where, <≡ = .„,'<.... > 1 K1 = (⅜1) ~" σ-^∙α- κ, = (2ÿl) - σ⅛≈<■>
Price is a markup over marginal cost, which depends on the wage rate
and the output level (when σ < 1): output and employment depend on the
real wage and total output in the economy.
2.2 The Structure of Contracts in a GTE
In this section we outline an economy in which there are potentially many
sectors with different types of wage-setting processes. Within each sector
there is a more or less standard Taylor process (i.e. overlapping contracts
of a specified length). The economy is called a Generalized Taylor Economy
(GTE).Corresponding to the continuum of firms f there is a unit interval of
household-unions (one per firm). The economy consists N sectors i = 1...N.
The budget shares of the N sectors with uniform prices (when prices pf are
equal for all f ∈ [0,1]) are given by ai with ^n=1 ɑ-; = 1, the N vector (o⅛)n=1
being denoted a ,where a ∈ An-1.
We can partition the unit interval into sub-intervals representing each
sector. Let us define the cumulative budget share of sectors к = 1...i.
i
ɑi = J2 "fe
k=1
with d0 = 0 and dn = 1. The interval for sector i is then [di~1, di].
Within each sector, each firm is matched with a firm-specific union: there
are Ni cohorts of unions and firms in sector i. Again, we can partition the
interval [di~1, di] into cohort intervals: let the share of each cohort within the
sector be λij so that ^N= 1 ʌv = 1, with the Ni-vector λi ∈ Δn* 1 Again,
we can define the cumulative share Λij∙ analogously to dk. The interval of
firm-unions corresponding to cohort j in sector i is then
ʌ ʌ
(*i-1 + ∖j-1 ai, ai-1 + ʌijQ⅛
Clearly, if symmetry is assumed (cohorts are of equal size) Aij- = Ni 1 and
ʌij = j'Nf1.
The sectors are differentiated by the integer2 contract length Ti ∈ Z++,
which is the same for all cohorts within a sector. The timing of the wage
2We work in discrete time in this paper, although the model obviously generalises to
continuous time.