Complexity in international business: The implications for theory

Abstract

International business is inherently complex for four main reasons: the large number of countries, products, technologies and firms involved, the intricate connectivity of international transport and communications networks, the diversity of the political, cultural and regulatory environment, and the speed and unpredictability of change. The complexity created by these features can be measured using the techniques presented in this paper. IB has developed simple and powerful theories which abstract from inessential details and thereby reduce the complexity of theory to a minimum. The assumptions underlying this theory are common to other disciplines, and provide a basis for future inter-disciplinary research.

Résumé

Les affaires internationales sont intrinsèquement complexes pour quatre raisons principales : le grand nombre de pays, de produits, de technologies et d'entreprises impliquées, l’imbrication étroite des réseaux de communication et de transport internationaux, la diversité de l'environnement réglementaire, politique et culturel, ainsi que la rapidité et l'imprévisibilité du changement. La complexité créée par ces caractéristiques peut être mesurée à l'aide des techniques présentées dans cet article. Le domaine des affaires internationales a développé des théories simples et puissantes qui font abstraction des détails non essentiels et réduisent ainsi la complexité de la théorie au minimum. Les postulats qui sous-tendent cette théorie sont communs à d'autres disciplines et fournissent une base pour de futures recherches interdisciplinaires.

Resumen

Los negocios Internacionales son inherentemente complejos por cuatro razones principales: el gran número de países, productos, tecnologías y empresas involucradas; la intrincada conectividad del transporte internacional y de las redes de comunicaciones, la diversidad del entorno político, cultural y regulatorio, y la velocidad e imprevisibilidad del cambio. La complejidad creada por estas características puede ser medida usando técnicas presentadas en este manuscrito. Negocios Internacionales ha desarrollado unas teorías simples y poderosas las cuales se abstraen de los detalles no esenciales, y, por lo tanto, reducen la complejidad de la teoría al mínimo. Los supuestos subyacentes a esta teoría son comunes a otras disciplinas y proporcionan una base para futuras investigaciones interdisciplinarias.

Resumo

Negócios internacionais são inerentemente complexos por quatro razões principais: o grande número de países, produtos, tecnologias e empresas envolvidas; a intrincada conectividade de redes internacionais de transporte e comunicação, a diversidade do ambiente político, cultural e regulatório e a velocidade e imprevisibilidade de mudanças. A complexidade criada por essas características pode ser medida usando as técnicas apresentadas neste artigo. IB desenvolveu teorias simples e poderosas que abstraem de detalhes não essenciais e, portanto, reduzem a complexidade da teoria ao mínimo. Os pressupostos subjacentes a esta teoria são comuns a outras disciplinas e fornecem uma base para futuras pesquisas interdisciplinares.

摘要

国际商务本质上是复杂的, 主要有四个原因: 涉及的国家、产品、技术和公司数量众多; 国际运输和通讯网络错综复杂的连通性, 政治、文化和监管环境的多样性, 以及变化的速度和不可预测性。由这些特征产生的复杂性可用本文介绍的技术来测量。国际商务(IB)开发了从非本质的细节中抽象出来的简单而强大的理论, 从而将理论的复杂性降至最低。这一理论所依据的假设与其它学科相同, 并为未来的跨学科研究提供了基础。

Appendix: Case study of the measurement of structural complexity in a simple IB model

The complexity of IB studies and the power of IB theory may be illustrated by a simple example. Consider a world composed of N different countries, populated by H firms, all of which are potential MNEs. Each firm uses a different proprietary technology to the others, although consumers regard their final products as basically the same. It is desired to determine which firms supply which markets, what prices will prevail in each market and what profits each firm will make.

Each firm has to decide whether to serve each national market and, if so, where to locate its production for that market. Each firm serves a given market from a single location, but can serve different markets from different locations if it wishes to do so. Whether a firm becomes an MNE depends on the choices that it makes; if it decides not to produce abroad then it does not become an MNE. It is assumed to begin with that headquarters and R&D are collocated at a fixed location. Firms with inferior technologies may not operate at all.

Consider a set of tables summarising the solution of this problem. One subset of tables relates to production and trade. For each firm, there is an N × N table showing how much it supplies from each production location to each market. There are H firms and therefore H such tables and, taken together, they have a total of HN² cells. There is a smaller table with N cells recording the prices that prevail in each market, and another table with H cells reporting the profits made by each firm (firms that do not operate make a zero profit). The solution is therefore encoded in HN² + H + N cells. This number is a measure of the ‘tabular complexity of the solution’.

The solution varies according to the assumptions on which the theory is based. Suppose that there are two general principles: that firms maximise profit, and that they compete for market share in each country. Suppose, in addition, that each customer in each market demands a fixed amount of each product and refuses to pay more for the product than some reservation price, p*. Then, the amount of product demanded in each market at or below the reservation price is some amount, q. The prices and quantities demanded vary across markets according to local population, incomes and tastes.

Suppose also that there are constant unit costs of production and transport and that there are no fixed costs. Let the total cost to firm h of supplying a unit of product from a plant in location i to a market j be c_hij (h = 1,…, H; i, j = 1,…, N). The elements c_hij are measured gross of production costs, transport costs, tariffs and technology transfer costs. They number HN² and constitute the elements of H individual N × N tables, each of which represents the cost structure faced by an individual firm.

The other quantitative data required to specify the problem concern the structure of the individual markets: the amount of the product demanded in each market, q_j, and the maximum price that consumers will pay p*_j (j = 1,.., N). The data is therefore contained in HN² unit costs cells, a column of N market sizes and another column of N reservation prices. These comprise a total of HN² + 2N cells. This is almost the same as the number of cells that need to be filled by the solution; indeed, if there were no reservation prices (so that each market was always served), then the two would be identical). This number represents the ‘tabular complexity of the data’.

Each firm can serve any given market from any location: one option is to serve a market by local production and the others are to import from plants in other locations. Each firm plans to serve a given market from the cheapest location, i.e. the location i*_hj where its unit cost is a minimum, c*_hj = min_i c_hij.

The firm with the lowest cost, c**_j = min_h c*_hj will serve the entire jth market. They will drive out their competitors by setting price just below the unit cost of their closest competitor, which is the firm with the second-lowest unit cost. There are two exceptions, however: if the lowest unit cost is above the local reservation price, then no firm will serve the market at all; and if the second-lowest unit cost exceeds the reservation price, then the firm will charge the reservation price because otherwise it will lose the market altogether.

Let p_j* be the price set in the jth market when that market is served by its least cost firm. Let q_j be the size of the market, as measured by the quantity of sales. Revenue is equal to R_j = p_j*q_j, and cost is C_j = c**_j q_j. In the absence of fixed costs, the profit of the firm serving the jth market is π*_j = R*_j – C*_j.

There is no limit to the size or geographical diversification of any firm. Its decisions about whether to serve a particular market are not constrained by its decisions to serve other markets. According to this competitive outcome, some firms may be entirely domestic, serving their home market by local production; some may serve their home country only by imports; others may produce in the home country for export, and perhaps also for their domestic market; while some may serve one or more foreign markets, either by exports from their home country or from a third country.

By counting up the number of arithmetical operations involved in the solution process, a measure of ‘computational complexity’ can be obtained; such measures are widely used to assess the efficiency of computer algorithms. The solution involves four main steps, as indicated above. The first step is to determine for each firm the least cost production location from which to serve each market and the unit cost associated with it. This is effected by moving along the list of location-specific costs for each combination of firm and market and recording the lowest figure. This process involves HN² operations. The second step is to compare the costs across firms for any given market; it is the least-cost firm that serves the market. This involves HN operations. The third step is to determine market prices by calculating the minimum of the reservation price and the lowest cost in each market. If the reservation price is the minimum, then the market is not served. If the least cost is the minimum, then it is necessary to compare the second least cost with the reservation price. Whichever is the minimum determines the market price. This involves reprocessing the information obtained at the first stage; the amount of reprocessing depends on the number of firms involved. Overall, therefore, the calculations involve a minimum of HN(N + 1) operations; this may be regarded as a measure of the computational complexity.