In the present framework with quality-improving goods, growth is interpreted as the increase over
time of the representative consumer utility level, hence the symmetric growth rate is obtainable from
(1) as follows:
ln u(c(t)) = 01 ln( λcω))dω+ln 01λ (ω) dω = ln( ^^ ))+ J Λ(ω,t)ln λ (ω) dω
where Λ(ω, t) = fft I(ω, τ)dτ is the expected number of innovations in industry ω before time t. Since
in steady-state I(ω,τ) = I = n∕μ, we obtain Λ(ω,t) = ʃθ1 [ʃθ I(ω, τ)dτ] dω = t I = t (n∕μ). The
growth rate is obtained by differentiating ln u(c(t)) with respect to t:
g=
— = tj log λ (ω) dω = n∕μ J log λ (ω) dω.
(20)
As usual in semi-endogenous growth models with increasing complexity the steady-state arrival rate
of innovation in every industry is a linear increasing function of the population growth rate, and the
stationary growth rate is pinned down by population growth. Growth is semi-endogenous in the sense
that policy has only temporary effects on the growth rate. Every policy measure capable of increasing
the innovation arrival rate I(ω), and thus the growth rate, will also raise the R&D difficulty index X(ω)
according to (TEG) and in the long-run the growth rate will not be affected. For what follows it is
important to notice that, although policy has no effects on steady-state growth, it has permanent level
effects. In particular, since we are interested in the relative demand and supply of skills, we will see
that temporary changes in the innovation arrival rate will affect these levels (or ratios) permanently.
Proposition 1 If ω-Tg < (1-2γ)φμσ(γ+nφμ-n) a steady state always exists for every distribution of
λ(ω) > 1 and G(ω) > 0. At each steady state the following properties hold:
a. G(ω) > G(ω'') implies x(ω) > x(ω,) and ∂x(ω)∕∂G(ω) > ∂x(ω,)∕∂G(ω,) iff λ (ω) > λ(ω,)
b. θo is an increasing function of Ω
Proof. See the Appendix. ■
Proposition 1a suggests that an increase in government spending in sector ω stimulates innovation
in that specific industry through a market size effect - according to (TEG) the difficulty index x (ω) is
proportional to investment in innovation in sector ω. Moreover the proposition shows that 1 dollar of
government spending is more effective in stimulating innovation when directed towards sectors with
high quality jumps. The importance of proposition 1b will become clearer later; for the moment it
suffices to note that it shows that the share of unskilled workers θ0 is increasing with the technology-
adjusted average government spending Ω.16
5 Fiscal policy rules
Here we specify rules for public spending and derive the basic result of the paper. The fiscal policy
rule that we use is a linear combination of two extreme rules: a perfectly symmetric rule in which
every sector gets the same share of public spending, that is G(ω) = G , and a rule that allocates public
16The average goverment spending is G = J01 Gωdω.
12