate-
nominal demand (7) in the domestic country can be rewritten as

Likewise in the Foreign country the aggregate nominal demand is proportional to money

P_fY_f ≡ ɪ P_f(z)Y_f(z)dz = M_f.

Jo

⁶This can be easily proved by using the relation (1O) into the individual budget constraint as follows:

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