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

of one type that, in turn, can be manufactured by a continuum of monopolistic competitive
firms in a variety of brands indexed by z ∈ [0,1]. The main feature of such a hypothesis is
that the degree of substitutability between types differs from the degree of substitutability
between brands.

Labor is the only factor of production and is supplied in a variety of types defined in
the continuous interval (0, 1). All labor types are unionized and distributed equally among
trade unions. For a given wage, each agent is willing to provide whatever quantity of labor
is required to clear the market.

Henceforth we will focus mainly on the domestic country so as to compare its macro-
economic performance under a floating exchange rate (Cuciniello, 2007) and in a MU.

2.1 Supply side

Each firm is the sole producer of a particular brand z that is produced by using a continuum
of labor types according to the following decreasing-return-to-scale technology

where Y_h(z) is the output of the Home-produced brand z, Li(z) is the labor type i, σ
captures the elasticity of substitution among labor types and a is representing the return
to scale parameter. Firms are assumed to have market power in the product market but
not in the labor market so that they take wages as given. Cost minimization implies the
following demand for each labor type i

Li(z)= (W) ' (Yh(z))¹                           (1)

is the aggregate wage index defined as the minimal nominal cost of producing a unit of
output and Ph(z) is the price for a brand z charged by a domestic firm at Home.

2.2 Preferences

Each agent consumes a continuum of differentiated goods and supplies a differentiated
labor type. The agent j^,s utility is defined over consumption and hours worked as follows:

^uj = log C_j - I ⁽log ^Lj^{)2 ,}        к > ^α

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