= ∕1 Uj dj -
Jo
βu ≥ О-
(16)
The parameter βu is the CB’s degree of conservatism (Rogofl:, 1985a). If the level of
conservatism is zero the CB becomes a benevolent planner who cares only about the
agents’ welfare.
2.7 Timing structure of the model
In the first stage (at time 1), each union chooses the rate of growth of the nominal wage of
her members in a simultaneous game with Foreign and the other domestic unions so as to
maximize her objective function (15). Moreover, in the maximization problem each union
anticipates the reaction of the CB and of firms to her wage choice. The timing sequence is
built on the notion that nominal wages are substantially stickier than prices and monetary
policy. The rationale for such an assumption is that workers are normally under contract
for at least a year; thus, wage setters are committed to the bargained wage over the whole
period of the game.
In the second stage (at time 2) the common CB sets the money supply taking as given
the preset nominal wages and internalizing the reaction of firms. Monetary policy is hence
stickier than price setting12.
In the last stage (at time 3) each monopolistic competitive firm sets the price of her
own brand so as to maximize her profit, taking the general price level, nominal wages and
money supply as given13.
The three-stage game between firms, the monetary authority and labor unions is solved
by backward induction so as to find the Nash sub-game perfect equilibrium.
3 Price setting
In the last stage of game each domestic firm maximizes the real profit function
∏(z) =
Z h ,Yh(z) - ⅛ Г WiLi(z)dι
ʃ ʃ Jo
(17)
under the following constraints:
Jq1 WiLi(z)dτ = WYh(z)⅛ and Yh(z) = (^ад} (Hf)
-1
cw.
(18)
12Models with a New Keynesian orientation à la Clarida, Gali and Gertler (1999) suppose that price
setters move first than the monetary authority. However, the assumption of prices stickiness is more
debatable than wages stickiness (see Cukierman, 2004).
13Notice that the timing of the game implies no precommitment of the CB. Monetary policy is hence
set in a "discretionary" way. Moreover since firms are the last to move, prices may be considered as fully
flexible.