Preliminary: Please do not circulate.

Love of Novelty, Innovation Di¤usion, and Growthin the Presence of Worker Heterogeneity
Yuichi Furukawa, Chukyo University
September 1, 2019

Abstract
By considering heterogenous workers’love of novelty and their role in endogenous innovation di¤usion within a standard innovation-based growth model, we …ndthat a stronger love of novelty and/or a larger population of ordinary workers (whoare also called majority workers) leads to a higher rate of innovation di¤usion. The
higher di¤usion rate then leads to a higher long-run rate of economic growth, provided that new technologies, which have not been di¤ used, i.e., are still unavailable
to majority workers, generate a moderate amount of knowledge spillovers for innovators. In a case where the spillovers are very e¢ cient, the growth e¤ect is reversed,
and becomes negative. We extend our consideration to a two-country version of themodel, we also …nd that the domestic majority workers’population and their love ofnovelty are conducive to domestic innovation di¤usion and world economic growth,
but the e¤ects on international specialization and international innovation di¤usion
are nontrivial. In particular, the e¤ect on international innovation di¤usion can beseen to form the shape of an inverted U.

1Introduction

Economics literature commonly states that culture, along with institutions and geography, is a fundamental determinant of cross-country di¤erences in macroeconomic performance (Acemoglu et al. 2005). An immense volume of literature has long concerned itself
with trying to answer questions related to various dimensions of culture, such as religion,
values, and family ties (see below for details). Recently, Gören (2017, 2018) reported
novel empirical evidence that suggested that individual “love of novelty”is an important
aspect of culture responsible for determining macroeconomic performances like economic
growth and development.1
Some might think the public’s openness to new technologies and products enhances
innovation and innovation-driven growth. However, the cross-country evidence suggeststhat love of novelty has an ambiguous e¤ect on per-capita income (Gören 2017).2 Subsequent studies also show di¤erent e¤ects of a stronger love of novelty on di¤erent stages
The author would like to thank Martine Carré-Tallon, Kenji Sato, and meeting/seminar participants
at Paris Dauphine University and RIETI for their helpful comments on an earlier version of this paper.
1
See also Furukawa et al. (2019) for another piece of empirical evidence.
2
More precisely, Gören’s research addresses novelty-seeking traits, which should be an essential aspect
for consideration when examining individual love of novelty. He uses genome data to index a nation’s
average level of novelty-seeking traits.

1

of innovation, such as basic and applied research.3 Although we do need to pay close
attention to caveats, particularly the fact that we still have only a few pieces of empiricalevidence, each with its own technical limitations, such as causality issues, the evidence todate seems to at least raise a theoretical question that is worthy of consideration: Whatis the role of individual love of novelty in innovation and innovation-based growth? The
answer is not as obvious as it seems.
In this study, we will theoretically characterize the macroeconomic role of the love ofnovelty. Speci…cally, we will consider the role of worker heterogeneity in terms of thesesubjects’innate trait for openness to new technologies. To do so, we introduce the essenceof Rogers’ (1962) innovation di¤usion theory into an innovation-based growth modelthat features expanding varieties a la Romer (1990). Following Rogers (1962), we may
venture that there are di¤erent types of agents, who exhibit di¤erent levels of an innate
willingness to accept/adopt new things. We speci…cally have (i) innovators who innovate
new technologies, (ii) early adopters who adopt and use these new (and still uncommon)
technologies at work in the production sector, and (iii) the more abundant group, majority
workers, who only use relatively old technologies that have already been di¤used into
the economy (and which should have more user-friendly interfaces as a result).4 In themodel, as is considered in Roger’s theory, innovations (i.e., newly innovated technologies)
gradually di¤use. To model such gradual di¤usion, we emphasize …rms (innovators) thatassume a proactive role by investing in order to encourage the di¤usion of their innovatedtechnologies. From a realistic viewpoint, investment aimed at di¤usion should cover awide range of activities, including process innovation, marketing, advertisement, and soon. When an instance of di¤usion investment succeeds, the …rm’s technology becomes
available to majority workers. In such cases, we assume that the investment activity
aimed at technology di¤usion is stochastic, and we consider a success probability (or aPoisson arrival rate) an increasing function in the …rm’s investment level (endogenous)
and also in majority workers’intrinsic love of novelty (exogenous).
The core …nding of this study is that when majority workers’love of novelty is stronger(and/or their population is larger), the speed of technology di¤usion is higher, and thereby
the long-run rate of economic growth is higher, in most cases. This suggests that the
public’s love of novelty is a fundamental source of technology di¤usion and innovationbased growth in the long run. However, if knowledge spillovers from newly innovatedtechnologies (which are yet to be di¤used) are very e¢ cient, the e¤ect can be reversed; astronger love of novelty and/or a larger population size of majority workers can decrease
the rate of economic growth, even though it still has a positive e¤ect on the speed ofinnovation di¤usion. This negative growth e¤ect arises because of an endogenous decreasein the ratio of newly innovated technologies to di¤used technologies. In our model, thenewly innovated technologies play a role as seeds for innovation di¤usion, and thus thelong-run rate of economic growth can be expressed as a product of the speed of technology
di¤usion and the amount of seeds for di¤usion (i.e., new technologies). A smaller amountof seeds has a slowing e¤ect on economic growth, but economic growth can become3

While Gören (2018) …nds that there is a positive e¤ect on basic research such as scienti…c knowledge
creation, Furukawa et al. (2019) suggests a negative e¤ect on applied research as it relates to inventions
that are eligible for intellectual property rights protection (e.g., patents and trademarks).
4
Rogers (1962) proposes a more detailed set of classi…cation categories: innovators, early adopters,
early majority, late majority, and laggards. Thus, our modeling o¤ers a simpli…ed version of his theory,
probably without any loss of generality. Note that the essence of his idea is that innovation di¤usion
gradually occurs through social communications between di¤erent individuals who adopt new ideas todi¤erent degrees.

2

dominant when seeds, or new technologies, bring about larger knowledge spillovers.
We then extend the baseline model to a two-country setting simply by allowing forinternational trade and foreign direct investments.5 Given this extension, we obtain a
new insight on the role of the public’s love of novelty from an international perspective.
A stronger love of novelty or a larger population of the majority worker in one country
leads to a higher speed (rate) of domestic innovation di¤usion. Although this increasein the domestic di¤usion rate creates more production possibilities for goods originatingin the home country, it rather causes a decrease in the production share of the homecountry because …rms endogenously choose the production location through foreign direct
investments. This crowding-out e¤ect interacts with a growth-enhancing e¤ect as in thebaseline (closed-economy) model, possibly to generate a non-monotonic e¤ect on thelong-run speed of international technology di¤usion from the foreign country to the homecountry. Speci…cally, when internationally transferred technologies (i.e., innovated in theforeign country but used in the home country through foreign direct investments) candeliver su¢ ciently large knowledge spillovers for the home country, the e¤ect of a stronger
love of novelty/larger majority worker population on the speed of international di¤usion
takes the form of an inverted U: in other words, a too strong or too weak public loveof novelty in a country can slow down the international di¤usion of technologies in the
direction of the home country from overseas.
Since we work under the belief that individuals’ personal degree of love of novelty
is an intrinsic or cultural trait, our analysis treats people’s love of novelty as a culturalparameter. Thus, our study contributes to the body of literature on the macroeconomicrole of cultural heterogeneity; see Doepke and Zilibotti (2014) for a review. Many theoretical studies on innovation and growth have addressed the role of cultural preference
parameters like the time discount rate and the rate of risk aversion. Recent studies such
as Galor and Michalopoulos (2012) and Doepke and Zilibotti (2014) consider the joint
determination of an endogenous coevolution of entrepreneurial traits (in terms of risk tolerance) and technology. The present paper contributes to this growing body of literatureby focusing on worker heterogeneity in terms of workers’innate willingness to welcome
and adopt new technologies as new aspects of culture within the framework model ofinnovation-based growth.6
Outside the …eld of economics, the love of novelty has actually long been a prominentissue across various disciplines, although it is a relatively new concept to economics itself.
In psychology, for example, Cloninger (1986) refers to a human personality trait associatedwith “exhilaration or excitement in response to novel stimuli” as novelty seeking, which
is an essential aspect of studying an individual’s love of novelty. Subsequent papers haveshown that the degree of novelty-seeking varies among individuals (see Chandrasekaran
and Tellis 2008, Tellis et al. 2009). Such a view has also been considered in …elds such as
consumer research (e.g., Hirschman 1980) and business (e.g., Rogers 1962). By focusing
particularly on Rogers’(1962) theory, we develop a new innovation-based growth modelthat incorporates worker heterogeneity and endogenous innovation di¤usion.
This paper proceeds as follows: section two sets up a baseline model, section threecharacterizes the dynamic equilibrium of our model and shows our main results, section
four introduces an international perspective through extension and extrapolation, andsection …ve concludes.
5

We essentially follow Lai (1998) in modeling foreign direct investments and …rms’choice of production
location.
6
See Furukawa et al. (2018, 2019) for empirical and theoretical research on consumers’ love of novelty.

32

A Growth Model of Innovation and Innovation Diffusion with Heterogenous Workers

We introduce a formal theoretical setting for endogenous innovation di¤usion a la Rogers(1962) into the innovation-based growth model a la Romer (1990). In doing this, we
also consider worker heterogeneity in terms of degrees of workers’innate willingness toadopt new and/or uncommon technology, to which we would like to apply the somewhat
imprecise label of “love of novelty.” As in the standard model, time is continuous andextends from 0 to 1: There is a single consumption good, Ct ; that is produced by perfectlycompetitive …rms using a number of intermediate goods, xt (j): Intermediate goods areproduced from heterogeneous labor.

2.1

Consumption and Heterogeneous Workers

An in…nitely lived representative agent inelastically supplies three di¤erent classes of labor: I units of innovators, E units of early adopters, and L units of majority workers,
following Rogers’ innovation di¤usion theory. The key idea is that the three di¤er intheir abilities and attitudes toward new technology. Innovator I; with the strongest loveof novelty, will work on research and development (R&D) activities and innovate technologies (for producing intermediate goods). Early adopter E; with the second strongest
love of novelty, will adopt such a newly created technology and work on production activities for new intermediate goods. Majority worker L; with a relatively weak love ofnovelty, can use old and/or common technologies only. As argued in Rogers (1962) andmany subsequent studies, the population of early adopters is typically smaller than thatof majority workers. Accordingly, we assume " E=L < 1:
The representative agent solves a standard dynamic optimization on consumption andsaving. The lifetime utility is de…ned by
Z 1
U=
e t ln Ct dt;(1)0

where Ct denotes consumption and > 0 is the subjective discount rate. We also havean intertemporal budget constraint; we omit to write down the constraint because it isstandard. Solving the dynamic optimization,
C_ t
= rt
Ct

;

(2)

where rt > 0 denotes the (real) interest rate.

2.2

Final Good

The …nal good is produced by perfectly competitive …rms using a number of intermediate
goods. We take Ct as the numeraire. There are two kinds of intermediate goods: new andold ones. Let At be the number/set of “old”intermediate goods that are already common
to all workers in the economy. Let Nt be the number/set of “new” intermediate goods

4that have freshly been innovated and/or are still uncommon.7 We consider a constantelasticity of substitution (CES) technology:
Z
1
1
;
(3)
Ct =
xt (j) dj
j2fAt [Nt gin which > 1 denotes the elasticity of substitution between any two intermediates.
These production functions re‡ect the assumption that sector l has limited access to theset of intermediate goods.
Solving the pro…t maximization yields the market demand functions as
xt (j) = Ct pt (j)(4);

in which pt (j) denotes the price of intermediate good j:8

2.3

Intermediate Goods

Recalling the considerations stated in the introduction, we recognize two types of labor.
Majority workers can work only for old intermediate-good sectors, j 2 At , but early
adopters can also work for new intermediate-good sectors, j 2 Nt : As a result, sectors
with j 2 At hire majority workers, L; and those with j 2 Nt hire early adopters.9 Asin the standard growth model, the market structure is one of monopolistic competition.
It follows that each sector is occupied by a monopolistic producer (who is originally an
innovator, as explained below). We assume a so-called one-for-one technology, converting
each one unit of labor into one unit of an intermediate good.
By (4), the price elasticity of demand for any j is constant at > 1; so the monopolistic
prices are given by
wL for j 2 At
1 t
:
(6)
pt (j) =wE for j 2 Nt
1 t

Here, wtL and wtE are wages for majority workers and early adopters. The equilibrium
production levels are given by(
for j 2 At
xA
Ct
wL
t
1 t
(7)
xt (j) =EN
Ctw
xt for j 2 Nt
1 t
and the equilibrium pro…ts are given by8( 1) 1
Ct
>
<
wtL )
(
t (j) =
( 1) 1Ct>:(wtE )1At

for j 2 At

1Nt

for j 2 Nt

(8)

7

In this study, for the sake of descriptive simplicity, we use “new”and “old”for Nt and At , although
Nt could include goods that are not so fresh from the birth but still unavailable for majority workers.
8
There is one more equilibrium condition to equal the price to the marginal cost:
1="Z

pt (j)1

j2fAt [Nt g

9

dj

#11

:

(5)

We assume a parameter restriction under which the wage for early adopters is alwasy higher thanthat for majority workers. Thus, there is no incentive for early adopters to use old technologies and workat old intermediate good sectors.

5These equations show the standard e¤ect of a higher factor price, wtL or wtE ; that decreases
the equilibrium supply and pro…t, xt (j) and t (j):2.4

Endogenous Innovation and Adoption of New Technologies

Following Romer (1990), we will examine endogenously expanding varieties. There are
a number of potential R&D …rms, and each R&D …rm can invent a new technology
to produce a new intermediate good, j; by hiring 1=Kt units of innovators I: Here, Kt
stands for the knowledge stock of the economy. The R&D …rm entering the market would
hire some early adopters to produce the new intermediate good, earning a monopolistic
pro…t, t (j) for j 2 Nt : Following the standard literature to assume Kt = At + Nt ; inwhich 2 [0; 1]: When = 1; Kt is equal to the total number of technologies, as in thestandard Romer model. When < 1; the knowledge externality from new and uncommon
technologies is weaker than that from old and common technologies, which may seem tobe a more natural state.
Let VtN be the expected present value of a newly innovated technology (or a newly
innovated intermediate good). Here we focus on the symmetric equilibrium of R&D …rms,
so we omit any index for an R&D …rm. Free entry in innovation requires
VtN

wtI
with
Kt

VtN

wtI
Kt

nt = 0;(9)in which nt
0 denotes the number of newly innovated technologies for intermediate
good production.

2.5

Endogenous Innovation Di¤usion

In order to introduce a simple process for innovation (technology) di¤usion, we put forward that the successful R&D …rm would hire innovators to di¤use newly innovatedtechnology more widely by designing it to be user-friendly. As a result, the new technology becomes di¤used and available to all types of production workers, including majority
worker L: While economic activities aimed at di¤usion should logically include advertisement, marketing, process innovation, and so on, we do not go so far as to speci…cally label
these activities within the scope of this study; it will su¢ ce to simple refer to di¤usion
activity.
We assume a linear technology:10 For a short time interval of dt; the …rm can successfully di¤use the technology at a probability t dt by hiring t =Kt dt units of innovators.
Here, the Romer-type knowledge spillover e¤ect from Kt is also assumed. The parameter
determines the e¢ ciency of di¤usion from the smaller group of fewer early adopters,
E; to the larger, more abundant group of majority workers, L. Although there should
be a number of factors a¤ecting the e¢ ciency of di¤usion ; we intend to focus on ordinary people’s openness to or love of novelty. If majority workers, L; have a stronger
love of novelty, it is safe to say that the di¤usion process of new technologies from E to
L becomes smoother and more rapid. Therefore, we may label as the public’s love ofnovelty.
10

The linear technology we consider here essentially aligns with the concept of quality improving
innovation in the canonical quality ladder model (Grossman and Helpman 1991).

6

If di¤usion successfully occurs, the …rm with technology j hires majority workers to
produce what we call an “old” intermediate good; technology j moves out from the setof new goods, Nt ; into the set of old goods At : Let VtA be the present value of the …rm
whose technology is already di¤used. Then, the optimization problem for a successful
R&D …rm is given as11
max
t

N
t =

N
t

wtI t
Kt

_N
t dt) Vt dt +dt + (1At dt Vt:(10)

Following the standard argument,12 we can ignore the term (dt)2 or (dt)3 :13 Therefore,
the …rst order condition gives rise to
VtA

wtI
with
Kt

VtA

wtI
Kt

t = 0;(11)

in which t is the equilibrium value of t :Considering the standard asset choice problem, using (11), the Bellman equation for
VtN iswtI_N
VtA
rt VtN = N:(12a)t + Vt + t
Kt
|
{z
}
=0

Since there is no obeisance risk, the Bellman equation for VtA is the standard one:A_A
t + Vt :rt VtA =

2.6

(13)

Evolution of Technology Stocks

Due to endogenous innovation and innovation di¤usion, the stock of new/uncommon
technologies, Nt ; and the stock of old/common technologies, At ; endogenously grow overtime. The in‡ow to Nt is determined by the number of newly innovated technologies thatare successfully adopted by the early adopters E: It is nt : The out‡ow from Nt arises frominnovation di¤usion, whose number is equal to the new technology stock Nt multipliedby the rate t of innovation di¤usion. Then, the law of motion governing an evolution of
new technology stock Nt follows
N_ t = nt

t Nt :(14)

In the meantime, the in‡ow to At is equal to the out‡ow from Nt ; that is, t Nt : For
simplicity, we do not consider any force generating obsolescence of At : Thus, the law of
motion governing an evolution of old technology stock At follows
A_ t = t Nt :
11

(15)

This setting is mechanically the same as the one used in growth models with endogenous …rm survival(e.g., Furukawa 2013, Niwa 2018), although existing analyses neither consider endogenous innovationdi¤usion nor worker heterogeneity. That is to say, the theme of the present paper is completely di¤erent
from those.
12See, e.g., Grossman and Helpman (1991, Chapter 4).
13
Note this:Narg max N
wtI t =Kt dt + V_ tN dt + t dt VtA :
t
t =
t
t

7

2.7

Labor Market Clearing

All markets are cleared in equilibrium at any date, t . In the market for innovators, thelabor supply is equal to I; and the demands are from innovation and innovation di¤usion:
I=

Nt
nt
+ t :
Kt
Kt

(16)

In the market for early adopters, the labor supply is equal to E; and the demands arefrom new intermediate-good sectors:
Z
(17)
E=
xt (j)dj = Nt xN
t :
j2Nt

In the market for majority workers, the labor supply is L; and the demands are from oldintermediate-good sectors
Z
xt (j)dj = At xA
t :

I=

(18)

j2At

3

Dynamic Equilibrium: the Role of Public Love ofNoveltyIn this section, we characterize the dynamic equilibrium of our model. First, we de…nea key variable: ! t
wtE =wtL : This ! t denotes wage income inequality (between early
adopters and majority workers). Thus, ! t captures a premium on wages for workers who
have the innate love of novelty or, to phrase it more simply, a love-of-novelty premium.
We combine the labor market equilibrium conditions for E and L, (17) and (18) with thelabor demands from (7). It yields the equilibrium relationship between ! t and the ratioof new technology to old technology, Nt =At :14
!t =

Nt
"At

1

:

(19)

Recall that " E=L denotes the relative abundance of early adopters in the total population. (19) shows the two standard e¤ects: the price e¤ect (i.e., the negative e¤ect of
the resource abundance for E on the relative price ! of E) and the market size e¤ect(i.e., the positive e¤ect of the relative market size for E on the relative price ! of E).15
The following lemma assures global stability of the economy and characterizes thelong-run ratio of new technology to old technology, Nt =At :Lemma 1 De…ne"Then, Nt =At converges to

1

:

(20)

and reaches there in …nite time.

Proof. We follow the proof of Proposition 1 in Acemoglu and Zilibotti (2001). De…nethe following inequality:
Nt
1:
>"
(21)
At
14

By assuming < 1; we restrict our analysis to the case of ! t > 1; in which early adopters have no
incentive to work for an old-good sector.
15
See Acemoglu (1998) for a detailed explanation of these two e¤ects.

8In this proof, we will prove that under (21), both nt = 0 and t > 0 hold.
First, note that in order for Nt and At to both expand (that is, nt > 0 and t > 0),
we need to have VtN = VtA ; from the free entry conditions, (9) and (11). Then, combine
the two Bellman equations, (12a) and (13), to rt Vtz = zt + V_ tz for z = N; A: This implies
A
that VtN = VtA = wtI =Kt is possible if and only if Nt : However, it must holdt =At if (21) holds,Nt <noting (8) and (19). Therefore, as long as (21) holds, VtN < VtA = wtI =Kt holds;16
nt = 0 and t > 0 (that is, N_ t = 0 and A_ t > 0). Under (21), Nt =At converges down toand reaches there in …nite time.17 In order to complete, we must consider a similarargument for a case with the opposite inequality in (21).
Lemma 1 reveals that Nt =At reaches
in …nite time, and so the economy eventually
falls into a balanced growth path on which Nt and At grow at the same rate, say g :Lemma 1 also shows that the long-run ratio of new to old goods, Nt =At = ; increases
with the abundance of early adopters, "; but decreases with the majority workers’love ofnovelty, .
For the sake of explanation, it is bene…cial to de…ne an inverse of
by a separate
parameter, like
1:
(22)
" 1
This is the product of the relative population of majority workers, " 1 ; and the strength
1 (the factor facilitating the di¤usion process). It capturesof their love of novelty,
the total abundance of the love of novelty held by the majority workers as the ordinary
people of our economy, so we may simply call public love of novelty.
To examine the e¤ects of public love of novelty ; we combine (3) with (17) and (18)
to derive the long-run output of the consumption goods as
1

Ct = At

1

L

1

1

1

+( ) E

1:(23)

Thus, the long-run growth rate of consumption is
1

gc =

A_ t
=
1 At

1
1

g :

(24)

Finally, we will demonstrate that the growth rate, g ; is determined with the growthof two technological stocks, At and Nt : Using (15), we have the expression of long-run
growth rate g as a product of new technology ratio
and innovation di¤usion rate :
g =
16

(25)

:

Note slightly modi…ed de…nitions on Vtz :
VtA

Z 1

e Rs

A
s ds

Z 1

e Rs

N
s ds;

t

and
VtN

t

Rs
where Rsr dt:
t17
We implicitly restrict our analysis to the more natural situation where initially, the new good is not
too abundant, such that N0 (A0 + N0 ) <(or, equivalently, N0 < ( = (1 + )) A0 ).

9This captures two determinants of long-run growth in the model: the aggregate output Ct
grows faster (i) when there are more new technologies in the market (higher ) and/or(ii) when these technologies are di¤used to majority workers more smoothly (higher ).
Therefore, the determinants of long-run growth are (i) the seeds for technology di¤usion(the relative number of new technologies), ; and (ii) the speed of di¤usion, : As
explained later, our economy has a trade-o¤ on resources between these two determinants,
and ; which plays a role in our main results.
Given thatis already characterized in (20) as the inverse of public love of novelty,
we derive an expression for the long-run rate of innovation di¤usion by using (14) and(16) with (20) and (25):
( + )
I:
(26)
=
1+2
From (26), we can show that public love of novelty (i.e., the total abundance of the
majority workers’love of novelty) facilitates the process of innovation di¤usion. Note thatis supported by the scarcity of early adopters E; the abundance of majority workers L;
and the majority workers’love of novelty. First, since the role of early adopters E is topick up and adopt newly innovated technologies, scarcity in early adopters (smaller E)
leads to a smaller demand and pro…t dyad for the innovation activity of a new technology.
Then, in contrast, the role of majority workers L is as the users of a di¤used technology,
so a larger population L of majority workers or the majority workers’ strong love ofnovelty leads to a larger demand and pro…t dyad for the di¤usion activity. These twoe¤ects increase the relative pro…tability of di¤usion investment to innovation investment;
as a result, the di¤usion rate increases through the conditions of free entry and market
clearing for innovators I:
Proposition 1 The public love of novelty
long-run rate of innovation di¤usion :has a monotonically positive e¤ect on the

Proof. Straightforward from (26).
Given that the speed of innovation di¤usion is one of the two key components oflong-run growth g from (25), Proposition 1 suggests that the public love of novelty(larger L and and smaller E) has a direct positive e¤ect on the long-run growth rate, g ;because it accelerates the speed of innovation di¤usion, : However, given that anothercomponent of g ; i.e., the relative pool size of seeds for di¤usion ; is inversely related toby (20) and (22), the public love of novelty also has an indirect negative e¤ect on g ;noting g =: These two opposite e¤ects interact with each other, possibly generating
an environment in which the public love of novelty is placed in an ambiguous role. The
following proposition formally characterizes this e¤ect.
Proposition 2 The public love of novelty has a monotonically positive (negative) e¤ect
on the long-run rate g of innovation and growth if the knowledge externality from yetto-be-di¤used technologies, 2 [0; 1], is weaker (stronger) than 1=2.
Proof. Substituting (20) and (26) into (25) yields
g =

+
+ 0:5

I
;
2

with which proving the proposition is straightforward.
10

(27)

A perusal of Proposition 2 reveals that there is a trade-o¤ between the two determinants of long-run growth (g ), which are the seeds for technological di¤usion, ; and the
speed of di¤usion, : The balance of this trade-o¤ is governed critically by the e¢ ciencyof knowledge spillovers from new (yet-to-be-di¤used) technologies, Nt :When the spillover e¤ect is weak, the main driver of long-run growth (g =)is innovation di¤usion because the di¤usion of technologies increases At and therefore
the knowledge stock Kt = At + Nt is relatively dominant (since is small). With asmaller ; the balance of the trade-o¤ on growth possibility between
andis morebiased toward .
However, when the spillover is large enough, the main driver of long-run growth
becomes the pool of seeds (new technologies) for technology di¤usion
because a larger
pool size (a larger number of new technologies, Nt ) has a stronger e¤ect to increase theknowledge stock Kt = At + Nt (since is high). Here, the key player shifts to the user of
new technologies, which is the early adopter who encourages new technologies, Nt ; rather
than At . With a larger ; the trade-o¤ between andis more biased toward :Remark 1 An increase in the public love of novelty has opposite e¤ects on the twodeterminants of long-run growth: it increases the speed of technology di¤usion , but
decreases the pool size of seeds for di¤usion= 1= , through an increase in the relative pro…tability of di¤usion to innovation investments. Which determinant is dominantdepends on the e¢ ciency of spillovers from new innovations.
1. When is smaller, the balance of trade-o¤s between
andis biased towarddi¤usion ; changes speeding up the di¤usion process enhance long-run growth.
Such changes are ones that increase the public love of novelty ; including increasing
the number of majority workers L and the degree of their love of novelty
ordecreasing early adopters E.
2. When, on the other hand,is large enough, the trade-o¤ is biased toward thetechnology pool ; changes encouraging the creation of new technologies enhancelong-run growth. Such changes are ones that decrease the public love of novelty ;including decreasing L and or increasing E:

4International Innovation Di¤usion under Heterogenous Love of Novelty

In this section, we extend the baseline analysis to incorporate an international context.
The reason for this widening of scope is that there is concrete evidence showing thatdi¤erent people or regions typically have di¤erent attitudes toward novel things on average(e.g., Rogers 1962, Tellis et al. 2009); thus, love of novelty can be seen as a national
characteristic that might a¤ect not only domestic but also international technologicaldi¤usion. A question naturally arises: What is the role of cross-country di¤erences in the
public love of novelty ? We then consider a two-country version of our baseline closedeconomy model . In doing so, we should capture exactly what is added by the introductionof international factors. Thus, given the extension of context to include an examination11

of the international, we begin by focusing on a particular situation with = 0:5; in which
the growth e¤ects of in the closed economy (characterized in Propositions 2) cease toexist. Note that g becomes g = I=2 and free from when is exactly on the cuto¤
point, 0:5; noting (27).
Think about two countries, H and F: By a superscript of i = H, F; we assign any
variables to country i from here on. The two countries are basically identical except
for the public love of novelty i = ("i ) 1 ( i ) =( 1) ; where i = H; F: To introduce
international aspects, we assume that all goods are tradable, including the …nal good,
Cti ; and the intermediates, fxit (j)g : We also postulate a globally integrated market for…nancial capital (as the form of ownership for shares of …rms), where the world interest
rate is denoted as rt :We consider the life cycle of a technological innovation, j; to produce an intermediate
good as follows. When, …rst, a …rm in one country, say h; innovates a new technology to
produce a new intermediate good, j; the innovated technology is adopted only by local
early adopters, E H : Then, the …rm produces its innovated good j in country H: Afterthe investment aimed at technological di¤usion succeeds (with an endogenous arrival rateof Ht ), the …rm becomes able to produce the good j using majority workers of either
country, LH or LF ; then, at each point in time, the …rm chooses whether to produce thegood j in country H or to shift production location to country F through foreign direct
investment (FDI).
As in the standard models, such as Lai (1998), there is no …xed cost for FDI. Therefore,
under free trade, the production location for any old good (AH or AF ) is a country where
the pro…t is higher, and thus, the wage rate for majority workers, wtHL or wtF L ; is lower
in equilibrium. If wtHL = wtF L ; the two countries are indi¤erent to the …rm as a place for
production.
Note that in the extended model there are the following six types of intermediate
goods: (i) new goods, NtH ; in country H, which are produced in H; (ii) new goods,
NtF ; in country F , which are produced in F ; (iii) old goods, AHH; that are originallytinnovated in country H and produced in country, H; (iv) old goods, AHF
t ; that are
originally innovated in country H and produced in country F ; (v) old goods, AFt F ; thatare originally innovated in country F and produced in country, F ; and (vi) old goods,
AFt H ; that are originally innovated in country F and produced in country H: Denoteas AH (AF ) the number of old goods that are originally innovated in country H (F );AH AHH + AHF (AF AF H + AF F ).
As in the baseline model, we consider that the knowledge stock for each country,H
say country H; depends on its own innovation experience; KtH depends on AH
t + Nt .
To see the role of international knowledge spillovers, we consider that this too depends
on the foreign country’s innovation through FDI, which can be represented by AFt H ;i.e., the number of technologies that are innovated in F but produced in H via FDI.
Parameterizing the e¢ ciency of international knowledge spillovers with
0, we provideHa revised de…nition on Kt :H
FH
KtH = AHt + Nt + At :(28)

The de…nition on KtF is analogous to (28).
Those types of intermediate goods are all combined by perfectly competitive global…rms to produce the single …nal good, Ct ; which is sold to consumers in both countries.

12

The production function, (3), can be rewritten as
Ct =

"Z

xt (j)H
F
F
j2fAH
t [Nt g[fAt [Nt g

1

dj

#

1

:

(29)

It is worth showing a revised version of the pro…t and supply functions: the pro…t for a…rm producing in country H is8( 1) 1Ct
HA>[ AFt Hfor j 2 AHH
<
1
t
t
HL
w
(
)
H
t
:
(30)
t (j) =
( 1) 1Ct
HN>
for j 2 NtHH [ NtF H
:
1
t
HE
(wt )

Note that the pro…t for old goods depends only on production location and is free fromF
consideration of the …rm’s original nationality (regardless of whether AHt or At ). The
analogous expression for Ft (j) also holds. The equilibrium supply of intermediate goods
is, then, given by
(
Ct
wtHL
[ AFt HxHA
for j 2 AHHtt
H
1xt (j) =:(31)
for j 2 NtHH [ NtF H
xHN
wHE
Ct
t
1 t
The analogous expression for xFt (j) also holds.

4.1

International Equilibrium

To ensure the existence of balanced growth, we naturally focus on an equilibrium in which
both countries are engaged in innovation, di¤usion, and production. Since any …rm canproduce old goods in either country, a non-arbitrage condition for location choice requires= Ft A holds
that the two locations are indi¤erent to the …rms producing old goods: HAtin this equilibrium. By de…nition and (30), the …rm values for the old goods and thewages for majority workers must also be equated; VtHA = VtF A and wtHL = wtF L :It is a straightforward task to show the revised equilibrium conditions in accordancewith the two-country environment, but we will only write down the important ones inorder to save space (see Appendix A for the detailed derivations). First, the labor market
equilibrium condition, (19), becomes
i

! =

1

1
Nti
"i Aiit + Amit(32)

for each i: New is the term of Ami
t ; i.e., the old goods that are innovated in the foreign country but produced in the home country via FDI. Through the labor market
equilibrium, the domestic wage di¤erential between early adopters and majority workers
decreases with Ami
t : With the R&D-related conditions, (32) leads to
i

i

= "i

1

;

(33)

which is a country-speci…c version of (20). Let’s de…ne country i’s public love of nov=( 1)elty by i("i ) 1 i
: Note that along a balanced growth path in the current
13international setting, both countries grow at the same rate there: H H = F F must
hold.
Using (32) and (33), we can demonstrate the steady-state values of the domestic
di¤usion rate of innovation i and the world growth rate g :18
i

i
Kti
I=
= i
Nt 1 + 2 i

i
i

1+2

1+2

for each i; and
g =

I
2

i

2
1+
H
2 + 1=+ 2 + 1= F

i

!

(34)

I
:
2

(35)

Here, i 2 [0; 1] is a new and important component in this extension; i denotes aninternational share of the old goods that are produced in one country. We can also derive
the steady-state value of the production share i of country i for old goods:19
i=

2 + 1= i(36)

2 + 1= i + (2 + 1= m )for (i; m) = (H; F ), (F; H) : Accordingly, we can de…ne a rate of international innovationiidi¤usion as ~mi
A_ mi
g ; capturing a rate in which FDI from country m increasestt =At =
the stock of old goods in country i:
As in the baseline model, the public love of novelty i always has a positive e¤ect on
the rate of domestic innovation di¤usion, i ; noting (33), (34), and (36). This di¤usionenhancing e¤ect does not alter in the international environment. The …rst new resultthat we can obtain by considering the extension of context to include an internationalsetting is on the international production share, i :Proposition 3 An increase in the public love of novelty in country i;e¤ect on the production share i of the home country, i.

i; has a negative

Proof. Straightforward from (33) and (36).
Proposition 3 shows that a stronger public love of novelty in country i; i ; leads toa decrease in the production share i of the home country, by crowding out some …rms
producing in country i to the foreign country. The reasoning is as follows. In the …rst
place, as mentioned, a larger i facilitates the domestic di¤usion i of new technologies,
by increasing the relative pro…tability of di¤usion investment. It increases the numberof old goods in country i and thereby increases the labor demand for majority workers
in country i: While the wage rates for majority workers are internationally equated inequilibrium, this increased labor demand in country i would lead to an increase in thewage rate in country i, wtiL , o¤ equilibrium.20 Responding to the wage increase, some…rms begin to ‡ee from country i to the foreign country, m, by virtue of enjoying alower wage rate there. With such capital ‡ight, the labor demand and the wage rate
decrease (increase) in country i (country m), and this trend continues until the wage gap
18

See Appendix A for derivations. Note that we incorporate = 0:5 from this point on.
In Appendix A (speci…cally, the last two lemmas there), we provide some conditions under which
0 < i < 1 holds for each i: Note that 0 < i < 1 always holds when = 0:5:
20
In our model, a lower wage necessarily implies a higher pro…t.
19

14

ceases to exist, at which point the wages are internationally balanced again. Throughthis o¤-equilibrium process, the equilibrium production share i of country i decreases.
The second result that we obtain within the international setting pertains to theinternational di¤usion rate of innovation, ~mi .
Proposition 4 An increase in the public love of novelty in country i, i , has a negativee¤ect on the international di¤usion rate ~mi of innovation from country m to country i if
the e¢ ciency of international knowledge spillovers via FDI is equal to or smaller than
2=(2 + m ). The e¤ect is an inverted U-shape if is higher than 2=(2 + m ):Proof. See Appendix B.
Proposition 4 shows that factors speeding up the domestic innovation di¤usion i ,such as a stronger love of novelty i ; can slow down international innovation di¤usion(which actually occurs if the spillover e¤ect of international di¤usion is su¢ ciently
small). To understand the mechanism, …rst, recall that the international di¤usion rate
~mi = i g for country i is a product of the production share i and the world growthrate. Then, when the public love of novelty in country i is stronger (since, for instance,
the population L of majority workers is larger or their loveof novelty is stronger),more innovations are domestically di¤used within country i (higher i ), whereby someproductions migrate overseas through the above-mentioned crowding-out e¤ect (lower i )as shown in Proposition 3. The decrease in the production share of country i; i ; candiscourage international innovation di¤usion from country m to i (~mi = i g ) becausesome of the productions moving out from i to m have a foreign origin (Amit ).
However, when the international knowledge spillovers are su¢ ciently e¢ cient ( issu¢ ciently large), the encouraged di¤usion i and resulting increase in old goods incountry i (an increase in Ait ) can strongly contribute to the accumulation of knowledge stock in both countries, noting the last terms with for both knowledge stocks,
i i
i
m
m
m
At : Through these terms,
Am
Kti = Ait + Nti + 1
t and Kt = At + Nt +there is a positive e¤ect on the world growth rate g : Since g is another component ofinternational innovation di¤usion (recall ~mi = i g again), there is also a positive e¤ect
on ~mi : Therefore, when the e¢ ciency of international spillovers is su¢ ciently high, thispositive e¤ect of higher i on g becomes very strong, such that it dominates the negativee¤ect on i ; in this case, the monotonically negative e¤ect on ~mi will be bent to form
the shape of an inverted U. This is the thinking behind Proposition 4.
Just now, in the above text, we mentioned that a higher i has a positive e¤ect onworld economic growth g : Since this fact is also important, we will now summarize it asa proposition.
Proposition 5 An increase in the public love of novelty in either country, H or F; hasa monotonically positive e¤ect on the rate of world economic growth g :Proof. See (33) and (35).
We have made the following remark with regard to the extension of context to a
two-country, together with Figure 1.

15

Figure 1: Equilibrium e¤ects in the international economy

Remark 2 Let us begin by considering an increase in the public love of novelty in one
country, say country H: This increase in H ; emanating from an increase in the relative
population of majority workers LH =E H or their love of novelty H ; leads to an increasein the speed of domestic technology di¤usion, H ; as in the closed-economy model. Then,
this rapid technology di¤usion in country H has two di¤erent e¤ects on the rate of international knowledge spillovers from F to H, i.e., ~F H = H g :1. The increase in H decreases the production share of country H;
crowding-out e¤ect (Proposition 3).

H; through the

2. The increase in H increases the world economic growth rate, g ; by accelerating
the accumulation of knowledge stocks for both countries, KtH and KtF (Proposition
5).
The second positive e¤ect becomes relatively stronger than the …rst negative e¤ect
when the e¢ ciency of international knowledge spillovers is higher. In fact, as shownin Proposition 4, the e¤ect of an increase in i on ~F H = H g when is smaller thanthe cuto¤ value; however, the e¤ect is an inverted U-shape when is higher than it.

5Concluding Remarks

We investigate the role of the majority workers’love of novelty in innovation, innovationdi¤usion, and economic growth in the long run. To do so, we provide a new innovationbased growth model by introducing several types of workers and examining endogenous
innovation di¤usion from one worker type to another. To consider the role of love ofnovelty, we particularly focus on worker heterogeneity in terms of these subjects’innate
trait of how willing they are to welcome and adopt newly innovated technologies for the
production of goods (as it pertains to the somewhat imprecise label of an individual loveof novelty).
In the model, we include three di¤erent types of labor: innovators (working in R&D),
early adopters (working in production with newly innovated technologies), and the much
more voluminous group of ordinary workers, who are called majority workers (working in
production with relatively old, more user-friendly technologies). An innovated technology
endogenously di¤uses throughout the economy in such a way that it is …rst used only bya few people (the early adopters) but eventually becomes available to ordinary people16(the majority workers). Two key assumptions are (a) that innovation is di¤used tomajority workers endogenously owing to R&D …rms’ investment activity and (b) thatthe probability of success depends not only on a …rm’s investment level (endogenous) but
also on the strength of the love novelty that majority workers, as ordinary people, possess(exogenous).
We show that a stronger love of novelty and/or a larger population of majority workers
facilitates the di¤usion of innovated technologies to majority workers, leading, in turn,to a higher speed of innovation di¤usion in long-run equilibrium. Since a higher di¤usion
speed basically contributes to a higher long-run rate of economic growth in our analysis,
it suggests that the size of majority workers and their strong love of novelty are a fundamental source of innovation di¤usion and long-run economic growth. However, when
newly innovated technologies can cause su¢ ciently e¢ cient knowledge spillovers for R&D…rms and/or innovators, the growth e¤ect might be negative.
By extending the contextual scope to a two-country environment with free trade andforeign direct investments, we also show that majority workers’ number and degree oflove of novelty in any given home country can enhance world economic growth, but it
has a negative e¤ect on the international production share of the home country. It canalso result in an inverted U-shape e¤ect on the speed of international innovation di¤usion(from foreign to home countries) when the foreign-innovated technologies that are used for
production in the home country can generate su¢ ciently e¢ cient knowledge spillovers forhome-based R&D …rms/innovators. From an international perspective, a country’s public
love of novelty is a source of world economic growth; however, its e¤ect on international
specialization and international technology di¤usion can be more complex, potentiallyalso resulting in an inverted U-shape.
We intend to keep our analysis as simple as possible, without losing the core essence.
To that end, there are at least three caveats we should mention in order to conclude
the paper. First, motivated by existing research in psychology and other …elds, we treat
ordinary people’s love of novelty as a constant parameter because we focus on ordinary
people’s nature and their innate characteristics, which tend toward a willingness to adopt
new technologies. However, people’s behavior often changes in response to their new experiences as well as to changes in the macroeconomic environment, and behavior relating
to adopting new technologies should be no exception. Therefore, one can understand it
is exceedingly interesting to introduce an endogenous factor a¤ecting individuals’love ofnovelty (e.g., externalities, voluntary search, learning by experience, education, etc.).
The second caveat relates to the fact that population sizes are …xed to re‡ect, again,
our initial motivation (people’s love of novelty as an innate trait). However, for thesame reason stated as above, human behavior is prone to change, and it is possible
for some individuals to move in and out of the category of early adopter. Therefore,
one can understand it is deeply interesting to introduce endogenous skill acquisition andoccupational choice. For example, people are initially majority workers at birth, but they
can familiarize themselves with a newly innovated technology in order to earn a living at
a higher wage rate by investing time and/or money in education.
The third caveat is the absence of welfare analysis. From an international context inparticular, the domestic/global welfare consequences of ordinary workers’love of novelty
should be emphasized due to its signi…cance and its interest value. Unfortunately, thepresent model is too complex to analytically solve for dynamic welfare. As an inclusivealternative, one could consider a simpli…ed version of the model, which would be eligible
for welfare analysis by, for example, going with a more tractable production structure17

or assuming perfect depreciation of a technology stock. Otherwise, one could rely on
computational works and do a calibration analysis. While those issues are worthy ofinvestigation, we leave them up to future research.

References[1] Acemoglu, Daron, Simon Johnson, and James A. Robinson. “Institutions as a fundamental cause of long-term growth,” Handbook of Economic Growth, 1A: 386–464(2005).
[2] Chandrasekaran, Deepa, and Gerard J. Tellis. “Global takeo¤ of new products: Culture, wealth or vanishing di¤erences.”Marketing Science 27: 844-860 (2008).
[3] Cloninger, C. R. “A uni…ed biosocial theory of personality and its role in the development of anxiety states.”Psychiatric Developments 4: 167–226 (1986).
[4] Doepke, Matthias, and Fabrizio Zilibotti. “Culture, entrepreneurship, and growth,”
Handbook of Economic Growth, 2A: 1-48 (2014).
[5] Furukawa, Yuichi. “Leapfrogging cycles in international competition,” Economic
Theory, 59: 401–433 (2015).
[6] Furukawa, Yuichi. “The struggle to survive in the R&D sector: Implications forinnovation and growth,”Economics Letters, 121, 26–29: 2013.
[7] Furukawa, Yuichi, Tat-kei Lai, and Kenji Sato. “Novelty-seeking traits and innovation,”RIETI Discussion Paper Series 18-E-073 (2018).
[8] Furukawa, Yuichi, Tat-kei Lai, and Kenji Sato. “Novelty-seeking traits and appliedresearch activities,”Applied Economics Letters, forthcoming (2019).
[9] Galor, Oded, and Stelios Michalopoulos. “Evolution and the growth process: Natural selection of entrepreneurial traits.”Journal of Economic Theory, 147: 759–780(2012).
[10] Gören, Erkan. “The persistent e¤ects of novelty-seeking traits on comparative economic development,”Journal of Development Economics, 126: 112–126 (2017).
[11] Gören, Erkan. “The role of novelty-seeking traits in contemporary knowledge creation,”Working Paper, Carl von Ossietzky University Oldenburg (2018).
[12] Grossman, Gene M., and Elhanan Helpman. Innovation and Growth in the Global
Economy, Cambridge, MA: MIT Press (1991).
[13] Hirschman, Elizabeth C. “Innovativeness, novelty seeking, and consumer creativity,”
Journal of Consumer Research, 7: 283–295 (1980).
[14] Lai, Edwin L.-C.. “International intellectual property rights protection and rate ofproduct innovation," Journal of Development Economics, 55: 133–53 (1998).
[15] Niwa, Sumiko. “E¤ects of a blocking patent on R&D with endogenous survival activities,”Journal of Economics, forthcoming (2018).
18

[16] Rogers, E. M. “Di¤usion of innovations.”New York: Free Press (1962).
[17] Romer, Paul. M. “Endogenous technological change,”Journal of Political Economy,
98: S71–S102 (1990).
[18] Tellis, Gerard J., Eden Yin, and Simon Bell. “Global consumer innovativeness:
Cross-country di¤erences and demographic commonalities.”Journal of International
Marketing 17: 1–22 (2009).

19

Appendix A
In the extended model, the labor market-related conditions can be expressed as follows.
De…ning ! it wtiE =wtiL for each i = H; F; with (31), (16), (17), and (18) become
i
i
nit
t Nt
+
;
Kti
Kti

I=

i
E i = Nti xiN
t = Nt Ct

1

(A1)
wtiE

mH iA
Li = Aiit xiA
xt = Aiit + Ami
Ctt + At
t

(A2)

;

1

wtiL

;

(A3)

where (i; m) = (H; F ) ; (F; H). Combining (A2) and (A3) yields
Nti!i" = iimi
At + A ti(A4a)for (i; m) = (H; F ) ; (F; H). See (32).
= Ft A ; the two countries are indi¤erent as
Note that in the present case with HAta production location. Given that the pro…ts depend only on the production location(not on a technology’s origin/history), thus, the number of old goods, Aiit + Ami
t ; that are
produced in a particular country, say country i; can be written as a function of the totalF
At ; multiplied by a production share of old goods
number of old goods, AH
t + Atithat are produced in i; denoted as t 2 [0; 1]:it AtAiit + Amit =for (i; m) = (H; F ) ; (F; H) : Clearly,

H
t +

i

! =

F
t = 1: Accordingly, (A4) imply
1

1 Nti"i it At(A4b)

for i = H; F:
Let us move to the conditions related to innovation and di¤usion investments: (9),(11), (12a) and (13) will be revised to
VtiN =
rt VtiN =

wtiI
and
Kti

i

VtiA =

iN_ iN and rt VtiA = max
t + Vtfor i = H; F: (A5) and (A6) imply

wtiI
;
Kti
HA
t ;

iN
t =

i iA
t and thus

!i =

i

(A5)
FA
t

+ V_ tiA ;

(A6)

1
1

(A7)

for i = H; F:Finally, the law of motion in (14) and (15) is revised as
N_ ti = nit

i
i
i
i
_i
t Nt and At = t Nt

20

(A10)

for i = H; F:
We will characterize the steady-state equilibrium. Using (A4b) and (A7), we have
Nti
= "i
Ait

i

i

1

(A11)

for i = H; F: See (33). Then, from (A10), N_ ti =Nti = A_ it =Ait implies
nit
= it
i
Nt

Ni
1+ i
At

(A12a)

holds in steady state. From (A10), the international balance of growth rates also implies
H

H

= F

F

(A12b):

Substituting (A12a) into (A1) yields the steady-state di¤usion rate asi

Kti I i== i
Nt 2 + i

i

1

+ +

i

m
i At
Ait

i

I
2+

i

(A13)

;

also using (28). By (A12b) and (A13), we have the steady-state production ratio for old
goods as21
H

F

2+

=

H

1+

+ F

F

2+

F

H

1+

H

2+

=

F

(2 + F ) + F (2 + H )1+ H + H
2+ H 1+
H

F) +

(2 +

F

(2 +

;

(A14a):(A14b)F

H)

From (A10), (A13), and (A14), the steady-state innovation rate, g
A_ it =Ait = N_ ti =Nti for
i = H; F; is given by"#
H
1+ F + F 1+ H + H F
i i
g =
=
I:
(A15)
H
(2 + F ) + F (2 + H )It is easy to verify that @g =@ H > 0 if and only if
>

1
2

H F
H

+ F

(A16)

+1 :

Given that we now work on the equilibrium where both countries produce, we haveto ensure i 2 (0; 1) for each i: The following parametric condition does so:
1
1 + 1+<F
F

2+ H = 1+(2 + F ) = (1 +

H

H
F)

<1+

1+

H

:

(A17)

The following two lemmas state when (A15a) is satis…ed.
21

Here, having in maind s revised version of Lemma 1, we consider an economy that has alreadyH
reached the steady state, staying there permanently. Thus, AF
t =At is constant and simply determinedFH
H
as a function of its initial level A0 =A0 : We can freely take the steady-state value of AF
t =At as an initialF
H
condition; we set At =At = 1.

21

H

Lemma 2 (A17) holds for any; F > (0; 0) if and only if

2 2 1; 1 + minHotherwise, there exists some values of

H

; F

;

(A18)

; F such that the …rst inequality is violated.

Proof. The …rst inequality in (A17) holds for any

H

0 if and only if (i¤)

FF

It holds for any

Fin the case of
0:5;
0:5< 0:5 1 + F in the case of > 0:5:<

0 i¤
in the case of

0:5 <0:5 1 + F ;FH<

0:5 1 +

Fin the case of> 0:5 1 + F :These two facts mean that: (A) The …rst inequality in (A17) holds for any H ; F >(0; 0) if and only if 0:5 <0:5 1 + F ; otherwise, there exists some values of H ; Fsuch that the …rst inequality is violated. This gives a proof for the …rst half of the lemma.
The second inequality in (A17) holds for any H 0 i¤
in the case of

0:5 <0:5 1 + H ;HF

It holds for any

F<

0:5 1 +

Hin the case of> 0:5 1 + H :

0 i¤
H
H

in the case of
0:5;
0:5< 0:5 1 + H in the case of > 0:5:<

These two facts mean that: (B) The second inequality in (A17) holds for any H ; F >(0; 0) if and only if 0:5 < < 0:5 1 + H ; otherwise, there exists some values of H ; Fsuch that the second inequality is violated. The statements (A) and (B) complete theproof.
Lemma 3 Suppose that (A18) is violated. Then there exists an intermediate range ofH( F ) for which (A17) holds, given F ( H ) as constant.
Proof. When 2 2= 1; 1 + min H ; F ; (A17) has monotonicity in terms of H ; withwhich we can explicitly derive the range of i in which (A17) holds, given m : Noting thisfact would su¢ ce to complete the proof.

22

Appendix B
Proof for Proposition 4. With (35) and (36), we have
~mi =

i

g =

(2 + i )(2 + m ) + (2 +Di¤erentiating ~mi with respect tod~mi>0, 2+
d i

i

(2

i

i)

1+

2
(2 + F ) + (2 +

I
:
2

H)

;
(2 +

m

)) < (2 +m) (2 + (2 +

m

)) :

When
2=(2 + m ); the inequality always holds. When > 2=(2 + m ); the left-handside of inequality is monotonically increasing in i . As i ! 0; the inequality becomes
m

(2

(2 +

m

)) <

1+

2

(2 + (2 +m)) ;which always holds. As i ! 1; the inequality is eventually violated. It implies aninverted-U relationship between i and ~mi : Given the monotonic relationship of ("i ) 1 andi
to i ; it also implies an inverted-U relationship of ("i ) 1 and i to ~mi : Note that("i ) 1 and i are negatively related to i by (33).

23

Appendix C (not for publication)
This appendix shows saddle-path stability of our dynamical system together with thewage rates for three types of labor, wtI ; wtE ; wtL : To do so, let us think about an economy
that has already reached at t = 0 the state in which Nt and At grow at the same rate,g ; and Nt =At =holds for any t: By (2), (8), (13), and (15), we have
V_ tA
VtA

C_ t
Ct

A_ t
1
1
=
At
1+

Ct
At VtA(C1)( + g );
1

1 from (19) and (20).
which also uses the expression of wtL in (C2) below and ! t =1
1 ; we also have the wage rates for production
From (5), (6), and (19), with ! t =workers as

wtL = At
wtE =

1

1
1

(1 +
1

1

1
1

At

1

)
(1 +

1
1

(C2a)

;
)

1
1

(C2b)

:

By applying the standard argument for saddle-path stability to the one-dimensional dynamical system for Ct =(At VtA ); we can prove the following fact:Ct=
At VtA(1 +)( + g )c~ for any t

(C3)

0:

Finally, using (11), (23), and (C3), we have the wage rate for innovators as
wtI = At

1
1

(1 +
)
( + g ) (1 +

)

24

L

1

1

+( ) E

1

1:(C4)