spending in proportion to the quality jump in innovation, that is G(ω) = Gλ(ω). A linear combination
λ
of the two extreme rules yields the general rule
G(ω) = (1 - α)G + αG (λ (ω) ∕λ) ,
(21)
with 0 ≤ α ≤ 1.
Proposition 2 Every move from a symmetric spending rule to a rule promoting more heavily sectors
with above-average quality-jumps, that is an increase in α, increases both the relative demand and the
relative supply of skills. The relative demand shift is relatively stronger and the skill premium wH
rises.
Proof. The general rule yields Ω = G [ʃθ1 λ-α)dω + ɪ] and deriving Ω with respect to α we obtain
∂Ω∕∂α = G [- ʃŋ1 λ(ω)dω + =] : Jensen’s inequality implies that ∂Ω∕∂α < 0. Thus, a shift to more
asymmetric spending (an increase in α ) decreases Ω that, according to Proposition 1.a, generates a
decrease in the share of the population that decides not to acquire skills, θ0. Recalling that the skill
premium is wg = σ/ (θŋ — γ), we conclude that a higher α leads to higher wage inequality. ■
Proposition 2 contains the basic result of the model: when government switches to a policy promot-
ing high-tech sectors more aggressively there is an increase in both the relative supply and demand of
skilled workers, but the latter dominates and the skill premium rises. This theoretical result matches
two well known stylized facts of the US labor market in the 1980s: the contemporaneous increase in
the skill premium and in the relative supply of skilled workers (see Acemoglu 2002a figure 1). This
result is directly related to our heterogeneous-industry setting. One dollar of public money in more
innovative sectors yields more additional profits than those lost taking one dollar away from less inno-
vative sectors, and the net result is an increase in aggregate profits and innovation activity. 17 When
industries are symmetric the profit rate is the same in all industries and aggregate profits are not
affected by a reshuffling of government spending. As stated in proposition 1.a., public spending is, at
the margin, more efficient when directed to more innovative industries, that is: G(ω) > G(ω,^) implies
x(ω) > x(ω') and ∂x(ω)∕∂Gω > ∂x(ω')∕∂G(ω') if and only if λ (ω) > λ(ω').18 Thus, reshuffling public
spending towards sectors with higher innovation potential raises the overall innovation activity until
the increase of the difficulty index brings back the economy to the exogenous growth rate g . Since in-
novation has become more difficult, to keep the steady-state growth rate we need more labor resources
invested in innovation, thus the increase in the ‘level’ of labor demand produced by the policy shock
is permanent.
Finally, the increase in the relative demand for skills raises the skill premium and triggers, through
the skill-acquisition process, an increase in the relative supply of skills. Proposition 2 shows that the
demand shift dominates the supply and that in equilibrium the skill premium rises.
17From (9) we know that λ(ω) coincides with the markup over the unit cost for the sector ω. It follows that markups
are higher in high-tech sectors.
18 Notice that increases in the arrival rate of innovation show up in a higher steady-state difficulty index x(ω), and
does not affect the steady-state innovation and the growth rate g.
13