semi-endogenous” growth models∙15
For industries targeted by innovation, the following free entry condition applies:
q(ω) (λ (ω) — 1) . .
(12)
v(ω) ≡---—— ---- = bwHX(ω)∙
ρ+ I(ω) — n
where the marginal benefit of innovation is equated to the marginal cost. The usual Arrow or “re-
placement effect” implies that the monopolist does not find it profitable to undertake any innovation
activity at the equilibrium wage (Aghion and Howitt 1992).
4 Balanced growth paths
We are now in a position to analyze the general equilibrium implications of the previous setting. Since
each final good monopolist employs unskilled labor to manufacture each commodity, the unskilled
labor market equilibrium is
N(t)θ0 = q q(ω)dω = N N(t) f —c- + G^'ʌ dω = N(t) [Γc + Ω] .
0 0 λ (ω) λ (ω)
Therefore:
(13)
(14)
_ θo - Ω
c = Γ ,
where Γ = Jθ1 λ(1ω)dω and Ω = f1 GG(J))dω. Eq.s (8), (10), and (12) imply that
Nt) [c + G(ω)] = bwHX(ω)
λ(ω)
ρ+ I(ω) - n
(λ (ω) - 1) ,
(15)
which - since Wh = θoσ-γ and (14) holds - can be rewritten as:
1 θ θo — Ω , 4 ∖ bσ , 4 ρ +1(ω) — n r ,
λ ,, I γ + G(ω) = θ-----x(ω) λ , .---f, for all ω ∈ [0, 1],
λ(ω) Γ θo — γ λ(ω) — 1
(16)
where x(ω, t) ≡ XNtt) denotes the population-adjusted degrees of complexity of product ω, which will
be constant in steady-state∙ Similarly, the skilled labor market equilibrium implies:
(θo + 1 — 2γ) (1 — θo) φ∕2 = b j0 Iωx (ω) dω.
(17)
.
In steady state all per-capita variables are constant and therefore X^’t) = n∙ Hence, the specifi-
cation of the R&D difficulty index (TEG) implies I = n∕μ. Hence we can rewrite (16) and (17) as
follows:
1 θ o—- ω , ʌ bσ ρ ρ ρ + n∕μ - n .∙ 11 z- m 1ι
+Gω P + Gω = -a----x (ω) —ι ——, for all ω ∈ [0, 1],
λ (ω) Γ θo — γ λ (ω) — 1
(18)
(θo + 1 — 2γ) (1 — θo) φ∕2 = b— f x (ω) dω ≡ b—x.
μ Jo μ
(19)
15 See Aghion and Howitt (2005) and Jones (2005) for a discussion of semi-endogenous and fully-endogeous growth
models∙
11
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