3. New Open Economy Macroeconomic Model
the risk of dropping out of the market. In other words, non-zero profits are feasible in this model of
monopolistic competition.
Let individual domestic output be produced according to the following linear production function:
Yt(h) = AtLt(h). (21)
This is a production function in labor only. For the sake of simplicity, real capital shall be omitted as
additional input factor throughout the analysis. This step can be justified by the short- to medium-run
perspective of the model. A shall be a random variable denoting an exogenous aggregate productivity
shock, interpretable as a transitory process innovation. This productivity shock shall be positively cor-
related with its foreign equivalent A*, whereby the positive correlation may be interpreted as exogenous
R&D spill-over effects associated with ”technology sourcing” as described in Griffith et al. (2006, pp.
1859-1861). In the present set-up, technology sourcing would then have a mutual nature.
Households need not be self-employed, but it is assumed that domestic firms can employ domestic labor
only as well as foreign firms shall be allowed to employ foreign labor only. In other words, there is no
migration in this world.
Individual foreign output is produced using the same technology (21) as at home. Nonetheless, Y * (f)
may differ from Y (h), A* from A, as well as L* (f) from L(h).
Producers’ instantaneous profits Γt (h), which have already been introduced above, are then given by:
Γt(h) =Pt(h)Yt(h) -WtLt(h). (22)
Relative to the producer’s own price, equation (22) rearranges to:
ph. Y Yt(h) ^ W L(h) = Y(h) ^ PTh) ɪ = Y∙(h) ^ KtY(h). (23)
Pt(h) Pt (h) Pt(h) At
where one has made use of the production function (21). In (23) κ := W/[P (h)A] is defined as individual
real marginal production cost.
For now assume all goods prices to be flexible. Then each domestic producer charges the same price
denoted by the domestic PPI (PH = P (h)). Thus, instantaneous profits rearrange to:
Γt (h) = Pt,HYt(h) - WtLt (h). (24)
Maximizing equation (24) with respect to Y(h) and using the fact that in case of goods market clearing
output of a single producer equals global demand for the differentiated good (Y (h) = Cw (h)), we get the
standard first order condition for a profit maximum in a model of monopolistic competition:
∂ Γ t ( h )
∂Yt ( h )
, Wt
pt,H At
Pt H + Yt(h)dptH- - Wtdpph) = Pt h 11+--1---ʌj - Wtɪ
t,H +t () ∂Yt ( h ) t ∂Yt ( h ) tH + ec ( h ) ,P ( h )) t At
ptH μ1+ɪ ) - Wt At=0
θ - 1 flex
„ := κt ■
(25)
Note that an analogous equation to (25) also holds abroad and that κflex = (κ* )flex = (θ — 1)/θ.
Equation (25) states that in a profit maximum associated with flexible prices, the corresponding real
marginal production cost defined as κffex equals (θ — 1)/θ.15
15Note that if one solved equation (25) for PH, one would obtain the domestic PPI as a mark-up on marginal unit labor
costs W/A : Ph = [ θ/( θ — 1)] W/A with θ/( θ — 1) = 1 / κfex denoting the flexible-price mark-up factor.