The dynamics of international exploitation

Abstract

This paper develops a framework to analyse imperialistic international relations (IIR) and the dynamics of international exploitation. A new exploitation index is proposed which captures the territorial structure of IIR: wealthy nations are net lenders and exploiters, whereas endowment-poor countries are net borrowers and exploited. Capital flows transfer surplus from countries in the periphery of the global economy to those in the core. However, while international credit markets and wealth inequalities are central in generating international exploitation, other factors, including labour-saving innovations, are shown to be essential in explaining its persistence.

Keywords

International exploitation imperialism unequal exchange uneven development capital movements

Introduction

During the last four decades, national economies have become increasingly integrated and have widely adopted neoliberal policies. This phenomenon, often labelled ‘globalisation’, has far-reaching implications, and it has stimulated a vast debate (Coe and Yeung, 2001; Harvey, 2003, 2005; Sheppard, 2016). Globalisation has significant effects within each country, but special attention has been paid to its repercussions on the relations between countries. Different, if not opposite, analyses have been proposed, even outside of the neoclassical camp. Some argue that ‘globalisation’ is just a new name for old imperialistic practices, including the use of force (Amin, 1999; Petras and Veltmeyer, 2001). According to others, a new world is taking shape, in which such practices play no role, and the classical concept of imperialism is not useful to understand the global economy (Hardt and Negri, 2000).

While admitting that classical approaches may be outdated, this paper defends the theoretical and empirical relevance of the concept of imperialism to analyse current international relations and features of geographic stratification of the global economy.

Based on Roemer’s (1982) theory of exploitation, a theoretical (albeit not historical) distinction can be drawn between a notion of feudal imperialism, in which the use of force and non-competitive distortions play a definitional role – as in ‘classical’ theories of imperialism (Hobson, 1954 [1902]; Lenin, 1970 [1917]; Luxemburg, 1951 [1913]) and neo-Marxist theories of dependency (Baran, 1968; Frank, 1978).¹ And a notion of capitalist imperialism, in which exploitation and mutual gains from trade may coexist. Capitalist imperialism is thus related to Hobson’s (1954 [1902]) ‘internationalism’ and to the concept of ‘informal imperialism’ (Griffin and Gurley, 1985), in that power relations between states and exploitation stem primarily from economic activities, rather than extra-economic coercion. It also captures some key aspects of Harvey’s (2003, 2005) own seminal notion of capitalist imperialism, such as its emphasis on ‘imperialism as a diffuse political and economic process in space and time in which command over and use of capital take primacy’ (Harvey, 2003: 26).

More precisely, we conceive of capitalist imperialism as a system ‘based on the export of capital from advanced countries to less developed regions. . .accompanied by the utilization of political and military resources to protect and maintain the means of production over which control has been acquired’ (Evans, 1979: 16), and by segmented labour markets. Empirically, this allows us to incorporate two crucial features of the contemporary global economy, namely capital mobility and restrictions to labour movement (Harvey, 2003, 2005; Sheppard, 2016). Theoretically, this makes our approach conceptually close to theories of unequal exchange (Emmanuel, 1972; Foot and Webber, 1983; Roemer, 1983; Sheppard, 1984; Sheppard and Barnes, 1990; Webber and Foot, 1984).

This paper aims to show that, even granting that the feudal aspects of colonial relations may have become less significant, the concept of capitalist imperialism is relevant to analyse structural features of the global economy. First, we propose a new measure of unequal exchange across borders based on the theory of exploitation – an exploitation intensity index. Contrary to the received view, this measure is theoretically robust and logically consistent. Indeed, it can be used to precisely define the concept of capitalist imperialism and the notions of core and periphery of the global economy that are central in dependency theory and in world systems theory (for a comprehensive review, see Ricci, 2021: chapter 2).

Far from being metaphysical, the exploitation index is empirically measurable based on widely available data. We calibrate our model to analyse the exploitation status of all countries in 2017 and use the index to characterise the full structure of Imperialistic International Relations (henceforth, IIR). Unlike in post-modern approaches to globalisation, such as Hardt and Negri (2000), which depict IIR as immaterial and deterritorialised, the economic and geographic structure of imperialism can be identified, whereby wealthy nations gain, and endowment-poor countries lose from exploitative relations, as surplus is transferred from the latter to the former.²

The second contribution of the paper is the analysis of the mechanism that allows such surplus transfer to occur. Unlike in classical approaches, where ‘characteristic of [imperialism] are: lending abroad, railroad constructions, revolutions, and wars’ (Luxemburg, 1951 [1913]: 419), the role of capital movements is emphasised. This is an important feature of recent accounts of imperialistic practices, according to which the imposition of global free trade and the free international circulation of capital are among the main components of globalisation (Duménil and Lévy, 2004: 659), and countries’ positioning in highly connected credit markets are a primary channel through which imperialistic relations manifest (Harvey, 2005: 134–135).

This paper shows that competitive markets, profit-seeking and international wealth inequalities are central in generating IIR. The exploitative nature of IIR can be understood focusing on credit relations and international capital flows: wealthy nations are net lenders and exploiters, and form the core of the global economy, whereas endowment-poor countries are net borrowers and suffer from exploitation, and are relegated to the periphery.

Crucially, IIR can be explained without any controversial assumptions on the existence of some inherent contradiction of capitalism that ‘spurs capital on to a continual extension of the market’ (Luxemburg, 1951 [1913]: 347) due to realisation problems (Hobson, 1954 [1902]; Lenin, 1970 [1917]; Luxemburg, 1951 [1913]), overaccumulation (Harvey, 2003, 2005) or the falling rate of profit (Carchedi and Roberts, 2021). Accumulation is unnecessary to understand IIR. As argued by Howard and King (1999), countries in the core have an incentive to exploit those in the periphery independently of accumulation needs: the incessant quest for profits.

While competitive markets and inequalities in wealth and development are crucial in generating IIR, we prove – and this is the third contribution of the paper – that they are not sufficient to make them persistent. Lacking any countervailing tendencies, accumulation eventually makes capital abundant, leading to the disappearance of international exploitation. This result is in stark contrast with the reality of the global economy (Sheppard, 2016) and it raises the issue of the mechanisms guaranteeing the persistence of IIR. In this paper, we consider endogenous technical change and adaptive consumption norms, which introduce a degree of non-linearity and cyclicality in the interaction of accumulation and distribution – arguably, two important features of the dynamics of capitalist economies (Bergmann et al., 2009; Plummer and Sheppard, 2006; Plummer et al., 2012). We see this as a first, crucial step in the analysis of the persistence of a spatially differentiated, unequal international economy.

As our analysis of the structure of IIR involves the adoption of a formal model and computational tools, we shall briefly discuss some methodological aspects of our research. This will also allow us to highlight some key differences with the recent literature.

Methodology

A detailed historical and institutional analysis is crucial for a thorough understanding of imperialism and economic inequality across regions. In this paper, we use theoretical abstraction – and specifically, mathematical formalism – for various reasons.

One key contribution of the paper is the proposal of a measure of surplus transfers across countries, and all measurement is theory-specific. We set up a theoretical framework using mathematical formalism in order to define an exploitation index that can be used in the empirical analysis of IIR. We use mathematics as ‘the language of theory’ (Plummer et al., 2012: 538) which is particularly useful ‘in clarifying and developing concepts’ (Barnes, 1990: 1004). The clarity and rigour afforded by formal methods is particularly important given the widespread scepticism surrounding exploitation theory in both mainstream and heterodox quarters.

We also aim to contribute to theoretical debates on the fundamental features of IIR, and use computational simulations to examine some simplified, counterfactual scenarios for three purposes. First, we use theoretical abstraction in order to isolate some key characteristics of the global economy. Therefore, although our key assumptions can be relaxed and all of our main insights continue to hold in more general, and realistic, settings, we deliberately focus on equilibrium states of one-good, perfectly competitive economies with perfect capital mobility, equal profit rates and free access to technology.³ We aim to show exploitation in international market exchanges ‘arises as a natural product of the capitalist mode of production on a global scale, in its purest form of a perfectly competitive world economy’ (Ricci, 2021: 7).

It is remarkable, from this perspective, that an exploitation phenomenon and IIR emerge even in the absence of a number of empirically relevant mechanisms that play a central role in various strands of the literature, such as discrepancies between actual and purchasing power parity exchange rates (Hickel et al., 2021; Köhler and Tausch, 2002; Ricci, 2021, 2022), productivity differentials and unequal access to technology (Baiman, 2006, 2014; Carchedi and Roberts, 2021; Ricci, 2021, 2022; Tsaliki et al., 2018), noncompetitive distortions and rentierism (Amin, 1999; Baiman, 2020; Cope, 2019; Petras and Veltmeyer, 2001), factor immobility and industrial specialisation (Baiman, 2006, 2014), international wage and/or interest rate differentials (Cope, 2019; Hickel et al., 2021) and price/value discrepancies (Carchedi and Roberts, 2021; Tsaliki et al., 2018). Without denying the relevance of these factors, our analysis forcefully brings to the fore the role of credit markets and the constraints that limited wealth imposes on countries in the periphery.⁴ Property relations and more specifically control over capital are, in our view, the defining feature of the capitalist world economy, both within and across borders.

Second, our analysis may be interpreted as showing that IIR can be condemned independently of the non-competitive and violent forms they may – and usually do – take. They can also be condemned without appealing to such factors as price/value deviations, exchange rate misalignments or productivity differentials, whose inherent normative relevance is not entirely obvious and which are empirically relevant, but nonetheless contingent, features of the global economy. In our view, a capitalist world system with wage equalisation, a common technology, perfect competition and no exchange rate misalignment might still be highly unjust.

The model provides the foundations for a condemnation of imperialism by specifying the theoretical counterfactual against which IIR should be evaluated – namely, an economy in which international disparities in wealth are annihilated. In the global economy wealth inequalities do seem to be morally arbitrary, as primitive accumulation in the core has taken place – to a large extent – at the expense of the periphery, as argued in chapter 31 of Capital I, where Marx (1976 [1867]: 926) famously refers to colonialism as robbery, looting and plunder, such that ‘capital comes dripping. . .from every pore, with blood and dirt’. The wealth inequalities captured by our data, and driving IIR, have embedded within them the long spatial history of colonialism and post-colonial domination (Cope, 2019; Hickel et al., 2021; Sheppard, 2016).

Third, our counterfactual analysis points to an explanatory gap by showing that competitive markets and wealth inequalities are crucial in generating IIR; but they are not sufficient to make them persistent. We think that this is an important insight: the issue of the mechanisms guaranteeing the persistence of IIR is central and in order to tackle it, it is necessary to go beyond the essentially static framework that prevails in much (though by no means all) of the extant literature. Indeed, by fully specifying the economic environment and making all relevant assumptions explicit, a general dynamic formal framework may produce unexpected results, and highlight mechanisms that would not be obvious otherwise.

Framework

Consider a dynamic extension of Roemer’s (1982) accumulating economy with a credit market and only one good produced and consumed.⁵ There are $N$ countries that compete in the world economy for $T$ periods. A country is generically denoted as $v$ .⁶ At the beginning of each production period $t = 0, 1, \dots, T$ , there is a (Leontief) production technique $(A_{t}, L_{t})$ that specifies the amount of the produced good, $A_{t}$ , and labour, $L_{t}$ , necessary to produce one unit of output, where $0 < A_{t} < 1$ and $L_{t} > 0$ . The technique $(A_{t}, L_{t})$ is not necessarily fixed: it may vary over time due to technological innovations. As argued in section ‘Methodology’, we analyse IIR abstracting from noncompetitive distortions and differences in the structure of production, and therefore assume that all countries have access to the same techniques.⁷

In every period $t$ , countries have (possibly different) endowments of effective labour, $l_{t - 1}^{v}$ , and capital, $ω_{t - 1}^{v} \geq 0$ , inherited from previous periods. The labour endowment consists of country $v$ ’s population, denoted by $ℓ_{t - 1}^{v} > 0$ , and its (average) skill level, or human capital, denoted by $s_{t - 1}^{v} > 0$ . Thus, country $v$ ’s effective labour endowment is $l_{t - 1}^{v} = ℓ_{t - 1}^{v} s_{t - 1}^{v}$ .

As in Roemer (1982), production takes time and every country must be able to lay out in advance the operating costs for the production activities it operates. A country $v$ endowed with $(l_{t - 1}^{v}, ω_{t - 1}^{v})$ can either use its own capital to operate the technique $(A_{t}, L_{t})$ to produce $x_{t}^{v} \geq 0$ , requiring an amount $A_{t} x_{t}^{v}$ of capital and $L_{t} x_{t}^{v}$ of labour; or it can borrow capital on international credit markets in order to operate $(A_{t}, L_{t})$ to produce $y_{t}^{v} \geq 0$ , requiring an amount $A_{t} y_{t}^{v}$ of capital and $L_{t} y_{t}^{v}$ of labour. Alternatively, it can lend its capital abroad, $z_{t}^{v} \geq 0$ . Countries can borrow or lend at a market rate $r_{t}$ .

Letting $p_{t - 1}$ denote the price of the produced commodity at the end of $t - 1$ and beginning of $t$ , the market value of country $v$ ’s endowment – its wealth – is $W_{t - 1}^{v} = p_{t - 1} ω_{t - 1}^{v}$ . The wealth that is not used for production activities, and is not lent abroad, can be saved and sold on international markets at the end of the period, $δ_{t}^{v} \geq 0$ .

As in standard Marxist theory, we conceive of capitalist economies as driven by the need to accumulate (formally, maximise wealth) subject to workers consuming $b_{t} > 0$ per unit of labour performed. Country $v$ ’s labour performed is denoted by $Λ_{t}^{v} = L_{t} x_{t}^{v} + L_{t} y_{t}^{v}$ . Within every period $t$ , we consider $b_{t}$ as a constant parameter, but we do allow it to change endogenously over time (see section ‘Persistent exploitation cycles in the global economy’ below). This is motivated by our focus on the dynamics of exploitation in a global economy characterised by a drive to accumulate, rather than on consumer choices. Theoretically, it is consistent with the classical-Marxian tradition where consumption is largely the product of social norms, rather than utility maximisation, and it allows us to analyse IIR abstracting from heterogeneous consumption behaviour.

Following Roemer (1982, 1983), we focus on Reproducible Solutions (henceforth, RS): at a RS, in every period (a) all countries maximise their wealth; (b) aggregate capital is sufficient for production (and speculative saving) plans; (c) the credit market clears; (d) aggregate supply is sufficient for consumption and accumulation plans. (A detailed description of the countries’ problem and the definition of RS can be found in Appendix A.)

Given the prices observed in period $t$ at a RS, $(p_{t - 1}, p_{t}, r_{t})$ , we can define an implicit wage rate $w_{t}^{n} = \frac{p_{t} - (1 + r_{t}) p_{t - 1} A_{t}}{L_{t}}$ at $t$ : $w_{t}^{n}$ is the (residual) payment of (unit) labour services in each country after all loans (including interest) are repaid. Unlike in some of the classic contributions in dependency theory, as all countries have access to the same technology, and international commodity and credit markets are competitive, the wage rate per effective labour performed is identical across countries even in the absence of an international labour market.⁸

One important feature of the concept of RS is that full employment of productive factors is not a generic outcome in equilibrium. Cogliano et al. (2019) have shown that a knife-edge condition can be derived which uniquely guarantees that both capital and labour are fully employed: $l_{t} = L_{t} A_{t}^{- 1} ω_{t - 1}$ , where $ω_{t - 1}$ is aggregate capital and $l_{t}$ is the global (effective) labour force.⁹ At any $t$ , if aggregate capital is not enough to employ the global labour force ( $l_{t} > L_{t} {A_{t}}^{- 1} ω_{t - 1}$ ) then the wage rate falls to the subsistence level. Conversely, if $l_{t} < L_{t} {A_{t}}^{- 1} ω_{t - 1}$ , then the global labour force is scarce relative to aggregate capital, which drives $r_{t}$ to zero.

Exploitation

Two structural features arguably characterise imperialistic international relations. First, certain countries systematically benefit disproportionately from interaction in the global economy compared to others. Second, a stratification of countries into a core and a periphery emerges based on their position in international markets, which highlights one key mechanism that allows the former to gain at the expense of the latter. We capture these two aspects of IIR focusing, respectively, on the notions of exploitation and classes.

Consider first the concept of exploitation. In the Marxist theory of exploitation as the unequal exchange of labour, exploitative international relations are characterised by systematic differences between the labour ‘contributed’ by agents in country $v$ and the labour ‘received’ by them via their national income. The labour contributed by country $v$ at $t$ is simply $Λ_{t}^{v}$ . As for the amount of labour received by $v$ , the key point to note is that focusing on actual consumption would be highly misleading: poor and rich countries may happen to have similar consumption levels and yet it would be counterintuitive to consider them as receiving similar amounts of labour.¹⁰ Conceptually, exploitation status should not depend on idiosyncratic choices and depend instead on potential consumption. Hence, we focus on the maximum level of consumption that a country can achieve subject to being able to reproduce itself over time.

Formally, for all countries $v$ and factor prices $(r_{t}, w_{t}^{n})$ , let $R_{t}^{v} (W_{t - 1}^{v}, Λ_{t}^{v}; (r_{t}, w_{t}^{n}))$ denote country $v$ ’s gross revenue, which depends on $v$ ’s endowments and on equilibrium prices:

R_{t}^{v} (W_{t - 1}^{v}, Λ_{t}^{v}; (r_{t}, w_{t}^{n})) \equiv (1 + r_{t}) W_{t - 1}^{v} + w_{t}^{n} Λ_{t}^{v} .

(1)

Gross national revenue is the sum of total earnings ( $w_{t}^{n} Λ_{t}^{v}$ ) and gross capital income ( $(1 + r_{t}) W_{t - 1}^{v}$ ). A country $v$ ’s potential consumption, $c_{t}^{v}$ , is then given by:

p_{t} c_{t}^{v} = R_{t}^{v} (W_{t - 1}^{v}, Λ_{t}^{v}; (r_{t}, w_{t}^{n})) - p_{t} ω_{t - 1}^{v} .

(2)

Equation (2) identifies a counterfactual, normatively relevant consumption level that a country could sustainably afford in period t. The first term is intuitive: a country’s potential consumption depends on gross national income which sets an absolute upper bound on aggregate consumption. The second term embodies the normative requirement that the country be able to reproduce itself over time: potential consumption is identified by subtracting the cost of replacing the country’s initial capital. If a country is so backward that it can barely reproduce its capital stock, then arguably it is not receiving any labour, whatever its actual consumption level.

The amount of labour embodied in one unit of the final good, $λ_{t}$ , is the sum of the direct labour spent in its production, $L_{t}$ , and the labour embodied in the inputs used in its production, $λ_{t} A_{t} : λ_{t} = λ_{t} A_{t} + L_{t}$ ; or equivalently, $λ_{t} = L_{t} {(1 - A_{t})}^{- 1}$ .

We focus on within period exploitative relations (Veneziani, 2007) and define exploitation status in every period $t$ as follows:

Definition 1 [Veneziani and Yoshihara (2017)]: Country $v$ is exploited at $t$ if and only if $Λ_{t}^{v} > λ_{t} c_{t}^{v}$ ; it is an exploiter if and only if $Λ_{t}^{v} < λ_{t} c_{t}^{v}$ .

Definition 1 incorporates standard Marxist intuitions concerning exploitation as the unequal exchange of labour and it provides a rigorous analytical framework to identify the countries in the core and in the periphery of the global economy. Yet it yields a rather coarse picture of IIR: international economies with similar numbers of exploiting and exploited countries may still be very different depending on how much the former exploit the latter.

The normative reach of Definition 1 can be extended to provide a finer and more comprehensive description of IIR, by focusing on the intensity of exploitation. For, it is certainly desirable to have a notion of exploitation that allows us to make statements such as ‘country A is more exploited than country B’, or ‘IIR are becoming increasingly exploitative over time’.

Based on Definition 1, a natural index of exploitation intensity is:

e_{t}^{v} = \frac{Λ_{t}^{v}}{λ_{t} c_{t}^{v}},

(3)

so that country $v$ is an exploiter (exploited) at t if and only if $0 \leq e_{t}^{v} < 1 (e_{t}^{v} > 1)$ .

The index allows for a much richer analysis of IIR. For example, one can say that the greater $e_{t}^{v}$ the more exploited $v$ is and, for any two countries $v, μ$ , if $e_{t}^{v} > e_{t}^{μ} > 1$ then $v$ is more exploited than μ. And so on. We can also analyse the dynamics of the distribution of $e_{t}^{v}$ , and ask a number of questions about the structure of IIR. A more polarised distribution of $e_{t}^{v}$ , for instance, suggests a worsening of IIR. More generally, the measurement of some aggregate degree of exploitation raises similar issues as the measurement of income or wealth inequalities.

Three important features of the index should be emphasised. First, it has robust theoretical foundations. It is conceptually related to the ‘New Interpretation’ of Marx (Duménil, 1980; Foley, 1982). In the New Interpretation, at the aggregate level, in a given economy, workers are exploited if the share of national income they obtain is lower than the share of labour they perform, and a similar intuition holds if one looks at the exploitation of different types of labour (Duménil et al., 2009). We extend this intuition to the international context and to individual countries. For Definition 1 can be equivalently interpreted as stipulating that a country is exploited (an exploiter) if the share of labour it contributes to the global economy is higher (lower) than the share of income it receives.¹¹ Indeed, by adopting the latter interpretation, Veneziani and Yoshihara (2017, 2018) have extended Definition 1 to $n$ -good economies with general technologies and preferences, while Veneziani and Yoshihara (2015, 2017) have used an axiomatic approach to prove that Definition 1 is the only definition that satisfies a small set of properties that capture the core insights of exploitation theory.

Second, the index embodies some intuitive normative views. For $e_{t}^{v}$ can be interpreted as the amount of (effective) labour supplied relative to the labour necessary to produce $v$ ’s potential consumption. Thus exploitative relations are equivalent to inequalities in labour hours supplied to earn one unit of income (measured in the labour numéraire). From this perspective, exploited countries need to work more than exploiters in order to secure an analogous standard of living, and the additional labour they contribute to the global economy is transferred to the latter. In IIR, exploitation represents an unreciprocated transfer of labour from the periphery to the core, and the higher the amount of labour transferred from a country in the periphery, the higher $e_{t}^{v}$ .

The exploitation index differs from most measures used in the empirical literature. Unlike classical measures of unequal exchange (Carchedi and Roberts, 2021; Foot and Webber, 1983; Tsaliki et al., 2018; Webber and Foot, 1984), $e_{t}^{v}$ does not capture price-value deviations, whose normative content is unclear (Schweickart, 1991). Nor does it capture value transfers arising from international wage differentials (Cope, 2019), discrepancies between market and purchasing power parity exchange rates (Hickel et al., 2021; Köhler and Tausch, 2002; Ricci, 2021, 2022), or productivity differentials (Ricci, 2021, 2022). Although these phenomena are of great relevance, the unfairness of international relations is not reducible to them. A capitalist global economy with equal wages, a common technology, perfect competition and no exchange rate misalignment might still be highly unjust. Further, unlike virtually all indices in the literature, $e_{t}^{v}$ takes into account both the quantity and the quality of labour flows.

Last, but most definitely not least, contrary to a widespread view, the exploitation index is all but metaphysical, as it is entirely based on empirically measurable magnitudes.

Exploitation in the world economy: A new map

This section derives the international distribution of the exploitation intensity index in 2017 using data from the Penn World Table (PWT; Feenstra et al., 2015). (A thorough description of the model calibration can be found in Appendix B.1.)¹² Our results should not be taken as providing a comprehensive picture of IIR: they are primarily meant to illustrate the power of our index, while bearing in mind that ours is an imperfect calibration of a simplified one-good model. With this caveat in mind, the results are rather striking indeed.

Figure 1 provides a map of exploitation intensity, where the shading of a country corresponds to its value of $e_{1}^{v}$ : a darker (brighter) colour indicates lower (higher) values of $e_{1}^{v}$ . The pattern in Figure 1 chimes with intuition and with the literature discussed in the Introduction, with a concentration of darker colours around the North Atlantic, Western Europe, Australia and Japan, while lighter colours dominate in Africa, Latin America and South Asia.

Figure 1.

Worldwide exploitation intensity – Basic economy.

The exploitation index can be used to identify the core and the periphery of the global economy. Using $e_{1}^{v} = 1$ as the relevant threshold, in Figure 2 we cluster countries into two clearly defined groups based on their exploitation status and graph $e_{1}^{v}$ against $ω_{0}^{v}$ per capita.¹³ Both panels show a strong, inverse relation between exploitation intensity and per capita wealth, with higher wealth associated with lower levels of exploitation. The core consists of exploiters (Figure 2a), whereas exploited countries are in the periphery (Figure 2b). Thus, Figure 2 clearly shows the economic and geographic structure of IIR, and in particular the crucial relevance of wealth, and productive endowments in general, in determining a country’s position within IIR.

Figure 2.

Exploiter and exploited countries – Basic economy: (a) exploiter countries and (b) exploited countries.

Tables 1 and 2 below show the complete listing of $e_{1}^{v}$ for all countries sorted by $ω_{0}^{v}$ per capita (exploiters are in Table 1, exploited countries in Table 2). Apart from the Latin American members of the club, all of the OECD countries are in the core, with an exploitation intensity index well below one¹⁴; while nearly all of the African countries are exploited, including the 20 most exploited.¹⁵ Further, among the main exploiters are oil-producing countries as well as countries at the centre of international credit networks. Although its exploitation index is too close to one to draw any definite conclusions, the classification of China as one of the exploiting countries is likely to reflect its increasing role in the world economy, which is moving it from the periphery to the core of IIR thus becoming one of the ‘smaller imperialist countries’ (Cope, 2019: 70; see also Ricci, 2022: 1333); and a similar point may be made about Indonesia (Kvangraven, 2020).

Table 1.

Exploitation intensity for exploiter countries at $t = 1$ – Basic economy.

	$e_{1}^{v}$		$e_{1}^{v}$		$e_{1}^{v}$
Indonesia	0.9928	South Korea	0.9223	Germany	0.8672
China	0.9935	Taiwan	0.8985	Portugal	0.7781
Venezuela	0.9912	Japan	0.9112	Sweden	0.8514
Mauritius	0.9788	United States	0.9114	Netherlands	0.8377
Uruguay	0.9820	Trinidad and Tobago	0.8675	Denmark	0.8352
Malaysia	0.9935	Finland	0.8857	Belgium	0.8027
Botswana	0.9816	United Kingdom	0.9010	Hong Kong	0.8081
Romania	0.9938	Cyprus	0.8435	Ireland	0.7972
Turkey	0.9409	Latvia	0.8605	Italy	0.7901
Lithuania	0.9711	Saudi Arabia	0.8252	Austria	0.7993
Russia	0.9750	Bahrain	0.7725	Switzerland	0.8159
Malta	0.9493	Czech Republic	0.8825	Norway	0.8116
Slovakia	0.9764	Slovenia	0.8720	United Arab Emirates	0.7268
New Zealand	0.9535	Greece	0.8431	Macao	0.7324
Croatia	0.9587	Canada	0.8794	Brunei	0.7048
Israel	0.9618	Australia	0.8679	Singapore	0.7811
Estonia	0.9529	France	0.8448	Luxembourg	0.7441
Hungary	0.9373	Spain	0.8256	Qatar	0.6277
Kuwait	0.8261	Iceland	0.8439

Table 2.

Exploitation intensity for exploited countries at $t = 1$ – Basic economy.

	$e_{1}^{v}$		$e_{1}^{v}$		$e_{1}^{v}$
Burundi	1.1305	Kyrgyzstan	1.1150	Sri Lanka	1.0516
Congo – Kinshasa	1.1292	Tanzania	1.0923	Morocco	1.0108
Malawi	1.1297	Haiti	1.0910	Namibia	1.0253
Mali	1.1241	Lesotho	1.0916	Ukraine	1.0581
Sierra Leone	1.1249	Bolivia	1.1085	Colombia	1.0373
Liberia	1.1257	Honduras	1.0993	Tajikistan	1.0516
Mozambique	1.1197	Vietnam	1.1045	Gabon	1.0441
Central African Republic	1.1218	Egypt	1.1026	South Africa	1.0435
Madagascar	1.1224	Belize	1.1095	Mongolia	1.0485
Niger	1.1160	Nicaragua	1.0896	Maldives	1.0258
Rwanda	1.1228	El Salvador	1.0878	Argentina	1.0459
Burkina Faso	1.1157	Guatemala	1.0790	Algeria	1.0187
Ethiopia	1.1112	Sudan	1.0675	Dominican Republic	1.0337
Zimbabwe	1.1221	Syria	1.0927	Jamaica	1.0270
Togo	1.1144	Laos	1.0755	Ecuador	1.0303
Benin	1.1146	Zambia	1.0908	Bulgaria	1.0405
Gambia	1.1100	Moldova	1.1002	Tunisia	1.0177
Kenya	1.1175	Fiji	1.0876	Kazakhstan	1.0346
Yemen	1.1110	India	1.0744	Serbia	1.0377
Uganda	1.1167	Iraq	1.0727	Albania	1.0234
Nepal	1.1100	Philippines	1.0821	Iran	1.0002
Cambodia	1.1115	Paraguay	1.0799	Poland	1.0333
Ivory Coast	1.1063	Armenia	1.0845	Mexico	1.0066
Cameroon	1.1091	Ghana	1.0685	Thailand	1.0035
Pakistan	1.1061	Jordan	1.0752	Barbados	1.0052
Senegal	1.0970	Congo – Brazzaville	1.0475	Brazil	1.0094
Myanmar	1.1005	Angola	1.0133	Panama	1.0025
Nigeria	1.1001	Eswatini	1.0426	Chile	1.0018
Mauritania	1.0966	Peru	1.0665
Bangladesh	1.1012	Costa Rica	1.0456

Although our empirical findings chime with intuition, they are by no means trivial and the exploitation index does yield different, complementary insights compared with other measures. Based on a standard Marxist approach, for example, Carchedi and Roberts (2021: 58) argue that China ‘clearly fits into the dominated bloc’. Further, Ricci (2021, 2022) focuses on trade between groups of countries and therefore our results are not immediately comparable. Nonetheless, in his analysis of 1990–2019 data, sub-Saharan countries are among the least harmed by unequal exchange in the periphery, while they are amongst the most exploited in our analysis. Similarly, countries in the Middle East – including the main oil exporters – appear to be suffering from a significant degree of unequal exchange in Ricci (2021, 2022), while oil exporters are amongst the main exploiters worldwide according to our index.¹⁶

Figures 1 and 2 and Tables 1 and 2 map the hierarchical structure of the global economy giving rise to spatially-driven injustices in the form of exploitative relations, and a transfer of surplus across borders. However, mapping exploitation status against wealth also suggests a possible causal relation whereby exploitative relations arise from asset inequalities. A general relation between wealth and exploitation status has been shown to hold by Roemer (1982, 1983) and Cogliano et al. (2019), and it can be shown to exist in our model too.

To see this, let the final good be the numéraire in every period t and let ${\hat{w}}_{t} \equiv \frac{w_{t}^{n}}{p_{t}}$ be the real wage rate at $t$ . Then, substituting equation (1) into (2) and plugging the resulting expression into (3) one obtains: $e_{t}^{v} = \frac{Λ_{t}^{v}}{λ_{t} (r_{t} W_{t - 1}^{v} + {\hat{w}}_{t} Λ_{t}^{v})} = \frac{1}{λ_{t} [r_{t} (W_{t - 1}^{v} / Λ_{t}^{v}) + {\hat{w}}_{t}]}$ . Hence, provided $r_{t} > 0$ , exploitation intensity at t is monotonically decreasing in wealth per unit of labour performed, which determines the exploitation status of each country:

country v is an exploiter $e_{t}^{v} < 1$ if and only if $\frac{W_{t - 1}^{v}}{λ_{t}^{v}} > \frac{1}{r_{t}} \frac{[1 - {\hat{w}}_{t} λ_{t}}{λ_{t}}$ ;

country v is an exploiter $e_{t}^{v} > 1$ if and only if $\frac{W_{t - 1}^{v}}{λ_{t}^{v}} < \frac{1}{r_{t}} \frac{[1 - {\hat{w}}_{t} λ_{t}}{λ_{t}}$ .

While exploitation status, and intensity, depend on a country’s assets, the actual economic mechanism driving this result is not immediately obvious. For there are in principle many reasons why greater wealth may allow a country to exploit others. A first hint at the institutional structure underpinning IIR comes from the following observation: the dependence of exploitation on wealth per capita holds if and only if $r_{t} > 0$ . In fact, recalling that ${\hat{w}}_{t} = \frac{1 - (1 + r_{t}) A_{t}}{L_{t}}$ , if $r_{t} = 0$ , then ${\hat{w}}_{t} = (1 / λ_{t})$ and $e_{t}^{v} = 1$ for all $v$ .¹⁷ This suggests that, in line with recent Marxist analyses of neoliberalism (e.g. Duménil and Lévy, 2004), the interest rate plays a pivotal role in IIR as it allows wealth inequalities to translate into exploitative international relations. Therefore we turn to the examination of international credit markets.

Credit markets and the dynamics of exploitation

In order to examine the structural features of IIR that allow international exploitation to emerge, we introduce a concept that identifies a clear stratification of countries based on their position in global markets.

Following Roemer (1982, 1983), in every period $t$ classes can be defined based on the countries’ position in the credit market. Consider a RS with $r_{t} > 0$ : $C_{t}^{1}$ is the class of net lenders, namely the set of countries such that $A_{t} y_{t}^{v} < z_{t}^{v}$ at all optimal solutions; $C_{t}^{2}$ is the class of countries that are neither net lenders nor net borrowers, namely the set of the countries such that $A_{t} y_{t}^{v} = z_{t}^{v}$ at some optimal solution; $C_{t}^{3}$ is the class of net borrowers, namely the set of countries such that $A_{t} y_{t}^{v} > z_{t}^{v}$ at all optimal solutions; $C_{t}^{4}$ is the class of countries with $W_{t}^{v} = 0$ .¹⁸

While the notion of exploitation captures a country’s position in the international structure of labour flows, the concept of class refers to a country’s position in the international structure of capital flows. It is a priori unclear whether a country’s location in the exploitation hierarchy and its position in the credit market are linked, as predicted in much of the literature discussed in the Introduction. The hypothesis that a tight relation exists between class and exploitation status is known as the Class-Exploitation Correspondence Principle (CECP, Roemer, 1982, 1983).

This section develops a computational analysis of the basic economy, in which technology, population and consumption norms are all constant over time (see Appendix A). Using again 2017 PWT data to calibrate the model, we derive the entire class structure of the global economy and illustrate the relation between class and exploitation status thus shedding some light on some key mechanisms allowing for the international transfer of surplus.

Further, while section ‘Exploitation in the world economy: A new map’ provides a snapshot of exploitative international relations and forcefully illustrates the importance of wealth inequalities for the emergence of IIR, here we examine the dynamics of IIR by performing a counterfactual exercise. We ask: what would happen if the world economy behaved as in our model? Would exploitation persist in a competitive economy with significant wealth inequalities, and a drive to accumulate?

The results of the simulation are shown in Figures 3 and 4. Figure 3 reports aggregate activity levels $(y_{t}, z_{t})$ and wealth $W_{t - 1}$ , the growth rate of capital $g_{t}$ , ${\hat{w}}_{t}$ and $b$ and $r_{t}$ .¹⁹ Initially, the global economy is capital constrained ( $L A^{- 1} ω_{t - 1} < l$ ), as aggregate capital is insufficient to employ all workers, the excess supply of labour pushes the real wage to the subsistence level and guarantees a positive return on capital. The economy then accumulates, with aggregate output $y_{t}$ , credit $z_{t}$ and labour demand $L A^{- 1} ω_{t - 1}$ all growing at a constant rate $g_{t}$ . As labour supply is constant, the economy eventually becomes labour constrained ( $L A^{- 1} ω_{t - 1} > l$ ) leading the wage rate to increase and $r_{t}$ to go to zero. In all panels, the dashed vertical line denotes the period in which the economy becomes labour constrained.²⁰

Figure 3.

Summary results – Basic economy.

Figure 4.

Class and exploitation status – Basic economy: (a) exploitation status, (b) class status and (c) CECP.

Figure 4a reports the dynamics of exploitation by providing a headcount of exploiting and exploited countries. While the economy is capital constrained there is no tendency for exploitation to diminish, and throughout the simulation the initial distribution of $e_{t}^{v}$ (as depicted in Figures 1 and 2) is replicated identically: endowment-poor (rich) countries are exploited (exploiters).²¹ When the economy becomes labour constrained, returns on capital and exploitation disappear, and $e_{t}^{v} = 1$ , for all countries $v$ .

Figure 4b derives the class structure of the global economy based on each country’s position in the international credit market: all countries belong to one, and exactly one, of $C_{t}^{1} - C_{t}^{4}$ . More precisely, empirically, countries belong either to $C_{t}^{1}$ or to $C_{t}^{3}$ : $C_{t}^{4}$ is empty because there is no country with zero wealth and producing only using borrowed capital, while $C_{t}^{2}$ is empty because no country satisfies the condition $A y_{t}^{v} = z_{t}^{v}$ exactly.²²

Figure 4c compares exploitation and class status by looking at the intersection of $C_{t}^{1}$ with the set of exploiters (solid line) and the intersection of $C_{t}^{3} \cup C_{t}^{4}$ with the set of exploited countries. The CECP holds in the world economy: in every period $t$ with $r_{t} > 0$ , countries that enjoy a privileged position in the credit market are exploiters, while net borrowers are exploited. This generalises Roemer’s (1982, 1983) classic insights to dynamic accumulating economies.²³

Figure 4 completes our depiction of IIR, and confirms common intuitions in dependency theory. A precise stratification emerges in the world economy whereby wealthy countries are net creditors and exploit poor countries which are net debtors. Surplus is transferred from poor to rich countries via global capital markets. This conclusion resonates with theoretical claims and empirical findings in the Marxist literature discussed in the Introduction. In a recent contribution, for example, Carchedi and Roberts (2021: 36) find that ‘The imperialist G7 countries run a persistent and rising annual net, primary income surplus that reached over half a trillion dollars in 2019, or 14% of G7 GDP . . . In contrast, the [developing] countries are leaking large amounts of net primary income’.²⁴

In summary, based on the concepts of exploitation and class, it can be shown that IIR are characterised by a hierarchical structure that emerges endogenously and that, contrary to postmodern claims, has a clear economic and territorial dimension: wealthy countries are exploiters and poor countries are exploited. Further, contrary to classical theories, IIR emerge from a competitive credit market, which allows surplus to be transferred from wealthy net creditors to poor net debtors. This provides rigorous foundations to the concepts of core countries – which enjoy a privileged position in the credit market and exploit – and peripheral countries – which need to borrow in order to activate production, and are exploited.

However, our results also confirm and generalise an argument originally suggested by Devine and Dymski (1991) and later proved by Veneziani and Yoshihara (2017): wealth inequalities and competitive markets are sufficient for class, exploitation and IIR, to emerge, but not for them to persist. Given the strong empirical evidence of persistent, if not widening, inequalities across borders, our simulation exercise suggests that something else is necessary to explain the dynamics of IIR. In the next section, we extend our analysis to incorporate some possible mechanisms to explain persistence of IIR, without having to assume the open use of force by core countries to stem the growth of those in the periphery.

Persistent exploitation cycles in the global economy

In this section we exploit the power of computational methods in dealing with complex, non-linear dynamics in economies with heterogeneous agents (Bergmann et al., 2009; Plummer et al., 2012) to allow both consumption and technology to change endogenously over time, and analyse their effect on IIR. This choice reflects both empirical and theoretical concerns. Empirically, the long-run evolution of capitalist economies has been characterised by an increase in (average) consumption opportunities and by an expansion of technical knowledge, leading to a progressive increase in labour productivity. Theoretically, a fundamental feature of capitalism as a dynamic system is its constant tendency to revolutionise production with a strong propensity, according to Marx, for labour-saving innovations.

Concerning consumption, we incorporate some Marxian insights on the social nature of consumption and assume that $b_{t}$ is the product of social norms, by making it an increasing function of the general level of development of the economy, as proxied by aggregate capital, and of the history of consumption itself. To be specific, we assume:

b_{t} = b_{t - 1} \cdot (1 + ϕ \frac{ω_{t - 1} - ω_{t - 2}}{ω_{t - 2}}),

(4)

where the parameter $ϕ$ captures the degree to which the development of the economy influences consumption norms.

Concerning technology, we incorporate key insights from the classical-Marxian and evolutionary analyses of technical change, in that the innovation process is fundamentally profit-driven and innovations are local. Technical progress is profit-driven because only profitable changes are adopted. This is a defining feature of the classical-Marxian framework, as Duménil and Lévy (2003) have argued. But the innovation process is linked to the trajectory of the profit rate also because significant declines in profitability spur innovation. This is consistent with standard Marxian insights, whereby ‘a declining profit rate will lead at some point to a structural crisis, and “something” will happen with respect to technical change’ (Duménil and Lévy, 2003: 203). Innovations are local because agents do not have a global scan of alternatives and search around existing processes (Duménil and Lévy, 2003). Therefore when innovations occur, they yield relatively small changes in technical coefficients.

To be specific, when the rate of return on capital falls beneath a threshold value $r^{*}$ , which depends on economic, institutional and even cultural factors, capitalists increase their efforts to innovate and introduce new techniques, thus leading $(A_{t}, L_{t})$ to change over time. Formally, R&D efforts lead to the discovery and adoption of a new technique at t, denoted as $(A^{'}, L^{'})$ if and only if at $t - 1$ profitability fell below the threshold $(r_{t - 1} < r^{*})$ and the new technique restores profitability. Technical change is capital-using $(A^{'} ≧ A_{t - 1})$ and labour-saving $(L^{'} < L_{t - 1})$ à la Marx. (For a detailed description of the simulation procedure, see Appendix B.2.)

Figure 5 reports the same information as Figure 3. Some differences clearly emerge: aggregate production $y_{t}$ , loans $z_{t}$ and capital, all increase over time but their growth path is no longer smooth, and $g_{t}$ exhibits a cyclical downward trend, without the economy reaching a stationary state. This is caused by the joint dynamics of distribution, consumption norms and technical change. Initially, the economy is capital constrained with $l > L_{t} A_{t}^{- 1} ω_{t - 1}$ , and so ${\hat{w}}_{t} = b_{t}$ . As accumulation proceeds, the subsistence norm, $b_{t}$ , increases, leading to an increase in ${\hat{w}}_{t}$ , and a decrease in $r_{t}$ . When the wage rate is at subsistence, growth can only be financed with profits. Hence, the fall in $r_{t}$ leads to a decrease in the growth rate of aggregate output, loans and capital, even before the economy becomes labour constrained.

Figure 5.

Summary results – Economy with endogenous $b_{t}$ and $(A_{t}, L_{t})$ .

As $r_{t}$ hits the critical threshold, however, capitalists introduce an innovation that restores global profitability, lowers employment and speeds up growth again, starting a new cycle. Throughout the cycles of accumulation and technical change the economy remains capital constrained, as recurrent Marx-biased technical change (cyclically) lowers labour demand (see the middle panel in the upper row of Figure 5). Therefore there is a secular increase in ${\hat{w}}_{t} = b_{t}$ , while $r_{t}$ oscillates between $r_{0} = 0.4$ and $r^{*}$ .

Despite the cyclical behaviour of $g_{t}$ and $r_{t}$ , the core/periphery structure of the global economy is remarkably stable. Throughout the simulation, 56 countries are exploiters and belong to $C_{t}^{1}$ , and 88 are exploited and belong to $C_{t}^{3}$ , and the CECP holds at all $t$ .²⁵ However, this draws only a partial picture of IIR, and beneath a seemingly unchanging surface, Figures 6a and b uncover an interesting phenomenon of ‘exploitation cycles’ that trace the cycles in $r_{t}$ . As accumulation progresses with a given technique $(A_{t}, L_{t})$ , the profit rate tends to fall and exploitation tends to decrease as $e_{t}^{v}$ tends to one for all $v$ . However, when a new technique is introduced, both profitability and inequality in exploitation intensity are restored, and the pattern of accumulation and exploitation resumes until another innovation is introduced.

Figure 6.

Exploitation intensity index – Economy with endogenous $b_{t}$ and $(A_{t}, L_{t})$ : (a) exploitation intensity across agents and (b) Gini coefficient of $e_{t}^{v}$ .

Figures 7 and 8 map the international distribution of $e_{t}^{v}$ at select $t$ . Unlike at $t = 1$ , these are counterfactuals: they show what the global distribution of $e_{t}^{v}$ would look like at different points in the cycles shown in Figure 5.²⁶ Panels (a) and (b) of each figure show typical distributions of $e_{t}^{v}$ in years with, respectively, low and high $r_{t}$ . In periods with high $r_{t} (t = 50)$ , international relations are more exploitative and $e_{t}^{v}$ is more disperse than in periods with low $r_{t} (t = 10)$ .

Figure 7.

Worldwide exploitation intensity – Economy with endogenous $b_{t}$ and $(A_{t}, L_{t})$ : (a) $t = 10$ and (b) $t = 50$ .

Figure 8.

Worldwide exploitation intensity versus wealth per capita – Economy with endogenous $b_{t}$ and $(A_{t}, L_{t})$ : (a) $t = 10$ and (b) $t = 50$ .

These results shed some light on the mechanisms that may contribute to explain the persistence of IIR. In the global economy, international trade and development raise (norms, expectations and therefore) living standards, including for countries in the periphery, which increases their reservation wage and tends to reduce the rate of return on capital. What can countries in the core do in order to counter this tendency, and maintain exploitation, without recourse to war and coercion? The previous analysis suggests that Marx-biased technical change may do the job as it makes capital persistently scarce relative to labour, thus maintaining the advantage of capital-rich core countries over labour-abundant countries in the periphery. In a competitive setting, countries in the core cannot coordinate their innovation efforts and therefore technical change tends to occur occasionally, which leads to cycles that capture the varying degree to which core countries are able to exploit the periphery over time.

In closing this section, we note that while the Gini of $e_{t}^{v}$ fluctuates widely around a mildly increasing trend, the Gini of the distribution of wealth remains constant at 0.8156 – as all countries accumulate at the rate $r_{t}$ – and the Gini of the distribution of income stays within a rather narrow range [0.780087, 0.810456].²⁷ This is an important point that was not evident in the basic economy: an analysis of international relations focusing on the concepts of exploitation and class is not reducible to a focus on income and wealth inequality (even though a strong relation exists between wealth inequalities and exploitation and class status, as shown above). The notions of exploitation and class identify the key economic and geographic structure of IIR, and the emergence in the global economy of a core and a periphery, in a way that international inequalities of income and wealth do not.

Conclusions

In closing the paper, we would like to reflect on some limitations of our analysis, which point out some avenues for further research. As noted in section ‘Methodology’, our model is not meant to provide a comprehensive description of the global economy and the many interlocked mechanisms driving international inequalities. We use theoretical abstraction in order to highlight one, in our view fundamental, aspect of IIR: the role of wealth inequalities, and credit markets, in generating exploitative international relations. In future research it would be important to consider how to integrate and develop the main lesson of our analysis into more comprehensive theoretical reasoning to explain the co-evolving features of wealth inequalities and IIR in the capitalist world economy within which the long spatial history of colonialism is embedded.

Further, it would be interesting to generalise the model to incorporate some of the features of the global economy that we have abstracted away and examine how different mechanisms interact to maintain the power status of rich countries. First, globalisation has coincided with a severe deterioration of the environment, and a major increase in CO₂ emissions. As climate change is likely to have a significant impact on accumulation (Baiman, 2022), it would be interesting to extend our model to include the environmental constraints on growth.

But globalisation has not had a uniform environmental impact across nations, and our analysis should be integrated with the growing literature on ecologically unequal exchange, which seems to provide a rather different picture of global processes. While the maps capturing ecological unequal exchange do ‘echo the divisions of the global economy into different roles within classic world systems analyses’ (Bergmann, 2013: 1358; see in particular Figure 3), like our index, there are some significant differences. For example, ‘net petroleum exporters of the semiperiphery are also strong net emissions exporters, providing more emissions for economic investment in other countries than they receive in return to build their own futures’ (Bergmann, 2013: 1358). And while countries in the Global North are generally strong net importers of carbon emissions, so are generally those in the periphery of the Global South. Thus the mechanisms underlying the ecological unequal exchange appear to differ from those driving international exploitation. Indeed, no individual index is likely to capture all of the normatively relevant aspects of the global economy, as international injustices are multidimensional, further suggesting the need ‘to develop epistemologies adequate to a quantitative pluralism’ (Bergmann, 2013: 1355).²⁸

Second, our model focuses on real flows and credit markets function only to transfer productive capital. However, it may be argued that fictitious capital is a central feature of the current global economy, advanced countries extract surplus from poorer ones by acting merely as rentiers (Baiman, 2014, 2020), and more generally the international monetary system and exchange rate deviations should be taken into account (Ricci, 2021, 2022).

Third, although we follow Roemer closely and adopt a relatively narrow interpretation of surplus value and wealth, the model may be interpreted more generally, or at least can be extended to include a broader notion of wealth, means of production and surplus which may encompass purely financial wealth and other monopolistic levers of market power over ‘non-commodifiable capital’ (such as social, distribution and telecommunications systems) which has become increasingly characteristic of advanced capitalism. Seen in this light, the conclusions of the paper may be consistent with the recent liberal egalitarian (Piketty, 2014), Post Keynesian (Mazzucato, 2018) and Neo-Marxist (Baiman, 2014, 2020; Hudson, 2015) literature emphasising the increasing role of rentierism in international economic relations.²⁹

Finally, we have abstracted from transportation costs and assumed each country to be a closed production unit. However, the world is not flat (the distance between countries varies, no matter how it is parameterised), and national economies do not operate in isolation but are interdependent (maximising wealth in a given national economy typically relies heavily on global production networks and global financial flows). It would be interesting to extend the model in order to analyse the distribution of the exploitation index taking into account global value chains and global production and transportation networks.

Supplemental Material

sj-pdf-1-epn-10.1177_0308518X231224618 – Supplemental material for The dynamics of international exploitation

Supplemental material, sj-pdf-1-epn-10.1177_0308518X231224618 for The dynamics of international exploitation by Jonathan F Cogliano, Roberto Veneziani and Naoki Yoshihara in Environment and Planning A: Economy and Space

Footnotes

A Mathematical appendix: The basic economy

This appendix analyses the basic economy, which is characterised by constant population, technology, consumption norms and human capital. Formally, let $N_{t}$ , $P_{t}$ denote, respectively, the set of agents and the set of available technologies at $t$ . In the basic economy, $N_{t} = N$ , $P_{t} = P {(A, L)}$ , $b_{t} = b$ and $l_{t - 1}^{v} = l^{v}$ for all $t$ and all $v$ . The basic economy provides a theoretical benchmark, but the framework and definitions presented here can be easily extended and the results derived continue to hold in more general economies (Cogliano et al., 2019).

We assume throughout that technology is sufficiently advanced to allow for the production of a surplus: 1−λb > 0, at all $t$ . This condition is equivalent to $(1 - b L) > A$ : it implies that if $A x$ units of capital are invested in the production process, gross output $x$ is sufficient for necessary consumption $b L$ and to replace capital used up in production: $x > b L x + A x$ .

In every $t$ , given $(p_{t - 1}, p_{t}, r_{t})$ , every country $v$ chooses $(x_{t}^{v}, y_{t}^{v}, z_{t}^{v}, δ_{t}^{v})$ to maximise its wealth subject to consuming $b$ per unit of labour performed (A1) and to the constraints set by its capital (A2) and labour (A3) endowments. Formally, every $v$ solves the following programme³⁰:

(M P_{t}^{v}) \max_{(x_{t}^{v}, y_{t}^{v}, z_{t}^{v}, δ_{t}^{v})} p_{t} ω_{t}^{v}

(A1)

subject to : p_{t} x_{t}^{v} + [p_{t} - (1 + r_{t}) p_{t - 1} A] y_{t}^{v} + (1 + r_{t}) z_{t}^{v} + p_{t} δ_{t}^{v} = p_{t} b Λ_{t}^{v} + p_{t} ω_{t}^{v},

(A2)

p_{t - 1} A x_{t}^{v} + z_{t}^{v} + p_{t - 1} δ_{t}^{v} = p_{t - 1} ω_{t - 1}^{v},

(A3)

L x_{t}^{v} + L y_{t}^{v} ≦ l^{v} .

The basic economy is defined by the set of countries, $N$ , technology $(A, L)$ , consumption bundle, $b$ , labour endowments ${(l^{v})}_{v \in N}$ and initial capital endowments ${(ω_{0}^{v})}_{v \in N}$ ; and is denoted as $E (N, (A, L), b, {(l^{v})}_{v \in N}, {(ω_{0}^{v})}_{v \in N})$ . Let $x_{t} \equiv \sum_{v \in N} x_{t}^{v}$ , and likewise for $y_{t}, z_{t}, δ_{t}, ω_{t}, Λ_{t}$ and $l$ . The concept of a reproducible solution (Roemer, 1982) can be defined.

At a RS, in every period (a) all countries maximise their wealth; (b) aggregate capital is sufficient for production (and speculative saving) plans; (c) the credit market clears; (d) aggregate supply is sufficient for consumption and accumulation plans.

Given the structure of the one-good economy, we shall focus on RS’s with strictly positive prices without loss of generality, and we can take the produced commodity as the numéraire, setting $p_{t} = 1$ , all $t$ . Therefore, first, $r_{t}$ represents the real interest rate at period $t$ , and country $v$ will invest or lend (rather than storing the good) provided $r_{t} ≧ 0$ . Second, this implicitly defines a real wage rate ${\hat{w}}_{t}$ at any $t$ . At any RS with positive production, the real wage must be at least enough to cover subsistence and the interest rate must be nonnegative. Formally, if $ω_{t - 1} > 0$ , then ${\hat{w}}_{t} ≧ b$ and $r_{t} ≧ 0$ , all $t$ .

Given the previous observations, by constraints (A1) and (A2), it follows that at any RS, for all countries $v$ , the following equation must hold in every period $t$

(A4)

ω_{t}^{v} = ω_{t - 1}^{v} + r_{t} (A x_{t}^{v} + z_{t}^{v}) + ({\hat{w}}_{t} - b) L (x_{t}^{v} + y_{t}^{v}) .

Equation (A4) implies that for all countries at the solution to $M P_{t}^{v}$ , if the interest rate is strictly positive, no wealth is used for speculative savings ( $δ_{t}^{v} = 0$ all $v$ ), and if the wage rate is above subsistence, then the labour constraint (A3) binds.

As Cogliano et al. (2019) have shown, this has some implications for the set of RS’s: the interest rate can be strictly positive and the real wage rate can be greater than the subsistence norm only if the aggregate (effective) labour and capital endowments satisfy the knife-edge condition $l = L A^{- 1} ω_{t - 1}$ . If capital (labour) is abundant, the interest rate (the real wage rate) drops to zero (the subsistence level). This observation provides the foundations for the analysis of the dynamics of the global economy in the simulations.

Recall that $W_{t - 1}^{v} = p_{t - 1} ω_{t - 1}^{v}$ , ${\hat{w}}_{t} = \frac{w_{t}^{n}}{p_{t}}$ and $p_{t} = p_{t - 1} = 1$ . The growth rate of capital for each country $v$ at t, $g_{t}^{v} = \frac{ω_{t}^{v} - ω_{t - 1}^{v}}{ω_{t - 1}^{v}}$ , can be derived from equation (A4): $g_{t}^{v} = r_{t} + ({\hat{w}}_{t} - b) \frac{Λ_{t}^{v}}{ω_{t - 1}^{v}}$ , and the aggregate growth rate of the world economy at t is $g_{t} = r_{t} + ({\hat{w}}_{t} - b) \frac{l}{ω_{t - 1}}$ .

Acknowledgements

We would like to thank Adam Aboobaker, Carolina Alves, Firat Demir, Giorgos Galanis, Makoto Itoh, Kazuhiro Kurose, Ingrid Kvangraven, John Willoughby, three anonymous referees and participants in the 2021 AHE conference, the 2021 IIPPE conference, the 2021 WAPE Forum, the 2022 ICAPE conference, the PSA2022 conference and the FMM2023 conference for thoughtful comments and suggestions on an earlier version of this paper. The usual disclaimer applies.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Jonathan F Cogliano

Supplemental material

Supplemental material for this article is available online.

Notes

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