Government spending composition, technical change and wage inequality

H(t) = βN(t) f         θθ² ds.

t-D               ²

Dividing by popula

'                     , β β

h(t) = -nh(t) + 2 e

tion, h(t) ≡ H(t)/N(t), and differentiating with respect to time:

^-nT^r(1-θo(t-Tr)) (1 + θo(t - Tr) - 2γ)-2e^-nD(1-θo(t-D)) (1 + θ₀(t - D) - 2γ),
(A 2.9)

implying steady st

We know from
time t is I(ω, t) and
case we have only

[eⁿ(^-T^r) - e^n(-D)] (1-θ0)(1+θ0-2γ)

ate level h = β¹-----------------------------.

2n                    ^.

the definitions in the text that the arrival rate of innovation in industry ω ∈ [0, 1]at
1 the per capita technological complexity index follows: X(t^,ω) = μI(t, ω) - n. In our
wo groups of sectors (low technology and high technology), hence we only have:

¹ (t) = μI₁(t) - n and                             (A 2.10a)

2⁽ ) = μI2(t) - n.                                   (A 2.10b)

x2(t)

Hence the skilled l

abour market equilibrium (where 2 for high tech and 1 for low tech - using equal

weight for each) is:

h(t) = 2I1(t)x1(t) + 1 I2(t)x2(t).                                (A 2.11)

Notice that, from t

he main text, the free entry condition into R&D is