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2019 | OriginalPaper | Chapter

5. Production Networks

Author : Robert P. Gilles

Published in: Economic Wealth Creation and the Social Division of Labour

Publisher: Springer International Publishing

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Abstract

This chapter introduces elements from network analysis to describe trade infrastructures through which the social division of labour is conducted. We consider connectivity properties and the description of how individual nodes can affect the trade flows in these networks. This leads to a theory of identification and measurement of the power of control in such trade networks. The notion of a critical node set captures these power structures in trade networks. We use these ideas and conceptions to describe production processes that are conducted in any social division of labour, leading to the notion of a production network. This chapter introduces a careful definition of these production networks and considers different topologies to represent different network-institutional production systems.

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previous chapter Objective Specialisation: The Smithian Perspective

next chapter Inequality in Network Economies

This institutional infrastructural matrix can be represented by a Leontief production system (Leontief 1936) or a Sraffian production model (Sraffa 1960). The relationship between Smithian perspectives on the social division of labour and these systems is explored in more detail in Chap. 4.

The fundamentals of critical positions and contestation have been developed in Sims and Gilles (2016, 2017). We draw on these two sources extensively in the discussion of criticality of positions and their contestation.

This includes the use of the symbol g for a network, which refers to the term “graph” as is common in pure mathematics (Diestel 2017).

Indeed, a multilateral relationship between \(k \geqslant 3\) agents can be represented by a set of bilateral relationships. So, let B = {1, …, K}⊂ A be some group of positions. Then the multilateral interaction in B is assumed to be representable by a set of bilateral relationships, namely the relationships between all a, b ∈ B with a ≠ b.

Standard notation in network theory for the complete network g _A on A consisting of n positions is also K _n. This alternative notation is justified by the fact that g _A is completely symmetric and the network is really determined by the number of positions rather than the names or indicators of the positions.

We distinguish here between a “position” and a “node”. A position is a theoretical construct, while a node refers explicitly to a graphical representation of a position.

Formally, this is represented as \(\mathrm {Diag} (G) = \left ( G_{11}, \ldots , G_{nn} \right ) =0\). This in turn implies that the trace of the adjacency matrix is given by Tr(G) =∑_{a ∈ A}Diag_a(G) =∑_{a ∈ A} G _aa = 0.

This refers to the simple idea that even though we do not know anybody in Beijing, China, there is a path between myself and any person in Beijing. This implies also that the activities of these positions in Beijing indirectly influence my socio-economic environment. This is most clearly illustrated by the fact that most of the durable consumption goods that we consume are produced in China. This refers to the idea that paths are not just made by people, but are based on economic interactions founded on the production and delivery of services and products. Through these outputs, positions can influence each other’s socio-economic environments.

We remark that connectedness of a network implies that every position is connected to itself in that network. Thus, \(\Omega _{aa} \neq \varnothing \) for every position a ∈ A.

This example is the simplest representation of an example of this fact and can also be found as Figure 6.15 in Newman (2010).

Recall here that a partnership really represents a set of positions that has significant control over the flows in the network. This implies that within a partnership the position has a relatively high influence and that, on the other hand, the position is a member of various of these small partnerships. Hence, the position is a valuable asset from a competitive point of view in the sense that it would command a high price if it were to sell its position in the network.

These measures are connected through a set of network statistics as identified by Bloch et al. (2016). However, a full axiomatic categorisation of these measures remains illusive and might well be impossible.

An axiomatisation is a list of properties that completely characterise a certain method of measuring the centrality or power of the position in a network. In this case, Brink and Gilles (2000) introduced four axioms that fully characterise the degree measure on the class of all directed networks. We emphasise here that we only work with “undirected” networks, that is, networks in which positions are equally powerful in direct relationships.

For technical details we refer here to Gilles (2010, p. 159).

Note that the D-matrix is stochastic, that is, all columns in the matrix add up to unity.

In fact, we can rewrite the formulation of the modified β-measure as \(\beta ^{k+1}_g = \mathbf {D} \beta ^k_g = {\mathbf {D}}^k \beta ^1_g = {\mathbf {D}}^{k+1} e\). Now β ^∗(g) =lim_k→∞ D ^k e.

For an extensive discussion of the PageRank measure and related centrality measuring methods, I refer to Newman (2010, Section 7.4).

Recall that a vector \(x \in \mathbb {R}^A\) is an eigenvector of the matrix G if there exists some number \(\lambda \in \mathbb {R}\) with G x = λx. The number λ is called the eigenvalue corresponding to the eigenvector x.

In fact, \(\alpha = \frac {1}{\kappa }\) corresponds to the Bonacich eigenvalue centrality measure.

The idea of brokerage is similar to the conception of betweenness centrality. In the betweenness measure, only geodesic paths were considered. For our notion of brokerage, we consider arbitrary paths; not necessarily just the paths with minimal length.

We must emphasise that an employment contract does not necessarily specify the requested services. The tasks required of the employee may be assigned on an ad hoc basis, depending on the need of the corporations on an ongoing basis.

In economics, platforms have recently been studied extensively. In the field of industrial organisation, Rochet and Tirole (2003) and Evans (2003) provided the groundwork for the theoretical study of these organisation forms. This was extended more recently in, for example, Evans and Schmalensee (2007) and Weyl (2010). Gilles and Diamantaras (2013) introduced an innovative perspective on platform provision by considering the ambiguity in the contestation of a platform.

We can also include Amazon here, since it offers space on its websites for third-party providers to sell their products. As such, Amazon offers platform brokerage services at a high premium to the third-party sellers.

The most prominent example of a TNC that is structured around this outsourcing model is Apple Inc. Except for the engineering and the design of its products, Apple outsources all other aspects of its business. Famously, its iMacs, iPads, and iPhones are “designed in Cupertino, CA, USA”, but produced in Taiwan and China.

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Title: Production Networks
Author: Robert P. Gilles
Publisher: Springer International Publishing
Book: Economic Wealth Creation and the Social Division of Labour
Print ISBN: 978-3-030-04425-1

Electronic ISBN: 978-3-030-04426-8

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-030-04426-8_5