Government spending composition, technical change and wage inequality

(12)

Therefore:

(13)

(14)

Nt) [c + G(ω)] = bwHX(ω)
λ(ω)

ρ+ I(ω) - n

(λ (ω) - 1) ^,

(15)

which - since Wh = θo^σ_-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 al}l ^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 al}l ^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∙

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