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

complete domestically and international equity trade is forbidden³. Moreover, in order
to pay for nominal expenses, cash in advance is needed. Under these assumptions, the
agent’s budget constraint is given by

Mj ≥ PCj = W_j L_{j +} Dj,

where Mj are individual j’s money balances, W_j is the nominal wage and Dj are agent
j^,s dividends received by all domestic firms.

2.4 Demand side

The allocation of a representative individual’s demand across the Home- and Foreign-
produced brands yields

_C Iz ∖-P ( ^{Ph (3)} V _c  -^{p Ри <г)} V ( ^Ph Y ' _C          O₁

^Cjp(z) = ~Л~РЙ~) ^Cjp =I ⅛^J  l"pj ^{Cj,        (5)}

1   ( Pf(z) y-'       ( Pf(z) ∖^-λ ( Pf Y^-1

^Cj-^F(z) = T—p ∖-pF^) ^c'¹∙^f =I p- TU ^{Cj         (6)}

where Ри(z) and Pf(z) are the prices for a brand z charged by a domestic and foreign
firm at Home, respectively⁴. The law of one price is assumed to hold across all individual
brands, so that P_c(z) = P*(z), Vz ∈ [0,1], where asterisks denote Foreign values of
the corresponding Home variables, and c ∈ [H, F] . Moreover, because Home and Foreign
agents have identical preferences, the law of one price implies that purchasing power parity
must hold for the consumer price indexes:

P = P *.

Thus integrating the demand for a Home-produced brand (5) and Foreign-produced
brand (6) across all agents yields the total demand faced by a firm z:

..... ( .   )■( P )^,C.                           _:„

where Cw ≡ 7C +(1 — 7)C is the total consumption in the world economy, C ≡ ¹ fj Cj dj
is the per capita consumption of a Home agent and C* ≡ ɪ--^ ʃ, Cjdj is the per capita
consumption of a Foreign resident⁵.

³However, securities markets are redundant in this model so as current accounts always balance in
equilibrium (Obstfeld and Rogoff, 1998).

⁴Recall that λ > 1 captures the elasticity of substitution among varieties, while the elasticity of substi-
tution between the domestic and foreign good is equal to 1.

⁵Note that C_w is both per capita and total world consumption.

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