The political reception of innovations

Jeffry Frieden∗ Arthur Silve†

September 19, 2020

Abstract

Why do some societies embrace innovation, while others resist it?New ideas, policies, and technologies often challenge existing patternsof social and economic activity. We present a model of the receptionof innovation by incumbent economic interests. The analysis revealsthe features of an innovation that determine whether it will be appro-priated by the incumbent (and entry regulated), blocked, encouraged,or taxed (and entry encouraged). These six features are: whetherits impact is broad or narrow; whether it complements or competeswith the elite’s sources of income; whether it is location-dependent,concealable, and easily replicable; whether it implies large fixed costs.While many of these factors have been considered on their own inother work, we assess them together. We provide illustrative evidenceof the relevance and generality of the model to understand the fate ofa variety of innovations.

Keywords: innovation, regulation, rent-seekingJEL classification: D72, L50, O30

∗Harvard University. Email: jfrieden@harvard.edu†Universite Laval. Email: arthur.silve@ecn.ulaval.ca

1

1 Introduction

The railroad first came to China in 1865, when a foreign merchant built ademonstration line in Beijing. The Imperial Government had the line torn up.Eleven years later, a group of foreign merchants opened a ten-mile railroadline in the Shanghai region. Within less than a year the Imperial viceroyordered it, too, to be dismantled. Over the succeeding decades, China’seconomy stagnated, falling farther and farther behind the rest of the world.

The railroad first came to Argentina in 1857, at a time when the countrywas a rural backwater. Domestic and foreign investors piled enthusiasticallyinto the sector. Along with the steamship and refrigeration, the railroadrevolutionized the country’s economy by making it practical to transportits abundant wheat and beef from the pampas to Europe. By 1914, theArgentine railway network was roughly as extensive as that of Great Britain,and Argentina was richer than all but four countries in the world.

Why did some countries welcome this extraordinary innovation in landtransportation, while others resisted it? More generally, why might somesocieties embrace innovation, while others discourage it? After all, economicgrowth and development depends upon the generation and application of in-novations. These innovations may be technological, such as the introductionof new means of production. They may be organizational, such as new waysof structuring economic activity. They may be governmental, such as a trans-formation of regulatory or macroeconomic policies. The innovations may bedeveloped within the society itself, or adopted and adapted from advancesmade in other societies. One way or another, however, growth and develop-ment rely upon the spur to economic activity represented by productivity-enhancing innovations. By the same token, policies toward innovation andrelated topics – investment, property rights, the rule of law, trade, regulation– have crucial effects on social structure and economic growth.

Yet incumbent elites are often ambivalent about innovation. New orga-nizational forms, technologies, discoveries, and policies may be at the coreof social progress, but they can threaten the order on which elite wealth isfounded. Innovations, indeed, often bypass, subvert, and even lead to changethat replaces the existing order (It is telling that two recent books compareinnovation to piracy: cf. Spar, 2003; Durand & Vergne, 2012).

Opposition to innovation is indeed common. Those who resist innova-tions are often considered “Luddites,” after the English textile-workers whoprotested – and sometimes destroyed machinery – in the early 19th century.

2

This is probably misleading, as the protests were usually more about wagesand hours than machinery itself. Nonetheless, there are many examplesof opposition to new technologies, methods, and policies from vested inter-ests who believe their livelihood is threatened by the innovation. (Mokyr,1992; Parente & Prescott, 1994, 1999; Krusell & Rıos-Rull, 1996; Acemoglu& Robinson, 2000; Solstad, 2020). Innovations do overcome opposition:the Republic of Letters of the Enlightenment against the Catholic Church;manufacturers against hostile guilds and merchants, abolitionists againstslavers and planters, pirate radio against the BBC, cypherpunks againstthe NSA. . . Nonetheless, reluctance about or opposition to innovative ideasand techniques are central to many accounts of the stagnation or economicdemise of societies (Rosenberg & Birdzell, 1986; MacMullen, 1988; Allen,2009; Rosenthal & Wong, 2011; Deaton, 2013; Stasavage, 2014; Hoffman,2015). In particular, Mokyr (1994) famously argued that the entrenchmentof innovators’ interests may explain why innovative spells often do not last.

This paper argues that variation in the willingness and ability of societiesto create and sustain an openness to innovative activity is affected by acontest over rents. The paper focuses on whether rulers and their supportersexpect to benefit from advances in productivity, or are threatened by them.This in turn determines whether they will encourage or restrict the advances,whether they will regulate or deregulate entry.

We start with a society dominated, formally or informally, by an economicelite. The elite earns rents from its privileged economic position; it thereforecares about the economic institutions that guarantee its rents.1

We posit an exogenously developed technological advance – a new tech-nology, an innovative new technique, a new policy. If implemented, theinnovation potentially provides rents to the innovators and those who deploythe innovation. It may also improve aggregate social welfare. From the pointof view of the elite, the innovation might either improve, or threaten, existinginvestments and corresponding claims on future income; it could also be asource of tax revenue.2

1The elite will also certainly care about the political institutions that provide it withthe political power to enforce its privileged position. In this paper, we ignore the potentialimpact of innovation on political power, a theme to which we hope to return. It is coveredwell by Acemoglu & Robinson (2000). In a highly relevant recent contribution, Solstad(2020) considers how political regime will react to a stream of innovations when it hasconsequences for the distribution of power.

2As Michael Faraday is reported to have justified the utility of electricity to William

3

To achieve its goals of protecting existing investments and extractingrevenue, the elite can use some combination of appropriation, taxation, andregulation of the innovation. The combination of these three strategies af-fects the definition and allocation of property rights to the innovation, andthe stream of income it creates. These strategies describe a battle for con-trol whose outcome determines who gets to implement the innovation in themedium run (Spar, 2003).

We show that elite strategies lead to four canonical outcomes, determiningthe extent to which the productivity advance will be realized or not, and whowill benefit from the corresponding rents.

1. Appropriate the innovation (or compromise to share rents with the in-novators), regulate entry, and realize the rents for its own benefit. Thisis attractive if the innovation is beneficial to the elite; if it could easilybe taken abroad (as appropriation ensures that it will be implementedat home); and if it requires large upfront payments.

2. Block the innovation. This is attractive if the innovation would com-pete with the incumbent elite’s own sources of rents, and if taxationis difficult and/or inefficient (whether because the innovation can betaken easily to the informal sector or to another jurisdiction).

3. Encourage the innovation and entry into supplying the innovation. Thisis attractive if the innovation would increase the incumbent elite’s rents,and if there is a threat that the innovation could be implemented eas-ily in another jurisdiction. If the innovation can easily be concealed,taxation is less effective – both to raise taxes and to affect supply ofthe rent-augmenting innovation. Finally, in this outcome, the elite en-courages entry to compete away some or all of the innovation-drivenrents.

4. Tax the innovation, and encourage entry. This is attractive to theincumbent elite if the innovation is potentially beneficial (complemen-tary) to the elite’s assets but the elite cannot, or prefers not to, takeover the innovation itself, and if the innovation is difficult to implementabroad or informally – although, as above, ease of concealment has anambiguous effect for complementary innovations. In this outcome as

Gladstone.

4

well, the elite encourages entry to compete away some or all of theinnovation-driven rents.

Appropriation, regulation, deregulation, encouragement, taxation, andblocking of the innovation each presents challenges. The attractiveness ofa strategy to the elite depends on a wide variety of factors: the structureof the elite, problems of collective action, and many more. Pre-existingproperty rights, norms, and customs may constrain elite strategies (Mokyr,1992, 1994, 2005; Khan & Sokoloff, 2001; Khan, 2002; Acemoglu, 2008). Thestructure of innovations in relation to each other may threaten to redistributepolitical power (Solstad, 2020). In this paper we largely abstract from theseconstraints in order to focus on the impact of elementary features of theinnovation itself and of the elite’s existing interests. Our contribution buildson that of Sokoloff & Engerman (2000), to whose emphasis on the effectsof factor endowments we add a connection to the nature of the potentialinnovation.

Our analysis identifies at least six features of an innovation that we expectto affect its reception by an incumbent elite: i) replicability, the ease withwhich the innovation can be reproduced. This could be due to inherent fea-tures of an innovation, the personalized nature of an exchange, trade secrets,or other factors that affect the extent to which entrepreneurs could repro-duce and deploy the innovation; ii) concealability, the extent to which theinnovation can be hidden from the state, which affects the impact of policyon its supply; iii) complementarity, as versus substitutability, the degree towhich the innovation adds to or detracts from the value of (competes with)the elite’s assets, which affects the elite’s incentives to encourage or discour-age the innovation; iv) location-dependence as versus mobility, the difficultyof deploying the innovation in another jurisdiction, which affects the extentto which the state can tax or otherwise limit the innovation; v) a generalpurpose, as opposed to a narrow impact. The more general the applicabilityof the innovation, the larger the share of the elite that is affected, whetherpositively or negatively; and vi) large fixed costs in production. Scholarshave addressed several of these features; we consider them together in anattempt to bring clarity to their relative roles and interactions.

These features work together, although not every combination is theo-retically interesting or empirically relevant. From the standpoint of growthand development, cases in which the elite has an incentive to limit supply ofthe innovation are particularly interesting, as they suggest reasons to resist

5

productivity-enhancing innovations. For example, if an innovation threatensthe elite’s assets and has a broad (general-purpose) impact, the elite hasstrong reasons to block it; blocking will be especially feasible if the innova-tion cannot easily be replicated or concealed. There are many other logicalimplications of the model; a subset of them are theoretically and empiricallyinteresting and we develop them below, after presenting the model.

In its essence, ours is a story about how an incumbent elite can usegovernment policy toward productivity-enhancing advances to its own benefit– whether by blocking, restricting, or encouraging the innovation. Inasmuchas elite strategies toward innovation are an important factor in economicgrowth, the approach is of broad relevance to patterns of development.

In what follows, Section 2 presents the formal analysis of how elite in-terests shape policy toward an innovation characterized by a combination ofthe six features. Section 3 gives another perspective on the predictions ofthe model, and provides illustrative evidence of its relevance and generality.Section 4 puts the implications of the model in perspective with a broaderdiscussion of the political economy of innovations, and section 5 concludes.

2 Elite rule with disruptive innovation

We model a society in which an elite controls economic policy, in particularfiscal and regulatory policy. Elite individuals also own a productive asset(capital). We ignore potential differences – and agency relationships (Comin& Hobijn, 2009) – between economic and political elites, and ignore therelationship of the political elite to a broader electorate or higher moralprinciples. Policies here serve the wealthy.

We consider the new availability of novel ideas, policies, and technologies,as well as geographic or resource discoveries – all considered as innovations.We focus on innovations not anticipated by the elite that may severely affectexisting patterns of social and economic activity (Rosenberg, 1996).

The elite is united by its wealth and power, but the sources of wealthmay vary: a diversified productive base implies heterogeneous elite economicinterests. An innovation may affect – enhance or disrupt – existing sourcesof income. Threatened members of the elite may obtain policies to protectreturns on their invested capital from detrimental effects of the innovation.The capital we consider is supplied inelastically.

Fiscal and regulatory policies respond to two main motives on behalf of

6

the elite: redistribution and factor price manipulation. The state accom-plishes the first by taxing the population (including innovators) and chan-neling funds into the hands of the elite. The state accomplishes the secondby controlling entry and supply, either by regulation or by taxation, so as tomanipulate factor prices to the benefit of the elite owners of affected capital.3

The following section presents a formal model of this dynamic, whichallows us to analyze the fiscal and regulatory response to an innovation.State policy affects the size of the rents to be earned and the identities ofthose who earn them; it also affects the extent to which the rents are taxedand redistributed. The analysis addresses two questions. First, will the eliteallow the innovation or will they block it? Second, should the innovation beallowed, who will reap the rents (if any) accruing to it: innovators, the elite,a wider group in the population, or no one? The model allows us to delineatethe assumptions we make and the logic of the argument.

We focus on the response of the elite to a given innovation, whose featureshelp determine the elite’s dominant strategy.4 We consider the followingtiming in the reception of an innovation:

0. Nature bestows an (unanticipated) innovation on the innovator(s).

1. The elite attempts to control the innovation and regulate entry.

2. Private third-parties imitate the innovation if they can.

3. The elite implements a fiscal policy that consists of taxation and redis-tribution (to the elite).

4. Assets are supplied, output is produced and consumed.

In the timing of this model, prior actions anticipate ulterior reactions,but cannot be adapted ex post, either because of timing (the game cannotstart before the innovation occurs in stage 0) or because the ulterior decisionis quicker to adapt than the prior one (allocating property rights in stage 1 isa more burdensome process than taxation, investment, and production). Inwhat follows, we solve this game by backward induction, starting with eco-nomic decisions (sections 2.1 and 2.3), then, when relevant, taxation (section

3The elite may also use its power for political purposes, to avoid the emergence of newsources of wealth that would generate new claimants to political power. We leave asidethis purely political motivation here.

4Spar (2003) provides a diverse array of anecdotal evidence along these lines.

7

2.2), entry and the decision to regulate (section 2.4), and finally, consideringthe decision to appropriate the innovation (section 2.5). See section 4.2 fora discussion of the assumptions that underlie this timing.

2.1 Production and the structure of the economy

The economy is composed of two groups taking unitary decisions, the elite,which supplies inelastically an asset K, and a class of innovators. The in-novators are inventors, entrepreneurs, explorers, or social leaders, and theircontribution to the economy is in the form of a new asset, in quantity M .To facilitate the exposition, we refer to K as capital, and to M as machines,although we intend the concept of innovation to cover a broader array ofeconomic developments than purely technological or mechanical innovations.One could imagine a landowning elite whose asset is land, and industrialinnovators. A guild elite could confront a new factory system. An earlymanufacturing elite might face the rise of a new form of producing or ofmanaging a corporation. A sheltered financial elite could face the prospectof opening the current and capital account to the rest of the world. In allcases, the new productive force or form would increase productivity, and alsoaffect the activities of the incumbent elite. A third group is implicit: workerssupplying labor. They are passive in the baseline model, and we abstractfrom considering labor supply.

There is one numeraire good produced and consumed under competitiveconditions. It combines capital and machines according to a technology de-scribed by the twice differentiable and concave production function G(K,M),with K and M the supply of each asset. Gross marginal returns to capitaland machines are given by the partial derivatives G′K and G′M . The concavityof the production function ensures that marginal returns are decreasing (ie.G′′KK , G

′′MM < 0). To capture the potential complementarity of machines and

capital, our discussion features centrally the cross-derivative G′′KM (Caselli,1999). If it is positive, the innovation is complementary to the elite’s capital,augmenting its return: mechanical reapers, fertilizers, or railroads, for exam-ple, benefit landowners (Krusell et al., 2000). Conversely, if G′′KM is negative,the innovation is a rival of the elite’s capital, supplanting the elite’s capi-tal: new methods of transportation that compete with existing elite-ownedmethods, or industrialization that threatens an agrarian elite by drawing la-bor away and raising wages (Comin & Hobijn, 2004, speak of ‘predecessor

8

technologies’).5 An innovation that exhibits constant returns to scale hasthe property that for any combination of the factors G′′KMK +G′′MMM = 0.This expression is positive if the innovation displays increasing returns toscale [IRS], and negative if decreasing returns to scale. A rival innovationdisplays decreasing returns to scale, and an innovation characterized by IRSis complementary.

Members of the elite own previously invested capital K in assets that theinnovation would affect, either positively or negatively. A specific innovationaffects a narrow set of economic activities, therefore fewer owners of capital,and a small amount of K. A general-purpose innovation (eg. railroads,electricity, computers) affects many economic activities, a large proportionof the owners of capital, and a large amount of K (Rosenberg, 1963).6 Ourdiscussion features affected owners of capital K prominently. We do not takethe general equilibrium effects of the introduction of machines on economy-wide returns to capital into account.

The economy includes a formal sector that the state can regulate and tax,and an informal sector which the state has greater difficulty reaching. Theformal supply of machines can be regulated and taxed, while the informalsupply cannot. The innovation’s technology of formal supply is describedby the (increasing) inverse supply function H; the possible technology ofinformal supply is described by the (also increasing) inverse supply functionH > H. It is more costly to produce machines informally, due both to thecost of evading the state and to the absence of the formal sector’s economicand legal infrastructure.

Equilibrium conditions for the competitive supply of machines are simple,and allow us to to introduce some notation. The elite may tax machines at

5G′′KM is closely related to – and has the same sign as – the (gross) Hicks elasticity ofcomplementarity, ie. G′′KMG/(G

′KG′M ). For a rigorous analysis of alternative definitions of

substitution and complementarity, see Stern (2011). Empirically, determining the ‘factorbias’ of technological change has been a recurrent question in the economic literature (seefor instance Rosenberg, 1969; Caselli, 1999; Acemoglu, 2002).

6In the academic literature, the term specific is used to describe sometimes a non-redeployable asset, sometimes a single-purpose asset, location-dependence, or even spe-cialized human capital (Williamson, 1983). Common usage also refers to an asset whosepurpose is narrow as specific. In context, the term could therefore be used in connectionwith four out of the six features we study: with replicability, complementarity, location-dependence, and with ‘general-purposeness.’ To prevent any confusion, we avoid usingthe term altogether in the remainder of the paper, and prefer to speak of the “narrowpurpose” of an innovation.

9

tax rate τ . Capital is inelastically supplied, so equilibrium in the market forcapital is K = K. While the new asset may also be in limited supply asit is introduced (eg. a newly discovered natural resource, or radio frequen-cies), we focus on equilibrium conditions with an elastic supply of machines.(If the limited supply constraint is binding, the model and its conclusionsbecome trivial.) We characterize formal supply as Mf , informal supply asMi; the aggregate supply of machines is M = Mf + Mi. To simplify nota-tion, we specify the arguments Mf of H, Mi of H, and K and M of G andits derivatives only when there is a possible ambiguity. Then, equilibriumsupply conditions are {

(1− τ)G′M = HG′M = H. (1)

These conditions characterize the response of formal and informal supplyto taxation. We assume that G′M(0) > H(0): otherwise there would be nosupply at any level of taxation. Let MO

f be equilibrium formal supply ofmachines in the absence of an informal sector and in the absence of taxation:G′M(MO

f ) = H(MOf ), and let M i be equilibrium informal supply of machines

in the absence of a formal sector: M i = 0 if G′M(0) ≤ H(0), and M i isdefined by G′M(M i) = H(M i) otherwise. Let τ be the tax rate above whichformal supply is not profitable: τ ≡ 1 − H(0)/H(M i) in the presence ofinformal supply, and τ ≡ 1 − H(0)/G′M(0) if M i = 0. Notice that in allcases, τ ∈ (0, 1). With these notations, we derive the following result:

Prop. 1. If the supply of machines is competitive,

1. formal supply decreases until τ ≥ τ , above which it is eliminated,

2. Below τ , informal supply

• increases if H(0) ≤ G′M(MOf ),

• if G′M(0) > H(0) > G′M(MOf ), there exists τ ∈ (0, τ) below which

it is crowded out of the market, and above which it increases, and

• if H(0) ≥ G′M(0), there is no informal supply at any τ , and

above τ , it is stable at M i. Finally,

3. aggregate supply decreases until τ , and then it stabilizes at M i.

10

The intuition of Prop. 1 is simple: formal supply decreases as taxationincreases, and informal supply may or may not increase to fill this gap. Thespecifics of the proposition are more interesting.7 Fig. 1 provides a visual-ization of the proposition. We focus first on the left side of the figure.

M

0 τ1

Mf

τ

MM i

MOf

MOf

τ

M

0 Mf

α(Mf )

M

0 τ1

Mf

τ

MM i

MOf

MOf

M

0 Mf

α(Mf )

Figure 1: Stylized representation of the supply of machines as a functionof the tax rate (LHS) and as a function α of formal supply (RHS). Top:G′M(0) > H(0) > G′M(MO

f ). Bottom: H(0) < G′M(MOf )

.

Formal supply declines as the tax rate rises, going to zero when the taxrate is prohibitive, τ ≥ τ . In Fig. 1 we do not present the case where informalsupply never matters (M i = 0 ⇐⇒ H(0) ≥ G′M(0)), which is trivial; buteven in the absence of informal supply (for example, if the innovation cannotbe concealed from the taxman), formal supply disappears when τ ≥ 1 −

7Throughout the paper, we refer the reader to the Appendix for proofs and formaldetails.

11

H(0)/G′M(0). Assuming that G′M(0) is arbitrarily high ensures the presenceof informal supply at high levels of taxation (M i > 0).

The technology of formal supply is more efficient than informal, so thatformal supply crowds out informal supply at lower levels of taxation. Whentaxation is low enough (below τ) formal production crowds out the informalsector completely (upper panel of Fig. 1). However, when H(0) < G′M(MO

f ),decreasing returns in the formal sector allows for production in the informalsector (lower panel). At intermediate levels of taxation both formal andinformal supplies coexist. Formal and aggregate supply decrease with τ ,while informal supply increases.

We can characterize two important features of an innovation, its mobilityand the ease with which it can be concealed, in terms of the model. Theslope of inverse supply H ′ captures the extent to which suppliers of the in-novation can adapt to expected changes in economic or fiscal conditions bymoving to another jurisdiction or hiding from the state (see the Appendixfor a more formal discussion of H ′ and for a generalization of the equilibriumsupply conditions 1). The more location-dependent and visible is the inno-vation, the more difficult it is for the owner of the asset to avoid taxationor regulation by moving or hiding (Mayshar et al., 2017, use the adjective“transparent” to describe output that cannot easily be concealed). For in-stance, a railroad, tunnel or canal, or the point-source extraction of naturalresources, are characterized by inelastic formal supply (ie. steep H) – theycannot be moved or concealed. On the other hand, contractual or organiza-tional innovations, trade secrets, and human capital can be easily taken toanother jurisdiction or hidden (ie. flat H). The inter-jurisdictional mobilityof assets (and of innovation) has large political repercussions (Mahon, 1996;Boix, 2003; Simmons et al., 2007). It is worth pointing out that mobility andease of concealment are sometimes confused in the literature, although theyare different and have different implications. Once a mobile asset is moved,its output does not automatically add to aggregate supply in its former ju-risdiction; the output of a concealable asset, on the other hand, typicallydoes.

A corollary of Prop. 1 is that equilibrium in stage 4 of our game can be de-scribed without ambiguity either by taxation τ , equilibrium aggregate supplyM , or equilibrium formal supply Mf : each one corresponds to a unique valueof the others. The right panels of Fig. 1 show aggregate supply as a functionα of formal supply in equilibrium. The shape of α indicates the extent towhich supply shifts to the informal sector, a function of concealability. If α

12

is flat, reducing formal supply by one unit leads to an increase of informalsupply by (almost) one unit: this would be the case of an innovation thatis easy to conceal, as owners move out of the formal and into the informalsector. Conversely, α′ close to 1 reflects an asset that is difficult to conceal,so that producers cannot easily move from formal to informal supply, andcannot easily reduce formal supply and increase informal supply. This wouldbe the case of major infrastructural or natural-resource investments. Likemobility, ease of concealment has large political repercussions (Scott, 2009;Besley & Persson, 2013; Sanchez de la Sierra, 2019).

To summarize, we consider the structure of an economy in which an inno-vation occurs, subject to taxation. In a simple setting, our analysis alreadyreveals four features of the innovation that matter in determining the in-tensity of taxation: complementarity or rivalry, narrowness or generality ofpurpose, mobility or location-dependence, and ease or difficulty of conceal-ment. The innovation complements existing capital if G′′KM > 0 and rivals itif G′′KM < 0. The innovation can be thought of as narrow if it affects a smallamount of invested capital K, and general-purpose if K is large. If an inno-vation is mobile or easy to conceal, H is flat, and if both location-dependentand hard to conceal, H is steep (see the Appendix for details). Additionallyif it is easy to conceal, α is flat, and if location-dependent, α is steep. Wewill later introduce two other features of an innovation: replicability, andfixed costs of production. These affect the extent to which the elite wouldregulate and appropriate an innovation.

2.2 Taxation

The elite controls the supply of machines indirectly through taxation. Im-plementable allocations correspond to τ ∈ [0, τ ]. Assuming a competitivesupply of machines, this is equivalent to (G′M − H)Mf ≥ 0. Note that weassume that the elite either is the same as the owners of capital, or that itacts as their perfect agent (we relax this assumption later in our discussionof φ). Fiscal policy maximizes the income of the elite (owners of capital). Afraction φ of all tax proceeds are redistributed among members of the elite.With these simplifications, we can write the full program of the elite:

13

maxτ

UE ≡ G′KK + φτG′MMf

s.t.

{0 ≤ τ ≤ τ(1− τ)G′M = H

where G′KK is the income of the fraction of the elite whose activity is directlyaffected by the supply of machines, and τG′MMf is the revenue from taxinginnovators in the formal sector. The first constraint ensures that the supplyof machines is implementable, and the second defines the equilibrium formalsupply of machines (with aggregate supply of machines given by M = α(Mf ),as specified above).

The elite, in other words, maximizes the combination of the return to itsassets as affected by the supply of (new) machines, plus the taxes levied andredistributed to the elite. These two arguments in the elite’s utility functioncorrespond to the factor-manipulation and tax-and-redistribute functions oftaxation in the model.

The parameter φ plays an important role here, as it affects the elite’sreturn to taxation: the higher is φ, the greater the portion of taxes levied bythe state that goes to the elite. This is subject to a number of interpretations;for our purposes we regard φ as capturing how completely the elite controlsthe public purse. The more pressure from the non-elite public forces the stateto spend on public goods, the lower the elite share of tax revenue and thelower the value of φ; the more tax revenue the elite can command withoutdiversion to public goods provision, the higher is φ. If fiscal revenue is usedexclusively to provide elite-specific private goods, φ = 1. If some of the taxproceeds have to be expended in the form of public goods, φ < 1.8

We can rewrite the program of the elite with Mf as its choice variable

maxMf

UE = G′KK + φ(G′M −H)Mf

s.t. (G′M −H)Mf ≥ 0.(2)

8Another interpretation could be that of Acemoglu (2006), who defines φ as a form ofstate capacity, with lower levels of the variable representing ‘leakage’ from the taxationsystem. This suggests thinking of φ as the efficiency of the bureaucrats who controltaxation and redistribution. 1− φ could also be interpreted as the degree of corruption ofbureaucrats, although bureaucrats play no role in this model. φ is clearly an institutionalparameter and therefore not our central focus in this paper. However, its interaction withfeatures of the innovation is too important for us to ignore in the general approach we areadopting.

14

where the condition subsumes the two conditions 0 ≤ τ ≤ τ . In stage 3 ofthe game, an elite that does not appropriate and apply the innovation itselfimplements its preferred policy.

Prop. 2. If UE is well-defined and strictly concave, then

1. if α′(MOf )G′′KM(MO

f )K ≥ φ(H ′(MOf )MO

f −α′(MOf )G′′MM(MO

f )MOf ), the

elite does not tax machines,

2. if α′(0)G′′KM(0)K ≤ −φ(G′M(0)−H(0)), it taxes machines prohibitively,and

3. between these two situations, the elite taxes machines non-prohibitively.Formal supply ME

f is such that

G′M −H = H ′MEf − α′(G′′MMM

Ef +G′′KMK/φ) (3)

Equation 3 captures the elite’s two concerns as it formulates its tax policy.The first concern is to extract maximum revenue from the innovators. Thesecond is to use tax policy to influence the supply of the innovation so as tomaximize the elite’s return on its existing investments.

The combination of these two arguments in the elite’s utility functioncreates potentially conflicting incentives in the formulation of the preferredtax policy. For example, a tax policy that encourages increased formal supplyleads to a wider tax base; however, the fact that returns are diminishingimplies lower revenue extraction per unit of formal supply. Meanwhile, onthe second, as tax policy either encourages or discourages an increase in theformal supply of the innovation, it affects the returns to elite investments– either positively or negatively, depending on the relationship between theinnovation and the elite’s investments.

To start with the LHS of Eq. 3, the term τG′M = G′M − H representsthe tax revenue that can be raised from the marginal unit of formal supply,which is set with the concerns expressed above in mind. The first two termson the RHS describe the optimal tax policy if the elite were only concernedwith maximizing tax revenue – the peak of the Laffer curve. So H ′−α′G′′MM

describes the corresponding loss in revenue per unit as the tax rate is low-ered, the result of two effects: the loss in revenue per unit due to attract-ing the marginal unit of formal supply −τ ′G′M = H ′ − α′G′′MMH/G

′M and

the additional loss in revenue per unit to compensate for decreasing returns

15

−τα′G′′MM = α′G′′MM(H/G′M − 1). The third term on the RHS captures theimpact of an additional machine on the returns to the elite’s investment K.

The elite taxes a mobile innovation less, and a location-dependent onemore, as revealed by the first term on the RHS of Eq. 3. Although we do nothere consider a full-fledged model of inter-jurisdictional competition for thelocation of innovation, Eq. 3 is pertinent to this issue, as it incorporates someconsiderations relevant to the mobility of the innovation. This finding is inline with the literature, which commonly argues that political competitionamong jurisdictions expands the space open to innovators (Mokyr, 1994,2008; Milner & Solstad, 2020).

In line with the need to balance tax revenue with factor returns, the elitewill modulate its desire for tax revenue in order to increase the supply ofa complementary innovation, or to obstruct a rival one.9 The elite will taxa complementary innovation less and tax a rival one more – even past thetop of the Laffer curve. This effect increases with the share of the elite’sassets K affected by the innovation. The fact that the elite is not only tryingto maximize tax revenue, but also to manipulate factor supply in its favor(Acemoglu, 2006), is reflected in the last term on the RHS.

The elite also taxes less an innovation that can be more easily concealed(in line with the evidence in Mayshar et al., 2017).10 Again, this comesdown to the first term on the RHS of Eq. 3: a steep H indicates thatthe innovation is both location-dependent and hard to conceal. This is not,however, the only effect of easy concealment: it also interacts with rivalry /complementarity in a non-trivial way, as revealed by the second term on theRHS of the equation. When it taxes a rival innovation, the elite balancesrevenue-seeking with the harm caused by the innovation to its assets: it setsa tax rate past the peak of the Laffer curve.

If the innovation is easily concealed, taxation in order to affect supply,and thus manipulate factor prices, becomes less effective. This makes thetax and redistribution-seeking motive comparatively more powerful, so thatthe elite lowers taxes to increase tax revenue. As a result, the elite taxes lessa rival innovation that can be more easily concealed. We have a symmetrical

9These results match the the empirical findings of Caselli & Coleman (2006), the intu-ition in Jha (2013) and, in a different framework, the formal argument in Silve (2018).

10Ahmed & Stasavage (2020) have a similar argument. They envisage concealabilityas an issue of asymmetric information between the ruler and the citizens, and show thatrulers were more likely to share their power with a council in the presence of informationasymmetries.

16

result only for the subset of complementary innovations that exhibit IRS.The more easily such an innovation can be concealed, the harder it will befor tax policy to affect supply and hence manipulate factor prices. Again,that means increasing tax revenue, hence a lower tax rate. The elite taxesmore an innovation that exhibits IRS when it can be more easily concealed.

It is something of a commonplace to argue that the threat of defectionforces the state to bargain with the owners of mobile assets in order to beable to tax them.11 However, this argument conflates the mobility of assetswith the possibility to hide them, and ignores an important nuance.. Whenit comes to raising taxes, for example, if the asset – the innovation, in ourwork – complements the elite’s assets, then the elite has a clear incentive tolimit taxation on a mobile innovation, as this will keep it from leaving thejurisdiction for a friendlier one. This is not as clear for a concealable one.Instead, the elite weighs the impact of raising the tax both on factor supplyand on redistribution. Qualitatively, mobility and concealability can onlybe conflated if the innovation is harmful (rival) to the elite’s assets: in thatcase, the elite has an incentive to maximize taxation for both mobile andconcealable innovations.

At the limit, the elite will not tax an innovation that is complementaryenough with capital (item 1 of the proposition). Taxing one unit of formalsupply brings in φ(H ′ − α′G′′MM) in revenue, but it also reduces the formalsupply of machines by α′ units, which costs the elite G′′KMK in returns onits assets. The elite will not tax an innovation only if it is complementary toenough of the elite’s assets, and not easily concealable (if it were concealable,taxation would have little impact on the supply of machines).

Conversely, the elite prefers to tax prohibitively, in order to block, aninnovation that is a substantial enough rival to its investments (item 2 ofthe proposition). It will block the innovation, inasmuch as the difficulty inswitching to informal supply permits it, ie. M i = 0. Every unit of formalsupply the elite allows brings in revenue of φτG′M but reduces the return oninvested capital K by α′G′′KM . The elite will therefore tax prohibitively toblock the innovation if the innovation is rival, and if it is rival enough tothe elite’s assets, and if the innovation cannot be too easily concealed (thatimplies both limited informal supply M i and limited crowding out α′).

As Eq. 3 makes explicit, φ has a direct impact on the importance to the

11In one prominent example, Bates & Lien (1985) formalize an argument of Hirschman(1978).

17

elite of taxation and redistribution, on the one hand, relative to factor pricemanipulation, on the other. When φ is close to 1, so that tax revenue ischanneled effectively to the elite, the elite can focus on this, even taking itsconcern about sunk capital K into account. As φ decreases, tax revenue isless surely redistributed to the elite, so that the impact of the innovation onthe return to the elite’s assets plays an increasing role. With lower φ suchthat the elite earns little from taxation, it has strong incentives to encouragea complementary innovation – so to tax it lightly if at all – while it has strongincentives to block a rival innovation.

To summarize, the elite uses taxation for two purposes. The first is toraise revenue from innovators for redistribution to the elite; the second isto affect the formal supply of the innovation, which allows the elite to ma-nipulate prices to its advantage. Our analysis reveals many forces pullingin different directions (this framework does not point to a monocausal argu-ment).

1. A location-dependent innovation can be taxed more easily.

2. An innovation that complements the elite’s capital will be more lightlytaxed in order to encourage supply.

3. The more general-purpose the innovation, the more important is factorprice manipulation relative to redistribution. This means taxing morea rival innovation, and less a complementary one.

4. An innovation that is harder to conceal can be taxed more easily. Easeof concealment also makes taxation for redistribution more efficientrelative to taxation to manipulate factor prices. This means taxing arival innovation less, and one that exhibits IRS more when they areeasier to conceal.

5. At the limit, the elite may wish to block a rival innovation, though theinnovation will still be supplied within the boundaries of the jurisdictionif it is easily concealed, and outside if it is mobile (foreign implemen-tation does not affect the returns to the elite’s capital, though).

2.3 Elite-controlled innovation

The elite can, given certain conditions, take control of the innovation andproduce it. We consider those who control the innovation to be those who

18

deploy it and earn the rents (if any) associated with it. In this section, weconsider how much the elite would supply of the innovation if it were underits control. We deal in more detail below with the factors that affect whythe elite might decide to appropriate the innovation or let it be developed byothers.

If a member of the elite controls the innovation, the elite does not extractrevenue through taxation. It maximizes the income from the innovation upto the point where the innovation still favors the elite’s existing investments.That is, the elite maximizes the sum of the utility accruing to that portionof the elite that does not control the innovation (including those affected bythe innovation), plus the surplus of innovators in the formal sector. In theinformal sector, a member of the elite cannot count on the legal protectionsof the state, and cannot be distinguished from a non-elite supplier. Hence,we can write the elite’s program in compact form as

maxMf

UAE ≡ G′KK +G′MMf +

∫Mf

H(m)dm (4)

where G′KK is the income of those members of the elite whose assets aredirectly affected by the supply of machines, and G′MMf +

∫Mf

H(m)dm is the

income the elite derives from controlling the formal supply of the innovation.An elite that has appropriated the innovation has no incentive to tax itself, sothere is no fiscal policy per se. The elite implements its preferred allocationMAE

f such that

Prop. 3. If UAE is well-defined and strictly concave, then

1. if α′(0)G′′KM(0)K ≤ −(G′M(0)−H(0)), MAEf = 0, and

2. otherwise, they supply MAEf such that

G′M −H = −α′(G′′MMMAEf +G′′KMK). (5)

The comparison of Eqs. 3 and 5 reveals the similarities and differencesin the supply by an ‘appropriating elite’ as opposed to supply by non-eliteinnovators. Define ‘surplus supply’ as the difference MAE

f −MEf , and note

the following points.

19

Corollary 1. There exists a value of φ2 ∈ (0, 1) such that for φ > φ2,surplus supply is positive for any production function, and for φ < φ2, sur-plus supply is negative in a boundary of any production function such thatα′(MO

f )(G′′KM(MOf )K/φ+G′′MM(MO

f )MOf ) = H ′(MO

f )MOf .

There exists a lowest value of φ1 ∈ (φ2, 1) such that for φ ≥ φ1, surplussupply is nondecreasing with complementarity.

Supply under an appropriating elite has several properties in commonwith supply under a non-appropriating one. The more general the impactof an innovation, the more the elite taxes a rival innovation and the less ittaxes a complementary one. The easier it is to conceal an innovation, theless the elite taxes a rival innovation, and the more it taxes an IRS one.Supply with an appropriating elite differs from supply with a non-appropri-ating elite in three ways. The elite is not concerned with the mobility ofthe innovation, as it controls the location; ease of concealment affects supplyonly in interaction with rivalry or complementarity (the appropriating elite isnot concerned with the loss of revenue due to the innovation being suppliedinformally); and the proceeds from the innovation are a private source ofincome (corresponding to φ = 1 in the previous section). As a result:

An appropriating elite blocks a smaller set of rival innovations (except ifφ = 1, in which case the elite blocks the same innovations whether it controlsthem or not); and

Supply is generally at least as large under an appropriating elite (ie. sur-plus supply is positive). This is always the case if φ is large enough (φ ≥ φ2).This is also always the case for a rival innovation and for innovations com-plementary enough. If φ is low, factor-price manipulation becomes a strongmotive for the non-appropriating elite, and there exist moderately comple-mentary innovations that it would encourage more than the appropriatingelite. Finally, Corollary 1 provides a comparative static on the effect of mo-bility on surplus supply.

2.4 Regulation, deregulation, and imitation

Up to this point, we have focused on the elite’s use of taxation both as asource of revenue and as a way to affect the quantity of the innovation sup-plied. However, the elite-controlled state can also dictate regulatory policyso as to affect who can bring the innovation to market. This is relevant tothe elite inasmuch as it affects control of the innovation as it is brought into

20

production. The elite wants to maximize the combination of the rents itearns from the innovation itself and the revenue it earns from taxation.

In order to discuss regulatory policy, we first need to go back one step.To establish Prop. 1, we have made one significant assumption: that formaland informal supplies are competitive. If instead we considered n formal pro-ducers with an identical technology described by the inverse supply functionH, each producer would supply mf such that

H(mf ) = (1− τ)G′M (1 + α′G′′MMmf/G′M)

where the term α′G′′MMmf/G′M captures the market power associated with

imperfect competition. A limited number of producers can affect the returnon their assets by affecting supply (notice that εd = G′M/(G

′′MMM) < 0 is

the elasticity of demand). The market power of an individual producer inthe formal sector corresponds to its market share mf/M , and is dampened ifinformal-sector producers are present (ie. when α′ is lower than 1). In equi-librium, the n identical producers supply the same quantity mf = Mf/n.Assuming that the elite has not appropriated the innovation, from its per-spective, the equilibrium supply condition now looks like

H(Mf/n) = (1− τ)G′M (1 + α′/εd ·Mf/(nM)) . (6)

Stage 2 of the game is straightforward: individuals both within and out-side the elite imitate the innovator if they can. As long as the sector isimperfectly competitive, imitators earn rents on the innovation. If the inno-vation is easily replicable, imitators enter until they dissipate these rents. Ifthere are fixed costs in production the industry remains imperfectly competi-tive, and oligopolistic suppliers earn some limited rents. Even in the absenceof fixed costs it may take time for the industry to become competitive, per-mitting early imitators to share in the rents.

In stage 1 of the game, the elite determines its policy toward the entryof the imitators, based on the expected impact of this entry on tax revenueand the return to elite assets. With imperfect competition in the supply ofthe machines, an elite that does not itself appropriate the innovation has thefollowing program:

maxτ,Mf ,n

UE ≡ G′KK + φτG′MMf

s.t.

{H(Mf/n) = (1− τ)G′M(1 + α′/εd ·Mf/(nM))τG′MMf ≥ 0.

(7)

21

To study the preferences of the elite over the structure of formal supply(ie. n), we do not need to solve this program in full. First, while we haveestablished Prop. 1 under competitive supply, we assume that its logic holdsunder imperfect competition: τ is uniquely determined by the elite’s choiceof Mf and n by the equilibrium condition, with ∂τ/∂Mf < 0 and ∂τ/∂n > 0.We can simplify the elite’s program accordingly. Second, using the notationλn ≥ 0 to denote the Lagrange multiplier associated with the conditionτG′MMf ≥ 0, and treating n as a continuous variable, with VE ≡ UE(ME

f ),the envelope theorem yields

dVEdn

= (φ+ λn)G′MMf∂τ

∂n> 0 (8)

taken at optimal values MEf and ME.

Prop. 4. The non-appropriating elite does not regulate the formal supply ofmachines, and encourages entry and competition.

The elite facilitates (does not regulate) the entry of imitators when theelite does not appropriate the innovation itself. Free entry increases competi-tion among suppliers and reduces the markup that suppliers can implement.Notice that a policy of free entry may not lead to a competitive supply: theinnovation may be difficult to replicate by imitators, or equilibrium compe-tition may be limited by large costs of entry. Nonetheless, generally the elitebenefits from more rather than fewer suppliers of machines. It is easy tounderstand why: with a given level of formal supply, increasing competition(to n + 1 firms) means less rents for the suppliers and more tax revenue,which unambiguously benefits the elite. Finally, the elite can even do betterthan holding formal supply constant, since ME

f does not maximize UE withn+ 1 competitors.

For an elite that appropriates the innovation, there are slightly morecomplicated (and more surprising) results. An elite that appropriates theinnovation faces potential competition from n−1 > 0 other formal suppliers.

We evaluate the elite’s problem in the light of four choice variables, thetax rate τ on formal supply, elite (formal) supply µf , aggregate formal supplyMf , and the number of private formal suppliers n:

22

maxτ,µf ,Mf ,n

UAE ≡ G′KK + (1− τ)G′Mµf +

∫µf

H(m)dm+ φτG′MMf

s.t.

{H(Mf−µfn−1

)= (1− τ)G′M

(1 + α′/εd · Mf−µf

(n−1)M

)τG′M(Mf − µf ) ≥ 0.

(9)

Notice that we assume that the elite has market power as well, in the interestof generality. We maintain the assumption that the elite is a unitary actor:members of the elite do not compete against each other to supply µf . Thefirst condition characterizes the equilibrium supply (Mf−µf )/(n−1) of eachof the n−1 private suppliers under tax τ , while the second condition ensuresthat neither formal supply nor taxation is negative.

Here too, we avoid solving this program in full, but a few additionalconsiderations are useful (see the technical Appendix for more details). First,we assume that τ is uniquely determined by the elite’s choice of Mf , µf , andn by the equilibrium condition, and τ increases with n. We can simplifythe elite’s program accordingly. Second, the elite optimally supplies a largershare of formal supply than its formal private competitors, but, when φ = 1,it does not eliminate them. Third, using the notation λAE to denote theLagrange multiplier associated with the condition τG′M(Mf − µf ) ≥ 0, withVAE ≡ UAE(MAE

f , µAE),

dVAEdn

= (φMf − µf + λAE(Mf − µf ))G′M∂τ

∂n, (10)

again taken at optimal values MAEf , MAE, and µAEf . Interestingly, VAE is

a quasi-convex function of n. If φ = 1, it increases with n: it is moreprofitable for the elite to tax competitive suppliers than to produce muchitself. If φ < 1, it decreases, then increases with n: only a fraction of taxrevenue accrues to the elite, and it may become more tempting for the eliteto earn rents from exploiting the innovation. Moreover, the innovation maybe difficult to replicate, entry may be limited by large costs of entry or otherinstitutional factors that protect innovators from imitation by third parties.All these reasons would limit the benefit for the elite of allowing others toimplement the innovation. Finally, when φ = 0, it prefers to supply machinesmonopolistically.

Prop. 5. There exists φ∗ ∈ (0, 1) above which the appropriating elite’spreferred policy is open entry to supply of the innovation, and below which

23

the elite’s preferred policy is monopolistic supply by the elite. φ∗ increases inthe presence of large costs of entry.

Interestingly, when all tax revenue goes directly to the elite (i.e whenφ = 1), the elite has an interest in the greatest possible implementation ofthe innovation, so as to maximize tax revenue even if it means competingaway any rents they might derive directly from imperfect competition. Thisgoal is tempered by the (undoubtedly common) circumstance in which theelite has to share tax revenue with other public or private purposes. Whenφ < 1, another possible equilibrium emerges, where the appropriating elitewould prefer to eliminate formal-sector competitors, limiting both the supplyof machines and entry. In this case, the elite erects barriers that protect itsrents, at great social cost (Tullock, 1967).

To summarize, the elite uses regulation (and fiscal policy) to manipulatethe structure of the supply of machines. Appropriation and regulation gohand in hand: the elite benefits from appropriation only if it can limit theentry of private competitors. In turn, limiting entry only makes sense ifthe elite cannot hope to directly benefit enough from taxation, ie. if φ islow enough. If the elite benefits from taxation, it prefers competition, andderegulates entry accordingly. In that case appropriation brings only limitedbenefits. The difference between the appropriating and the non-appropria-ting elite is striking.

2.5 Appropriation

In stage 1, the elite considers whether to appropriate the innovation. Thereplicability of an innovation is decisive in the preference of the elite forappropriation with regulation, deregulation and taxation, or blocking of theinnovation. It determines the feasibility of certain strategies discussed above:appropriation by a member of the elite (with the support of state regulation),and imitation by third parties (under the umbrella, or in spite, of stateregulation).

If there were no cost to appropriation, the elite would appropriate ev-ery innovation. In all generality, absent any costs of appropriation, considerthe decomposition of UAE(MAE

f ) − UE(MEf ) into two terms: UAE(MAE

f ) −UAE(ME

f ) is nonnegative because MAEf maximizes UAE, and UAE(ME

f ) −UE(ME

f ) is the positive income of one innovator under a non-appropria-ting elite. Examples of innovations that the elite can appropriate costlessly

24

abound. Some ideas, once revealed, immediately become self-evident to all,such as the assembly line and the Fosbury flop, cf. Goldenberg et al. (2010).Appropriation is costless when innovations give value to an asset that peopledid not use before, and did not bother regulate. Spar (2003) suggests severalinstances of such innovations. Soon after the invention of the radio, for in-stance, states stepped in to regulate the usage of electromagnetic waves forwireless transmission, effectively creating property rights where none existed,to the benefit of the elite. The discovery of a valuable mineral deposit makesit available, but if the society’s elite does not have the capital or technolog-ical capacity to extract and process the mineral, the mine is effectively notreplicable by the elite. In this case, as in other cases of non-replicability, ifthe elite wants to exploit the opportunity, it has to permit outside investorsto do so.

For some innovations, replication is only a matter of investing enoughtime, energy, and possibly money. Even if appropriation comes at a cost,the elite may be willing to pay that cost if the benefits are sufficient, asis often the case with military technology, for instance. But appropriationmay be too costly. An innovation may be protected by preexisting propertyrights: for instance, many recent innovations are protected under the rel-atively extensive umbrella of contemporary intellectual property regimes.12

This extends to other institutions (Blockmans, 2010, shows how merchantguilds came to protect citizens on their travels in eleventh to thirteenth cen-tury Europe), although we may keep in mind that the elite may selectivelydisregard inconvenient institutions, e.g. native claims on land usage (Camp-bell & Anaya, 2008; Medina, 2016; Gomez Isa, 2019). An innovation mayeven be protected by customs: Becker & Pascali (2019) show how Catholi-cism protected Jews from competition in supplying certain financial servicesin Medieval Germany.

Finally, some innovations are simply not technically replicable. Jha (2013)shows that Muslim traders were safe from harm when dealing with Hindupartners in Indian ports, not because of property rights, institutions, or cus-toms, but thanks to non-replicable links with overseas suppliers. Trade se-crets are another way to avoid replication (by the elite or by third-parties):for instance, for many contemporary innovations, the accumulation of large

12Preexisting property rights, when they are recognized and enforced, put the innovatoron an equal footing with the owners of affected existing investments. With property rights,they can mobilize their stake to future wealth as much as owners of capital and try toinfluence the policy decisions of the elite.

25

amounts of personal data makes it very hard to imitate the services offeredby certain tech companies (Simon & Sichelman, 2017; Levine & Sichelman,2019; Fromer, 2019), who secure a large first-mover advantage.

Non-replicability imposes a constraint on available strategies at two stagesof our model: it may prevent appropriation by the elite, and it may alsoprevent entry of private imitators even if the elite chooses to allow openentry to supplying the innovation.

Even if the elite is able to appropriate the innovation, the benefits maybe insufficient. Section 2.4 argued that different conditions can lead theelite to prefer either to eliminate any competition to its own formal supply,or to increase competition in the formal supply (Props. 4 and 5). Theappropriating elite may not be able to eliminate all competition, and highenough fixed costs may limit the extent of competition that the non-appro-priating elite can encourage.

In this section, we simplify the discussion by comparing the two extremesituations: an appropriating elite that would eliminate all formal competi-tors (n = 1), and a non-appropriating elite that effectively eliminates themarket power of non-elite suppliers (n −→ ∞). To simplify the discussion,let us write the benefit of appropriating the innovation with notations usedin section 2.4 and abstracting from φ (i.e. taking φ = 1) for a moment:

VAE(1)− VE(∞) =

∫ MAEf

MEf

(α′G′′KMK + α′G′′MMm+G′M −H

)dm

+

∫ MEf

0

H ′mdm.

(11)

What features of the innovation determine these benefits? Previous sec-tions reveal several features of the innovation that play a role: location-de-pendence, concealability, complementarity, general-purposeness, and costs ofentry. Let us consider each in turn (concealability has an ambiguous effect,whose discussion we defer to the Appendix).

The elite has greater incentives to appropriate a mobile innovation thana location-dependent one. In Eq. 11, this corresponds to the last term: anincrease in H ′ also increases the incentives to appropriate. The reason isthat a mobile innovation not controlled by the elite is harder to tax andbenefit from, as per Prop. 2. On the other hand, if the elite appropriates theinnovation it can exploit it regardless of its degree of mobility (Prop. 3). If

26

we re-introduced φ < 1 this would attenuate the impact of mobility on theelite’s benefit from appropriation, but not change its sign.

Both the appropriating and the non-appropriating elites benefit from acomplementary innovation. The outcome therefore depends on relative sup-ply under either elite. When φ = 1, the gain from appropriation grows withthe complementarity of an innovation, without ambiguity. In Eq. 11, thiscorresponds to the first term on the RHS. Per Corollary 1, the result remainstrue for any φ ≥ φ1.

The effect of complementarity or rivalry is magnified by the extent towhich the innovation has general effects. Finally, large costs of entry limitthe extent to which the non-appropriating elite can control entry and compe-tition. As a result, they unambiguously increase the benefits of appropriation.

We can summarize the factors that affect the elite’s strategy with respectto appropriating an innovation, regulating entry to its production, and taxingit. Our analysis is not simple or mono-causal; it does however point to thedirections in which different forces pull.

1. The more mobile the innovation, the greater the elite’s incentive toappropriate it.

2. The more complementary the innovation is to the elite’s assets, themore attractive it generally is for the elite to appropriate the innovation.In the special case where the elite does not benefit that much fromtaxation (ie. φ < φ2), the effect of complementarity is non-monotonic.

3. The more general-purpose an innovation is, the more magnified is theimpact of complementarity on the incentive to appropriate.

4. Finally, the greater the entry barriers, the greater the incentives for theelite to appropriate the innovation.

3 Discussion and illustrations

There are many implications of the model developed above. It speaks to theimpact of the six features we have considered, both on their own and in inter-action with one another. It leads to expectations about the circumstances inwhich innovations will be adopted by a society, and in which they generaterents, and for whom. The analysis suggests when an incumbent elite will

27

adopt an innovation itself, or allow others to adopt it, or block it (section3.1). In this section, we return to the motivation for this theoretical exerciseto illustrate how the model structures explanations of patterns of receptivityor resistance to innovation. We start with a description of four particularlyprominent outcomes of elite response to innovations, ranging from adoptingand accepting them enthusiastically to blocking them. We then turn to someempirical illustrations of how our theory helps explain the adoption, block-ing, or otherwise of innovation by an elite. These include the example thatled off the paper, the difference between Chinese and Argentine responses tothe railroad (section 3.2). We then consider some additional illustrations.

3.1 Four canonical outcomes

The willingness and ability of a ruling elite to accept new economic activities– new technologies, policies, or ideas – has a powerful impact on broaderpatterns of economic growth and development. In this context, we are par-ticularly interested in cases in which an incumbent elite blocks or restrictsthe scope of welfare-improving innovations, or conversely permits and en-courages them. We can simplify somewhat the logic and implications of ourtheory along these lines by describing conditions we associate with the fourcanonical outcomes we suggested earlier.

Appropriation. The incumbent elite always has an incentive to takeover the innovation, but it is not always able to do so. The elite can appro-priate an innovation if it can replicate it. Beyond that, the elite’s incentiveto appropriate the innovation increases with the extent to which the innova-tion complements the elite’s assets and has a general impact (at least whenφ ≥ φ1). The reasons for this are straightforward: the innovation enhancesthe elite’s broad economic interests. Mobility and large upfront investmentsalso increase the elite’s incentive to appropriate the innovation. Mobilitymatters because appropriation removes the threat of flight to another juris-diction. Upfront investments matter because they would allow outsiders toearn monopoly rents in the sector, limiting the benefit to the elite of taxingthe innovation.13 Empirically, we can think of this as a category in whichthe incumbent elite allows the innovation, but insists on controlling it itself

13Note that this is a different argument from the hold-up problem in international invest-ment: the elite may decide to step in even if it cannot expropriate the upfront investmentalready laid out by the innovator.

28

— even if this means it will extract monopoly rents in its provision (hencesupply less of the innovation than would be socially optimal).

Although appropriation may have benefits for the elite, it can also becostly or simply impossible, as discussed above. The elite’s willingness andability to appropriate an innovation depends upon its replicability. If theelite does not have the ability to replicate the innovation, for whatever rea-son (perhaps technical), it will have to let somebody who can control theinnovation. In this context, the elite has a continuum of strategies thatrange from blocking to encouraging the innovation.

Blocking. An incumbent elite’s incentive to block an innovation in-creases in the extent to which the innovation rivals (competes with) theelite’s assets and in the extent to which it is of general impact. The reasonsare straightforward: a rival, general-purpose innovation threatens the elite’seconomic interests directly. At the same time, the less concealable is theinnovation, the more effective would be the effort to block it. Empirically,we can think of this as an instance in which the incumbent elite blocks awelfare-improving advance.

Encouragement. On the other hand, an incumbent elite’s incentive toencourage (and not tax) an innovation increases in the extent to which theinnovation complements the elite’s assets and in the extent to which it is ofgeneral impact. The reasons are again straightforward: a complementary,general-purpose innovation enhances the elite’s economic interests directly.Incentives to encourage an innovation increase in its mobility and in thedifficulty of concealing it. Mobility matters because if an innovation is notencouraged it will go elsewhere. To increase the supply of a complementaryinnovation, the elite also encourages entry and competition. Empirically, wecan think of this as a category in which the incumbent elite encourages theinnovation both in its own interests and (coincidentally, not altruistically) inthe interests of society as a whole.

Taxation. Alternatively, the elite allows the innovation, does not takeit over, but taxes it, balancing two different motives: revenue seeking andfactor-price manipulation. Punitive taxation comes down to blocking theinnovation; conversely, the model could accommodate negative taxation ofa highly complementary innovation (subsidization). A search for revenuealone would lead the elite to seek to maximize tax revenue, at the top ofthe Laffer curve. The incentive to use taxation to manipulate supply of theasset and thus returns to the elite’s assets, on the other hand, leads theelite to ‘overtax’ a rival innovation and ‘undertax’ a complementary one.

29

The more complementary (rival) and general-purpose (narrow-purpose) isthe innovation, the farther away from the top of the Laffer curve (on therespective side) the elite sets the tax rate. The elite sets a lower tax rate ona mobile or easily concealable complementary innovation, in order to avoiddriving production abroad or into the informal sector. A more concealableinnovation would lead the elite to focus on taxation for revenue purposesrather than the manipulation of supply, hence taxing nearer the top of theLaffer curve. Again, the elite encourages entry and competition, in order toaugment the share of the surplus that it can take for itself.

3.2 Blocking or encouraging: Railroads

We motivated this paper with the distinction between the Chinese and Ar-gentine reactions to the railroad. Clearly railroads were an innovation ofenormous general impact – the greatest advance in land transportation sincethe wheel – and were immobile and not concealable. This heightens interestsand makes it crucially important to know whether railroads were comple-ments or substitutes to elite economic activity. In the Chinese case, railroadswould have (and eventually did) allow foreign goods to penetrate the localmarket, with major negative effects on elite economic interests; they couldbe blocked, and they were. In the Argentine case, railroads were quite theopposite: by dramatically cheapening the cost of transport to export mar-kets, they were a crucial complement to the country’s landholding elite. Hererailroads were encouraged, as was the entry of domestic and foreign investorsto increase supply. Sometimes rail transportation was even subsidized. Thepolar outcomes are expected given the general-purpose, immobile, and notconcealable nature of the innovation.

3.3 Appropriating: Raw material extraction (and canals)

The technology to exploit a raw material deposit is another innovation thatcan be important, especially in developing societies. Although there is vari-ation, the most common situation is that the resource is first and foremostof interest to the elite as a source of tax revenue. The resource could be acomplement to the elite’s assets if it is an input into their production, butthis is unusual -– most such primary production is for export. Certainlythe new ability to mine a natural resource is not a substitute for the elite’sassets, especially when (as is usually the case) it uses little local labor. Such

30

primary production normally requires substantial up-front costs, and inas-much as there are other potential deposits elsewhere it can be regarded asmobile — that is, there is an incentive for the elite to encourage it in itsterritory. In line with these considerations, governments almost everywhereincline toward ownership (or tight control) of the mining of raw materials —oil wells, copper mines, and the like.

There is an interesting twist in thinking about the political economy ofraw material extraction, having to do with replicability. From the standpointof the society where the raw materials are found, the innovation is the abilityto extract them — exploration and mining technology. If this is readilyaccomplished by the incumbent elite — if it is easily replicable -– then theelite will apply the extractive technology itself and earn the rents accruing tothe resource. However, it is common for a developing country not to have theability to replicate the technology itself, in which case the next best policy isto permit others to exploit the resource and tax it optimally. Over time, asthe society learns about the mining technology, it becomes replicable — andthe government nationalizes it. This is fact describes the course of resourceexploitation in many developing societies.14

The Suez and Panama canals may be seen as analogous to a major natu-ral resource that exists only as the result of quite extraordinary technologicalinnovations. Their history indeed parallels that of the natural resource bases.Unlike domestic canals — which are analogous to railroads – these are largelyirrelevant to pre-existing domestic economic activity and serve primarily asa source of tax revenue. When, initially, the host societies were incapableof implementing or managing the technology, the host government permit-ted foreign ownership. As local capability – replicability — grew, the hostgovernment eventually appropriated the canals.

3.4 Suggestive broad patterns

Other scholars have looked at the pattern of technological innovation anddiffusion from both theoretical and empirical perspectives. In a series of ar-ticles using a database of innovations in the past several centuries, Comin& Hobijn (2004, 2009) analyze inter-country differences in technology adop-tion. Two of their findings are particularly relevant to our approach. First,they find that more trade-open societies are more likely to adopt innovations.

14Frieden (1994), and see also Vernon (1971).

31

They suggest that trade encourages more acceptance of innovation as incum-bents need it to face international competition – the technologies are morelikely to complement incumbent assets. It is also the case, we suggest, thateconomic elites in trade-open societies are more likely to already be investedin economic activities that are closer to the technological frontier, thus lessthreatened by innovations on this margin. Second, they find that politicalinstitutions that empower narrower economic interests – a more limited elite– are more likely to resist innovation. In a study of the political economy ofinnovation and economic dynamism, Solstad (2020) similarly finds that coun-tries with a narrower elite coalition are more resistant to innovation. Thesefindings suggest, in our framework, that a narrower ruling coalition findsmore innovations to be rival – or, conversely, that a broad ruling coalitionfinds fewer innovations to be rival.

3.5 The political economy of financial services provi-sion

Financial development is a central theme in modern economic history, fromVenice and Genoa through the City of London to the present day. Yet thereare substantial differences in the extent to which societies accept or encouragefinancial development. Financial innovation – from double-entry bookkeep-ing to modern international finance – has involved major advances over thecenturies. Finance is, of course, both general-purpose and mobile, as bankerscan take their business elsewhere. Depending on the era, it may or may notbe replicable. Financial development may complement elite assets by provid-ing capital; but it could also threaten the incumbent elite by making capitalavailable to rivals.

In the seventeenth and eighteenth centuries, western European elites werein need of capital to expand their trading and industrial interests; they wel-comed financial development but appropriated it, often as part of the estab-lishment of new central banks. More generally, Rajan & Zingales (2003) findthat countries open to trade and capital flows, both of which increase theelite’s desire for financing, are more likely to embrace financial development,defined as “the availability of arm’s length market finance.” This certainlyappears to be the pattern that has generally prevailed in developing coun-tries: for most of the twentieth century, they severely restricted financialdevelopment, but as trade and capital flows grew they embraced it. This is

32

consistent with the view that the elite originally limited rivals by strictly con-trolling access to finance, but as external conditions changed they permittedfinancial development as a complement to their own economic activities.

As this indicates, elites have incentives to block financial innovation if itis going to strengthen rivals. Benmelech & Moskowitz (2010) find that moreelite-dominated American states were more likely to impose usury laws thatfavored incumbents and restricted innovation. Becker & Pascali (2019) findboth patterns. In German regions where religious doctrine prohibited lendingby Catholics, Jewish bankers were welcome as complements to local elites.But with the Reformation, in Protestant areas, with restrictions on lendingby Christians loosened, Jews were more likely to be persecuted as rivals— especially where they were significant potential competitors to Christianfinanciers.

4 Extensions

The model developed here focuses on the purely material motivations of theelite, but innovation also has political and cultural consequences (section4.1). In this section, we discuss some of these broader non-economic aspectsand implications. Finally, we reconsider the underlying assumptions in thetiming of the model in section 4.2, and suggest how our model could relateto a wider set of stylized facts.

4.1 Material incentives, political power and identity

The framework we propose addresses the contest over the rents of innovation,and brings together six features that until now have typically been consideredseparately. There are at least two other sources of opposition to innovationthat this paper does not address: when it threatens the sources of someone’spower (Acemoglu & Robinson, 2000; Solstad, 2020), and when it threatenssomeone’s culture and identity (Juma, 2016; Mokyr, 2016). We do not ad-dress culture, but we believe that our framework can be accommodated todiscuss power.

In many aspects the contest over political power accentuates the contestover rents. Allowing innovators to derive rents from their innovations im-plies, in some cases, that they will command vast resources in the future.With such resources, they may in turn claim some sway over policy decision

33

making and over institutions – in a word, entry into the elite. Following inthe steps of Veblen (1908), Pistor (2019) recently argued that the law is notonly a defining element of capital and wealth, it is also a crucial element ofany asset’s income-yielding capacity. In the worst-case scenario, the innova-tors challenge the incumbent elite’s rule, and establish a new regime,15 thatmay be less protective of the incumbent’s wealth (Acemoglu, 2003; Powell,2004). If political conflict indeed depends on having access to resources (Ace-moglu, 2006; Collier et al., 2009), the incumbent elite may prefer to starvethe innovators, even at a cost to itself, rather than allow entry, dilution ofits political power, and loss of control over the regulation and taxation ofthe innovation (in line with the view in Solstad, 2020). The importance ofthis mechanism may explain the common view that the weaker the state, themore innovation (Mokyr, 1992), although our analysis shows the need for amore nuanced picture.

4.2 The timing of the game

The timing of the game reflects a simplified description of real life. It leavesaside some observations that could lead to interesting extensions of the model.

First, the elite sometimes allocates property rights based on the recogni-tion of de facto utilization of an asset. In Roman law, occupatio was one ofthe common modes of acquisition of land, and res nullius, of personal prop-erty. More recently, in common law, the concepts of ‘adverse possession’ and‘acquisitive prescription’ recognize that continual possession or occupation ofland translates into legal ownership (under conditions that vary by jurisdic-tion) or even sovereignty (Lesaffer, 2005). The concept generally applies toland, but it has also recently been used for intellectual property (Bagley &Clarkson, 2003) and patent law (Broder, 2007). This implies that the defini-tion of property rights does not always anticipate entry and imitation of aninnovation: sometimes, it reacts to an established situation. In other words,stage 1 does not always precede stage 2. With this in mind, our frameworkremains best adapted to study property rights inasmuch as they are drivenby the elite’s redistributive goals (sections 2.4 and 2.5).

Second, the elite sometimes changes the fiscal rules after the investmenthas been made (in other words, after the fixed costs of production have been

15Per Stasavage (2014), “a political regime results in the provision of property rights fora specific group, accompanied by significant barriers to entry.”

34

paid). Governments cannot make commitments to bind their future actions(Acemoglu, 2003). Ex post renegotiation of fiscal policy (or even outrightexpropriation of investments) may affect the supply of the innovation as wedescribed in section 2.1. For instance, Frieden (1994) discusses this hold-upproblem in international investment and its institutional consequences. Thisobservation implies that stage 3 does not always precede stage 4. While weabstract from ex post renegotiation between the inventor and the elite, ourframework adequately captures a setting where inventors take investmentdecisions anticipating the actual implementation of the fiscal policy, even ifthis implementation does not correspond to ex ante fiscal promises.

5 Conclusion

Whether a society embraces innovations or resists them plays a powerfulpart in their economic growth and development. Modern economic history isreplete with striking examples of rapid technological adaptation, and retro-grade resistance. In this paper, we have attempted to provide a theoreticallens with which to understand which innovations are most likely to be re-sisted, and which societies are most likely to resist them. We have focusedon inherent characteristics of the innovation, and of the society.

We posit a ruling elite that controls government policy, which it can useto tax and spend. This fiscal policy has two goals. The first is to affect thesupply of productive factors to the economy, taxing more heavily those whosesupply it would prefer to limit. The second is to redistribute income fromthose taxed to the elite. We study considerations that affect the balance withwhich the elite-controlled government pursues the first goal – factor supplymanipulation – rather than the second goal – redistribution – and the extentto which it does either.

Our analysis emphasizes the nature of the ruling elite’s economic assets,starting with whether they are complements or substitutes to the innovativetechnology, product, process, or policy. Naturally, the more the innovationcomplements the elite’s assets, the more enthusiastic the elite is about theinnovation; and the more the innovation rivals the elite’s economic activity,the more the elite attempts to limit or suppress it. The elite, for exam-ple, will tax a strongly rival innovation so heavily as to effectively block itfrom being supplied, while it will not tax and perhaps subsidize a stronglycomplementary innovation.

35

In addition, we ask whether the elite will adopt the innovation itself, orwill allow it to be exploited and implemented by others in the society. Allelse equal, the elite would prefer to control the innovation itself. However,there may be technical or other reasons why the elite cannot itself put theinnovation into production – the innovation may not be easy to copy or repli-cate. Replicability by individuals who are not in the elite will also determinehow effectively the government can discourage or encourage entry, hence sup-ply of the innovation. As a result, replicability will affect the ability of thegovernment to tax the innovation to redistribute to the elite.

Other features of the innovation also affect the elite’s policy toward it.Whether the innovation can be easily concealed from the fiscal authorities,and whether it can be simply moved to another jurisdiction, affects the pol-icy pursued. Similarly, whether the innovation has a broad, general-purpose,impact on economic activity, or rather a narrower one affects the elite’s at-titudes toward it. So too does whether the innovation requires large upfrontinvestments, even if the innovators are not credit-constrained.

From these features of the elite and of the innovation, we derive expecta-tions about the elite-dominated government’s policies toward the innovation.These policies run the spectrum from welcoming and encouraging the innova-tion and its supply, through limiting it both to affect its supply and to raiserevenue that can be redistributed to the elite, to blocking the innovation.

We use our theory to structure a brief comparison of the different re-sponse of two countries to the same innovation (the railroad). We furtherillustrate how the passage of time can affect the response of an elite to anovel technology. We summarize results from multi-country analyses by oth-ers that appear consistent with our theory, and suggest an application tothe acceptance or less of financial development and modernization in bothhistorical and contemporary contexts.

Our theory does not take into account the potential political impact of aninnovation, an issue addressed by other scholars. It also ignores other non-economic causes and effects of innovative activity and its reception. Nonethe-less, with a relatively spare theoretical apparatus we derive important impli-cations of the economic and technological factors we address, for which weprovide some illustrative examples.

The reception of innovation is central to the process of economic growthand development. This paper presents an integrated theory of some of thefactors that influence whether a society will accept and adopt new ideas andtechnologies, or will resist and impede their use. Its implications are relevant

36

to major issues in the political economy of economic growth and development.

References

Acemoglu, D. (2002). Directed technical change. Review of Economic Studies,69(4), 781–809.

Acemoglu, D. (2003). Why not a political Coase theorem? social conflict,commitment, and politics. Journal of Comparative Economics, 31(4), 620–52.

Acemoglu, D. (2006). A simple model of inefficient institutions. ScandinavianJournal of Economics, 108(4), 515–546.

Acemoglu, D. (2008). Oligarchic versus democratic societies. Journal of theEuropean Economic Association, 6(1), 1–44.

Acemoglu, D. & Robinson, J. A. (2000). Political losers as a barrier to eco-nomic development. American Economic Review: Papers & Proceedings,90(2), 126–30.

Ahmed, A. T. & Stasavage, D. (2020). Origins of early democracy. AmericanPolitical Science Review, 114(2), 502–18.

Allen, R. C. (2009). The British Industrial Revolution in Global Perspective.Cambridge University Press.

Bagley, C. E. & Clarkson, G. (2003). Adverse possession for intellectual prop-erty: Adapting an ancient concept to resolve conflicts between antitrustand intellectual property laws in the information age. Harvard Journal ofLaw & Technology, 16(2), 327–93.

Bates, R. H. & Lien, D.-H. D. (1985). A note on taxation, development, andrepresentative government. Politics & Society, 14(1), 53–70.

Becker, S. O. & Pascali, L. (2019). Religion, division of labor, and conflict:Anti-semitism in Germany over 600 years. American Economic Review,109(5), 1764–804.

Benmelech, E. & Moskowitz, T. J. (2010). The political economy of finan-cial regulation: Evidence from U.S. state usury lawsin the 19th century.Journal of Finance, 65(3), 1029–73.

Besley, T. & Persson, T. (2013). Taxation and development. In A. J. Auer-bach, R. Chetty, M. Feldstein, & E. Saez (Eds.), Handbook of Public Eco-nomics, volume 5 chapter 2, (pp. 51–110). Elsevier.

Blockmans, W. (2010). Constructing a sense of community in rapidly growing

37

European cities in the eleventh to thirteenth centuries. Historical Research,83(222), 575–87.

Boix, C. (2003). Democracy and Redistribution. Cambridge University Press.Broder, A. N. (2007). Comparing apples to APPLs: Importing the doctrine

of adverse possession in real property to patent law. NYU Journal of Law& Liberty, 2(3), 557–98.

Campbell, M. S. & Anaya, S. J. (2008). The case of the Maya villages ofBelize: Reversing the trend of government neglect to secure indigenousland rights. Human Rights Law Review, 8(2), 377–99.

Caselli, F. (1999). Technological revolutions. American Economic Review,89(1), 78–102.

Caselli, F. & Coleman, II, W. J. (2006). The world technology frontier.American Economic Review, 96(3), 499–522.

Collier, P., Hoeffler, A., & Rohner, D. (2009). Beyond greed and grievance:Feasibility and civil war. Oxford Economic Papers, 61(1), 1–27.

Comin, D. & Hobijn, B. (2004). Cross-country technology adoption: makingthe theories face the facts. Journal of Monetary Economics, 51(1), 39–83.

Comin, D. & Hobijn, B. (2009). Lobbies and technology diffusion. TheReview of Economics and Statistics, 91(2), 229–44.

Deaton, A. (2013). The Great Escape: Health, Wealth, and the Origins ofInequality. Princeton University Press.

Durand, R. & Vergne, J.-P. (2012). The Pirate Organization: Lessons fromthe Fringes of Capitalism. Harvard Business Review Press.

Frieden, J. A. (1994). International investment and colonial control: a newinterpretation. International Organization, 48(4), 559–93.

Fromer, J. C. (2019). Machines as the new Oompa-Loompas: trade secrecy,the cloud, machine learning, and automation. New York University LawReview, 94(4), 706–736.

Goldenberg, J., Lowengart, O., Oreg, S., & Bar-Eli, M. (2010). How dorevolutions emerge? International Studies of Management & Organization,40(2), 30–51.

Gomez Isa, F. (2019). The UNDRIP: an increasingly robust legal parameter.The International Journal of Human Rights, 23(1-2), 7–21.

Hirschman, A. O. (1978). Exit, voice, and the state. World Politics, 31(1),90–107.

Hoffman, P. T. (2015). Why did Europe conquer the World? PrincetonUniversity Press.

38

Jha, S. (2013). Trade, institutions and ethnic tolerance: Evidence from SouthAsia. American Political Science Review, 107(4), 806–32.

Juma, C. (2016). Innovation and its Enemies: Why People Resist New Tech-nologies. Oxford University Press.

Khan, B. Z. (2002). ‘The Fuel of Interest’: Patents and Copyrights in Amer-ican Economic Development. Cambridge University Press.

Khan, B. Z. & Sokoloff, K. L. (2001). The early development of intellectualproperty institutions in the United States. Journal of Economic Perspec-tive, 15(3), 233–46.

Krusell, P., Ohanian, L. E., Rıos-Rull, J.-V., & Violante, G. L. (2000).Capital-skill complementarity and inequality: A macroeconomic analysis.Econometrica, 68(5), 1029–1054.

Krusell, P. & Rıos-Rull, J.-V. (1996). Vested interests in a theory of growthand stagnation. Review of Economic Studies, 63(2), 301–29.

Lesaffer, R. (2005). Argument from Roman law in current international law:Occupation and acquisitive prescription. European Journal of Interna-tional Law, 16(1), 25–58.

Levine, D. S. & Sichelman, T. (2019). Why do startups use trade secrets?Notre-Dame Law Review, 94, 751–820.

MacMullen, R. (1988). Corruption and the Decline of Rome. Yale UniversityPress.

Mahon, Jr, J. E. (1996). Mobile Capital and Latin American Development.Penn State University Press.

Mayshar, J., Moav, O., & Neeman, Z. (2017). Geography, transparency, andinstitutions. American Political Science Review, 111(3), 622–36.

Medina, L. K. (2016). The production of indigenous land rights: Judicialdecisions across national, regional, and global scales. PoLAR, 39(S1), 139–53.

Milner, H. V. & Solstad, S. U. (2020). Technological Change and theInternational System. Technical report, Unpublished. Retrievedfrom https://s18798.pcdn.co/gripe/wp-content/uploads/sites/

18249/2020/06/Technology_Diffusion_and_the_International_

System-Milner-Solstad-2020.pdf on Jul 6, 2020.Mokyr, J. (1992). The Lever of Riches: Technological Creativity and Eco-

nomic Progress. Oxford University Press. Revised ed.Mokyr, J. (1994). Cardwell’s law and the political economy of technological

progress. Research Policy, 23, 561–74.

39

Mokyr, J. (2005). Long-term economic growth and the history of technol-ogy. In P. Aghion & S. Durlauf (Eds.), Handbook of Economic Growth,volume 1B chapter 17, (pp. 1113–80). Elsevier.

Mokyr, J. (2008). The institutional origins of the industrial revolution. InE. Helpman (Ed.), Institutions and Economic Performance (pp. 64–119).Harvard University Press.

Mokyr, J. (2016). A Culture of Growth: The Origins of the Modern Economy.Princeton University Press.

Parente, S. L. & Prescott, E. C. (1994). Barriers to technology adoption anddevelopment. Journal of Political Economy, 102(2), 298–321.

Parente, S. L. & Prescott, E. C. (1999). Monopoly rights: A barrier to riches.American Economic Review, 89(5), 1216–33.

Pistor, K. (2019). The Code of Capital: How the Law Creates Wealth andInequalities. Princeton University Press.

Powell, R. (2004). The inefficient use of power: Costly conflict with completeinformation. American Political Science Review, 98(2), 231–41.

Rajan, R. G. & Zingales, L. (2003). The great reversals: The politics offinancial development in the twentieth century. Journal of Financial Eco-nomics, 69(1), 5–50.

Rosenberg, N. (1963). Technological change in the machine tool industry,1840-1910. Journal of Economic History, 23(4), 414–43.

Rosenberg, N. (1969). The direction of technological change: Inducementmechanisms and focusing devices. Economic Development and CulturalChange, 18(1), 1–24.

Rosenberg, N. (1996). Uncertainty and technological change. In R. Landau,T. Taylor, & G. Wright (Eds.), The Mosaic of Economic Growth (pp.334–56). Stanford University Press.

Rosenberg, N. & Birdzell, Jr., L. E. (1986). How the West grew rich: Theeconomic transformation of the industrial world. Basic Books.

Rosenthal, J.-L. & Wong, R. B. (2011). Before and Beyond Divergence: ThePolitics of Economic Change in China and Europe. Harvard UniversityPress.

Sanchez de la Sierra, R. (2019). On the origins of the state: Stationarybandits and taxation in Eastern Congo. Journal of Political Economy,128(1), 32–74.

Scott, J. C. (2009). The Art of Not Being Governed: An Anarchist Historyof Upland Southeast Asia. Yale University Press.

40

Silve, A. (2018). Asset complementarity, resource shocks, and the politicaleconomy of property rights. Journal of Conflict Resolution, 62(7), 1489–516.

Simmons, B. A., Dobbin, F., & Garrett, G. (2007). The global diffusionof public policies: Social construction, coercion, competition, or learning?Annual Review of Sociology, 33(1), 449–472.

Simon, B. M. & Sichelman, T. (2017). Data-generating patents. NorthwesternUniversity Law Review, 111(2), 377–437.

Sokoloff, K. L. & Engerman, S. L. (2000). Institutions, factor endowments,and paths of development in the new world. Journal of Economic Perspec-tives, 14(3), 217–32.

Solstad, S. U. (2020). Political Competition in Dynamic Economies. Techni-cal report, Unpublished.

Spar, D. (2003). Ruling the Waves: From the Compass to the Internet, aHistory of Business and Politics along the Technological Frontier. MarinerBooks.

Stasavage, D. (2014). Was Weber right? the role of urban autonomy inEurope’s rise. American Political Science Review, 108(2), 337–54.

Stern, D. I. (2011). Elasticities of substitution and complementarity. Journalof Productivity Analysis, 36(1), 79–89.

Tullock, G. (1967). The welfare costs of tariffs, monopolies and theft. WesternEconomic Journal, 5(3), 224–32.

Veblen, T. (1908). On the nature of capital. Quarterly Journal of Economics,22(4), 517–42.

Vernon, R. (1971). Sovereignty at Bay. Basic Books.Williamson, O. E. (1983). Credible commitments: Using hostages to support

exchange. American Economic Review, 73(4), 519–40.

Technical appendix

Proof of Prop. 1. The only difficulty in establishing the proposition isto show that formal and aggregate supplies decrease with τ , while informalsupply increases. The proof is in three steps. (1) An increase in τ mustcorrespond to a decrease of aggregate supply, since a contrario by the first(competitive) equilibrium condition we would expect a decrease of formaland by the second of informal supply, an impossibility. (2) By the second

41

condition, informal supply increases when aggregate supply decreases. (3) Ifaggregate supply decreases while informal supply increases, it must be thatformal supply decreases.

Micro-foundation ofH ′H ′H ′. For simplicity, we have made two assumptionson H and H in the main text: they are both univariate and increasing.Interactions between informal and formal supplies are limited to competitionin the supply of identical machines to the production function G; even whenthe technologies they describe feature economies of scale, marginal returnsdecrease locally. As a robustness check, let us consider a more completemodel of the supply of the innovation, formally and domestically, informallyand domestically, and externally, and the corresponding three equilibriumconditions:

(1− τ)G′M(Mf +Mi) = S(Mf +Mi +Ma) + cf (Mf )G′M(Mf +Mi) = S(Mf +Mi +Ma) + ci(Mi)

D′(Ma) = S(Mf +Mi +Ma) + ca(Ma),(12)

where, in addition to the notations of the main text, Ma is the supply of theinnovation abroad, where it faces the demand D(Ma), S is the marginal costof producing the asset M for any of the three markets, and c is the marginalcost of bringing formal, informal, and foreign supply to their respective mar-kets. We assume that S, ci, cf , and ca are all increasing functions, and thatD′ is a decreasing function (as in the domestic market, we assume decreasingreturns, or at least nonincreasing returns to using the asset abroad). Equi-librium on the external market determines Ma as a function β of domesticsupply Mf +Mi, with −1 < β′ < 0. If domestic supply decreases by one unit,external supply increases by −β′ units: −β′ captures a highly intuitive defi-nition of the mobility of the innovation. With this notation, we can rewritethe two domestic equilibrium conditions as:{

(1− τ)G′M(Mf +Mi) = S((1 + β)(Mf +Mi)) + cf (Mf )G′M(Mf +Mi) = S((1 + β)(Mf +Mi)) + ci(Mi)

which look very much like the equilibrium conditions in the main text, withH(Mf ) = S((1+β)(Mf+α(Mf )))+cf (Mf ) (it is easy to verify that the proofof Prop. 1 above remains valid, even now that H and H are not univariate).Deriving this expression, we obtain that:

H ′ = (1 + α′)(1 + β′)S ′ + c′f , (13)

42

with α′ ∈ (0, 1) capturing how hard it is to supply the innovation in the in-formal sector, β′ ∈ (−1, 0) how hard it is to move the innovation abroad, andS ′ and c′f structural descriptors of the production and formal marketizationof the innovation.

Notes on Prop. 2. The proposition is a simple consideration of thefirst-order condition associated with the program of the elite, including itstwo corner solutions.

One difficulty that we wave away is the second order condition. Wewave it away not because it is obviously true (it is not, and this may bea limit to the generality of the proposition), but because the discussion ofthe concavity of UE seems sterile. The second derivative of UE is composedof several terms, that feature second derivatives α′′, H ′′, and third-partialderivatives G′′′KMM and G′′′MMM , of whose sign we have no general intuition.Perhaps reassuringly, the second derivative of UE has only two terms whosesign we know: 2φα′G′′MM − 2φH ′ < 0.

In the discussion of the proposition (and throughout the paper), we estab-lish comparative statics on objects that are mathematically not scalars,but functions. We only characterize general-purposeness by the scalar K.We characterize location-dependence by β′ (in the main text, we simply saythat location-dependence is captured by H ′), difficulty of concealment intoinformal supply by α′, and complementarity with invested capital by G′′KM ,all functions of Mf . There is no obvious total ordering of innovations by howlocation-dependent, easy to conceal, or complementary they are. What doesexist are intuitive partial orderings. Formally, we say that an innovation ismore location-dependent if the derivative of its local vs. foreign supply β′ ishigher for a subset of positive mass, and lower almost nowhere. With thispartial order imposed on innovations, we can compare the mobility of some,albeit not all, innovations. When we do, the comparison is highly intuitive.Identically, we can impose a partial order on innovations according to howeasy they are to conceal (α′), and to their complementarity with investedcapital (G′′KM). The comparative statics we propose throughout should beunderstood as relying on these partial orders – holding the other features con-stant – and formally, also holding decreasing returns on machines (G′′MM),marginal costs of aggregate supply S ′, and marginal costs of the formal mar-ketization of the innovation c′f constant.

These partial orderings, and the corresponding comparative statics, implyno concession in terms of the generality of our results – on the contrary. Anyset of innovations on which we can impose a total ordering by complemen-

43

tarity, by concealability, or by mobility is a subset of the innovations thatwe consider here, and our results apply immediately. Parameterizing a set ofinnovations – for structural econometrics, or for further formal explorationof the properties of innovations, for instance – would keep all our results, andprobably yield several more intuitions, although maybe not with the samedegree of generality as ours.

As a last clarification on Prop. 2, we often refer to three subsets ofinnovations: rival innovations, such that G′′KM < 0 for all values of Mf andK, complementary innovations, such that G′′KM > 0 for all values of Mf

and K, and IRS innovations, such that G′′KMK +G′′MMM > 0 for all valuesof Mf and K. In the space of all possible production functions G, a verysmall subset falls into one of these three categories. We are interested inthese three categories for two reasons: (1) they occur frequently in formaland structural models, and (2) we can derive clear-cut general results aboutsuch production functions. Two technical comments on these subsets arein order. First, because we are always working under the assumption ofdecreasing returns to machines, ie. G′′MM < 0, IRS innovations are a subsetof complementary innovations, and rival innovations are a subset of decrea-sing-returns-to-scale innovations. It is possible that an innovation may becomplementary and display decreasing returns-to-scale. Second, with IRS,∀Mf ≤ M,∀φ ≤ 1, G′′MMMf + G′′KMK/φ ≥ G′′MMM + G′′KMK > 0. Thisconsideration is useful when we derive the comparative statics on the ease ofconcealment.

Notes on Prop. 3. Again, the proposition is a simple consideration ofthe first-order condition associated with the program of the elite, includingits corner solution. With the same caveats, we wave away the second-ordercondition.

In the paper, we look closely at the differences and similarities betweenthe appropriating and the non-appropriating elites. To compare the utilityof the elite in both cases, we need to add a term to UE, corresponding to theopportunity cost of not producing the innovation for the non-appropriatingelite, ie.

∫H(m)dm. This term plays no role in the decision of the non-ap-

propriating elite, which explains why we overlooked it when we wrote theexpression of UE. It plays a role when the elite considers appropriating theinnovation or not.

Proof of corollary 1. Consider the non-appropriating elite when φ =0. The elite blocks a rival innovation, and does not tax a complementaryinnovation. In the absence of taxation, formal supply is MO

f , characterized

44

by G′M(MOf )−H(MO

f ) = 0. If the innovation is complementary, with G′′KMlarger than, but close to 0, the appropriating elite supplies MAE

f such thatG′M −H ≈ −α′G′′MMM

AEf > 0. Since G′M −H decreases with Mf , it means

that MAEf < MO

f . Define

φ2 ≡−G′′MM(MO

f )MOf

H ′(MOf )MO

f /α′(MO

f )−G′′MM(MOf )MO

f

(14)

and for φ < φ2, the non-appropriating elite facilitates a larger supply of theinnovation than the appropriating elite with a production function such that

α′(MOf )(G′′KM(MO

f ) + φG′′MM(MOf )MO

f ) = φH ′(MOf )MO

f .

With a partial order on innovations by how mobile they are, we can imaginea number of norms in the space of innovations. Corresponding to any suchnorm, we can define the concept of a boundary of a production function asother production functions close enough to the first one. To fix ideas, considerthe intuitive norm |G′′KM(MO

f ) − F ′′KM(MOf )| between production functions

F and G.The determinants of surplus supply, with the exception ofK, are functions

H ′, G′′KM , G′′MM , α′. Spaces of functions are only partially ordered and donot have such an obvious associated measure as the Euclidean space, andtherefore no corresponding concept of derivation. With these difficulties, wedo not provide a formal proof of the second part of Corollary 1. With an abuseof notations, we can however illustrate its logic. If we consider G′′KM as ascalar parameter of the model for a moment, holding other features constant,we use the implicit function theorem to write, for an interior solution,

d(MAEf −ME

f )

dG′′KM= − α′K

2α′G′′MM −H ′+

α′K/φ

2α′G′′MM − 2H ′

where, for clarity, the first term on the RHS is taken at MAEf , and the second

at MEf . Because H ′ > 0, holding α′, G′′MM , and K constant between MAE

f

and MEf , the denominator of the second term is negative and larger than the

denominator of the first term. When φ is close enough to 1, the second termis negative, but smaller in magnitude than the first term, which is positive.To be more formal, take two innovations that can be ranked by their degreeof complementarity, and compare their formal supply under an appropriatingand a non-appropriating elite. Following the logic of the implicit function

45

theorem, we can laboriously show that when φ is close to 1, surplus supplyis larger for the more complementary innovation

The reasoning is identical when we consider a ‘comparative static’ on theease of concealment, but less fruitful. Again, abusing notations, we wouldwrite

d(MAEf −ME

f )

dα′= −

G′′MMMAEf +G′′KMK

2α′G′′MM −H ′+G′′MMM

Ef +G′′KMK/φ

2α′G′′MM − 2H ′

−(1 + β′)S ′ME

f

2α′G′′MM − 2H ′,

where the last term on the RHS is positive, but where, for the first twoterms, too many signs are contingent for any result to hold generally, andfor any specific results to be interesting. The last term corresponds to thedirect effect of concealment on the RS motive, that gives the elite an incen-tive to appropriate the innovation. The first two terms correspond to theinteraction between concealment and rivalry / IRS, but their combined signis inconclusive.

A note on the Lagrange multipliers in Eqs. 8 and 10. We haveconsidered throughout that the elites cannot subsidize the production of ma-chines, ie. establish a negative tax rate on the innovation. The Lagrangemultipliers λn and λAE correspond to that assumption. Changing the as-sumption does not affect our results. It would just simplify Eqs. 8 and 10by the corresponding terms.

Notes on and proof of Prop. 5. We do not need to solve the appro-priating elite’s program in full.

(1) We rely on an intuition from Prop. 1. We assume that τ is uniquelydetermined by the elite’s choice of Mf , µf , and n, by the equilibrium con-dition. Formally, we have only shown it in the competitive case. As before,we wave this discussion away, not because it is obviously true (it is not, andthis is maybe a limit to the generality of the proposition), but because thediscussion seems sterile. It would require again require careful considerationof third-partial derivatives of G and second derivative of α, of whose sign wehave no general intuition.

(2) We change variables, and consider X =Mf−µfn−1 . Holding Mf and n

constant,

46

1

n− 1

∂UAE∂X

= H(Mf − (n− 1)X)− H(X)

(1 + α′X/εd)2− H ′(X)X

1 + α′X/εd,

equal to 0 when X = 0 and negative when X = Mf/(n + 1). To establishthat in equilibrium µf ∈ ((Mf − µf )/(n− 1), 1), we would like to verify thatthe second partial derivative of UAE is negative. We can write

1

n− 1

∂2UAE∂X2

= −(n− 1)H(µf )−H ′(X)

(1 + α′X/εd)2+

2α′H(X)

εd(1 + α′X/εd)3

− H ′(X)

1 + α′X/εd+

α′H ′(X)X

(1 + α′X/εd)2− H ′′(X)X

1 + α′X/εd.

The five first terms of this expression are negative, and the sign of the lastterm is indeterminate. Not in all generality, but with a reasonable degree ofconfidence, we conclude that except in pathological cases, when φ = 1 (andby continuity, when φ is large enough), the elite supplier produces more thana private supplier, but leaves some space for private suppliers.

(3) Going one step further, we consider the fraction ν = µAEf /MAEf , equal

to 1 when n = 1, and converging to 0 as competition increases (this impliesthat the optimal market share of the elite when n is very large converges to0). Again, we assume a non-pathological situation where ν is a decreasingfunction of n. In that case, we find that dVAE/dn is positive iff n > ν−1((φ+λAE)/(1 + λAE)). As a result, VAE is a quasi-convex function of n.

Notes on the gain from appropriation. In the corresponding section,we do not feel that we can write a formal general proposition with enoughconfidence, although many of the intuitions we discuss hold with the mostcommon functional forms of the literature. To consider the effect of a featureof the innovation on the gain from appropriation, Eq. 11 implies we need toconsider how supply varies under appropriating and non-appropriating elitesand how the integrand varies with the feature under consideration. As anillustration, let us consider the feature whose effect is most uncertain, ie.the ease of concealment, which we have characterized implicitly with H ′ andexplicitly with α′ (when the innovation becomes harder to conceal, α′ andH ′ increase, in the partial order described above). To establish the result,for instance, that the gain from appropriation decreases with ease of con-cealment (holding constant other features of the innovation), it is sufficient

47

to establish that the sign of G′′KMK + G′′MMm is negative over the range(ME

f ,MAEf ), and that surplus supply is positive and increases; or that the

sign of G′′KMK+G′′MMm is positive over the range (MEf ,M

AEf ), and that sur-

plus supply is negative and decreases. These conditions are each sufficient.Neither is necessary, but it seems difficult to write a more encompassing con-dition without imposing functional forms. Corollary 1 is inconclusive aboutthe variation in surplus supply. Although we have shown above that thedirect effect of concealment on surplus supply is positive, the indirect effectthrough its interaction with rivalry / IRS is unclear. As the last consider-ation, per Corollary 1, if φ ≥ φ2, M

AEf ≥ ME

f . Therefore when φ > φ2,for an innovation that displays IRS, the gain of appropriation decreases withease of concealment. These promising considerations do not amount to anyconclusive result.

Ease of concealment is inconclusive, but the same reasoning on mobility,complementarity, and general-purposeness yields the considerations devel-oped in the main text. One specific note on complementarity: in the maintext, we propose formally that the gain of appropriation increases with com-plementarity when φ ≥ φ1. The result holds more generally. In particular,it holds whenever at 0, α′G′′KMK ≤ −φ(G′M − H) and whenever G′′KM islarge enough to ensure that MAE

f ≥ MOf . However, for φ < φ1, the range

MAEf −ME

f is not increasing everywhere with complementarity. For φ < φ2,there is even a subset of production functions on which supply under thenon-appropriating elite would exceed supply under the appropriating elite,ie. MAE

f < MEf , and on which the gain of appropriation would decrease with

complementarity.

48