Government spending composition, technical change and wage inequality



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)= N N(t) f —c- + G^= N(t) [Γc + Ω] .
0              0 λ (ω)   λ (ω)

Therefore:


(13)


(14)


_ θo - Ω
c = Γ ,

where Γ = Jθ1 λ(1ω)and Ω = f1 GG(J)). 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) .


(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 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) 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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