spending affects the market-size of all kinds of innovation activities, of which R&D is a relevant
component.
[FIGURE 2 ABOUT HERE]
In our opinion this set of facts provides a sufficient motivation to dig deeper into the links between
public spending composition, innovation and wage inequality.
3 The model
3.1 Households
Households differ in their members’ ability to become skilled workers, and the ability θ is uniformly
distributed over the unit interval. Households have identical intertemporally additive, separable, and
unit elastic preferences for an infinite set of consumption goods indexed by ω ∈ [0, 1], and each is
endowed with a unit of labor/study time whose supply generates no disutility. Households choose
their optimal consumption bundle for each date by solving the following optimization problem:
max
N0e-(ρ-n)t log uθ(t)dt
(1)
subject to
log uθ (t) ≡ 0
1
log
jmax(ω,t)
^ λj (ω) qθ (j,ω,t)
j=0
dω
jmax(ω,t)
cθ(t) ≡ 0
p(j, ω, t)qθ(j, ω, t)
dω
j=0
Wθ(0) + Zθ(0) -
∞° Noe- ⅞(r(τ)-n)dτT(t)dt = ∞° Noe-^t(r(τ)-n)dτcθ(s)dt
00
where No is the initial population and n is its constant growth rate, ρ is the common rate of time
preference, with ρ > n and where r(t) is the market interest rate. qθ(j, ω, t) is the per-member flow of
good ω ∈ [0, 1] of quality j ∈ {0, 1, 2, ...} purchased by a household of ability θ ∈ (0, 1) at time t ≥ 0.
p(j, ω, t) is the price of good ω of quality j at time t, cθ(t) is nominal expenditure, and Wθ (0) and
Zθ (0) are human and non-human wealth levels. A new vintage of a good ω yields a quality equal to
λ (ω) times the quality of the previous vintage, with λ (ω) > 1. Different versions of the same good ω
are regarded by consumers as perfect substitutes after adjusting for their quality ratios, and jmax(ω, t)
denotes the maximum quality in which good ω is available at time t. As is common in quality ladders
models, we assume price competition11 at all dates, which implies that in equilibrium only the top
quality product is produced and consumed in positive amounts. T(t) is a per-capita lump-sum tax.
The instantaneous utility function has unitary elasticity of substitution, implying that goods are
perfect substitutes, once you account for quality. Thus, households maximize static utility by spreading
their expenditures evenly across the product line and by purchasing in each line only the product with
11 All qualitative results maintain their validity under the opposite assumption of quantity competition.