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We develop a model of two parallel contests, asymmetric in quantity of homogeneous prizes open to contest, with a finite number of homogeneous risk-neutral bidders. Whether the bidder upon entry into a particular contest is aware of the realized number of competing contestants in the contest is irrelevant to the expected effort at equilibrium. At equilibrium the expected effort per capita in the larger contest (the contest with more prizes) is greater than that in the smaller one. The larger contest nonetheless does not attract enough contestants to achieve optimum in rent extraction from the bidders.

While the game-theoretic analysis of conflict is often based upon the assumption of multiplicative noise, additive noise such as assumed by Hirshleifer (1989) may be equally plausible depending on the application. In this paper, we examine the equilibrium set of the n-player difference-form contest with heterogeneous valuations. For high or intermediate levels of noise, the equilibrium is in pure strategies, with at most one player being active. For small levels of noise, however, we find a variety of equilibria in which some but not necessarily all players randomize. In the case of homogeneous valuations, we obtain a partial uniqueness result for symmetric equilibria. As the contest becomes increasingly decisive, at least two contestants bid up to the valuation of the second-ranked contestant, while any others ultimately drop out. In the limit, equilibria in the Hirshleifer contest converge to equilibria in the corresponding all-pay auction. Revised version, October 2022

The symmetric two-player Hirshleifer contest admits a unique equilibrium. The equilibrium support is finite and includes the zero expenditure level. We also establish a lower bound for the cardinality of the support and an upper bound for the undissipated rent.

We study optimal provision of public goods in the network, showing that the Samuelson condition and the Lindahl scheme can both be substantially extended to characterize the expenditure on such public goods. Couched in terms of the structure of the network, the extended Samuelson condition and Lindahl scheme formulate precisely how the local publicness of a local public good fundamentally determines its optimal provision and the personalized price that the Lindahl tax-payer faces. Independence of the optimal allocation from the distribution of resources at interior Samuelsonian solutions in the network generally fails to hold even for the Bergstrom-Cornes preferences.

The symmetric two-player Hirshleifer (1989) contest is shown to admit a unique equilibrium. The support of the equilibrium strategy is finite and includes, in particular, the zero expenditure level. We also establish a lower bound for the cardinality of the support and an upper bound for the undissipated rent.

We offer simple and intuitive proofs of the Euler equation and the maximum principle based on Gossen's Second Law, one of the best known results in economics.

The implications of the international demonstration effect (IDE) for the development of underdeveloped economies have long been studied and debated. Yet few formal analyses exist in the literature, especially regarding its implications for the growth of domestic markets and the division of labour in developing economies. We offer an analysis of endogenous specialization under IDE, the first of its kind, showing that, far more complicated than the scenario held by conventional wisdom, IDE makes more difficult the emergence of the market underpinning the domestic division of labour, but facilitates the expansion of the market once the market has been developed.

We develop a model of parallel contests, asymmetric in quantity of homogeneous prizes open to contest, with a finite number of homogeneous risk-neutral bidders assumed to have a linear effort-cost function. We show that at equilibrium the expected effort per capita in the larger contest is greater than in a smaller one. The larger contest nonetheless does not attract enough contestants to achieve the optimum in extracting the rent from the bidders. Such an optimum can be achieved by a careful design of the asymmetric entry fees across the contests. The asymmetry between the contest-specific entry fees decreases as the number of the bidders increases, and approaches zero in the limit.

We take a real analysis approach to characterize the symmetric mixed-strategy equilibrium (SMSE) of rent-seeking contests for any intermediate value of the decisiveness parameter, allowing for both the ratio-form and the difference-form of contest success functions (CSF) that are axiomatized in Skaperdas (1996). For the ratio-form Tullock contest, we reproduce the results obtained by Ewerhart (2015) by invoking sophisticated complex analysis that SMSE is supported by a countably infinite set of pure strategies that has zero bid as an accumulation point and that the rent is completely dissipated. For the Hirshleifer-style difference-form of CSF, we show that the support of SMSE is a finite set of pure strategies including zero bid as one mass point and that the rent is partially dissipated. The similarity and differences in the profile of SMSE between the two canonical forms of CSF in the literature of contests are thereby illuminated.

We investigate whether people are influenced to make investment decisions based on random shock signals and to what extent they do so by exploiting a unique data set from a popular Chinese lottery game with over one million observations. We first present evidence that people, as individual investors in the field, not only systematically commit the hot-hand fallacy in chasing the winners who happen to pick the lucky numbers in the latest round of the lottery game, but are also willing to bear a cost in doing so although winning the lottery is merely a random shock. We then propose a simple model to account for the observed market behaviors. We further estimate the lottery players’ willingness to pay for the random shock signals, and find that the market value of such illusion is significantly high.

Like their Greek counterparts, a number of Chinese thinkers of the “Axial Period” wrote extensively on the division of labour. In particular, Kuan Chung, Hsun Tzu and Ssu-ma Ch’ien explicitly discussed economic issues related to the division of labour, contributing sophisticated analysis on the subject. In this article, we first examine Kuan Chung and his followers’ fairly interesting analysis of the economies of agglomeration of specialists, and Ssu-ma Ch’ien's deep insight into the Taoist invisible hand of the market in coordinating the division of labour. The common ground between them is a sound understanding of the role of market exchange in facilitating the social division of labour, but the latter goes much further in appreciation of the spontaneous market order. We then turn to Hsun Tzu's profound scholarship of specialised learning or doing and his Confucian theory of the origin of social division, highlighting, in particular, his Confucian notion of natural equality and utilitarian accou...

When does everyone genuinely contribute in the private provision of a local public good? We first introduce a monotonic condition to characterize the relationship between the structure of the network that underlie the noncooperative game of private provision of local public goods on the one hand, and the preferences of the agents on the other, showing that the monotonic condition is a sufficient and necessary condition of existence of a distributed Nash equilibrium (DNE) in which each agent exerts a positive amount of effort to provision of the public good (Theorem 1). We then study the number of equilibria, and, by using the monotonic condition, characterize the condition under which the DNE set is a singleton, a continuum, or null (Theorem 2). As it turns out, the structure of the network and the agents’ preferences jointly shape the effort profile in the provision of local public goods.

The standard excess demand argument for existence of competitive equilibria in exchange economies invokes maximizing the market value of the aggregate excess demand function and thereby adjusting the prices toward equilibrium. By exploiting the Perron-Frobenius theorem on stochastic matrices, we offer an algebraic proof of the existence of a competitive equilibrium without resorting to such a device of excess demand.

Economies may be integrated through flows among them of production factors such as labour (immigration), capital and technology (FDI, technology diffusion, joint undertaken R&D activities, etc.), a...

A life cycle framework is developed to examine how the value of time (VOT) changes as one ages. We consider two risk-sharing schemes, the Tonti scheme under which wealth is actuarially insured, and the Robinson Crusoe scheme under which insurance institution is entirely absent. For the first time in the literature, we characterize the condition, in terms of key parameters for valuating VOT, under which VOT may increase, decline, or even display more complicated profiles, as one ages. Our analysis reveals the crucial role played by the relative magnitude of the market interest rate to other parameters (including the parameter of time preference, the age-specific mortality and the wage growth rate) in determining the age profile of VOT, and the difference in VOT that is caused by the insurance scheme.

Brody (1997) notices that for large random Leontief matrices, namely non-negative square matrices with all entries i.i.d., the ratio between the subdominant eigenvalue (in modulus) and the dominant eigenvalue declines generically to zero at a speed of the square root of the size of the matrix as the matrix size goes to infinity. Since then, several studies have been published in this journal in attempting to rigorously verify Brody's conjecture. This short article, drawing upon some theorems obtained in recent years in the literature on empirical spectral distribution of random matrices, offers a short proof of Brody's conjecture, and discusses briefly some related issues.

Nasir ad-Din Tusi's (born 1201 in Tus in northeastern Persia; died 1274 in Baghdad), has been far more influential for his various contributions to astronomy and mathematics, including founding the Maraghah observatory (in Iranian Azerbaijan) and his brilliant reformulations of the Ptolemaic planetary model, which served as an important inspiration for Nicolaus Copernicus (1473–1543) revolutionary work than for anything else. Nonetheless, he also stands as one major figure in the medieval Islamic philosophical ethics and a profound thinker on socio-economic matters, as is attested by his masterpiece Akhlāq-i Nāsirī (The Nasirean Ethics – titled after his first name), from which the following Fragment is taken. He may be deservingly credited as an important pioneer of the science of political economy.

The implications of the division of labor, capital, and technology for economic growth have long been a fundamental issue in development economics. This paper employs the bounds testing approach to cointegration to examine the relationship between the division of labor, capital accumulation, communication technology, and economic growth for China over the period 1952–99. We find that in the long run, capital stock and the division of labor both have statistically significant positive effects on growth, while in the short run the effects are not significantly positive. Telecommunication technology, rather surprisingly, has a statistically insignificant impact on growth both in the long run and in the short run. Our findings indicate that there exists a long run equilibrium relationship between capital and the division of labor on the one hand, and economic growth on the other, thereby lending support to the division of labor theory of growth.

This short article offers economically intuitive proofs of the Euler equation and the maximum principle based on one of the best known results in economics, namely that the marginal utility of one extra dollar spent on each consumption goods is the same for all the consumption goods as required by budget-constrained utility maximization.

Division of labour presents itself ubiquitously in economic activities, especially in knowledge economies of which a remarkable feature is the increasing specialization at the individual level, as well as at firm, industry, region and even economy and world levels. A central theme in classical economics, most prominently in the writings of Smith, Turgot, Marx and even in Marshall (Sun, 2005a), has been specialization and the division of labour. However, this virtually disappeared from economic analysis after the famous debate initiated by Piero Sraffa on the incompatibility between Marshall’s external economies and competitive equilibrium in the late 1930s. This was partly due to the lack of analytical frameworks that encompassed increasing returns to specialization and competitive equilibrium. However, things have changed dramatically in the last two decades. In fact, the rapidly growing literature on this subject matter, of which an up-to-date literature survey is Cheng and Yang (2004), is indicative of the point that the study of the division of labour may well, and should, be brought back to the core of the economics discipline. The central notion underlying most of the burgeoning literature is the concept of increasing returns to the division of labour, namely that the production possibility frontier (PPF) of the economy as a whole expands – and consequently the per capita income increases – with the nexus of exchanges and economic interdependence between its differing parts (for more involved elaborations, see, e.g. Buchanan and Yoon, 2000, p. 45; Sun, 2005b, pp. 16–17). Increasing returns to the division of labour are not the same thing as the concept of increasing returns to scale at the individual firm’s level that is conventionally adopted in the textbooks. Increasing returns to the division of labour are rooted in interdependence between the division of labour, which often occurs in the production sphere, and the extent of the market, which is of course associated with the process of market exchange. The so-called Smith Theorem (Stigler, 1951) that the division of labour is limited by the extent of the market is perhaps one of the best-known propositions to economics students. Less known, but no less important, however, is that the extent of the market is also dependent on the division of labour, which indeed largely determines productivity, and hence how much ‘surplus’ one can dispose of in the market exchange for other products/services. Each market participant’s choice of specialization in the exchange-nexus doesn’t just determine what and how

Lijphart (1997) endorses compulsory voting as a means to increase voter turnout. Considering the likely effects of the role of information (including its costs) on the decision to vote and taking an expressive view of voting, however, compels us to investigate two unexamined claims by such advocates: (i) that individuals are transformed by forcing them to vote, and (ii) that a compulsory electoral outcome is a more accurate reflection of community preferences.We argue that compelling those who are not particularly interested in, or informed about, the political process to vote increases the proportion of random votes and we show that under simple majority rule, compulsory voting may violate the Pareto principle; the less popular candidate is more likely to be elected. Our results cast doubt on the ”miracle of aggregation“ argument, which optimistically concludes that as long as uninformed votes are not systematically biased, they will have no effect on voting outcomes. We also briefly consider how information cascades can exacerbate this problem.

This Note takes a preliminary investigation into the axiomatic measurement of the division of labor. We first introduce a matrix that we refer to as labor specialization matrix (LSM) to describe specialization patterns of individuals, and then present some axioms for reasonable measures of the division of labor. Remarkable among the axioms are the Schur convexity and the transference condition, both being related to increasing returns to specialization. From the axioms are derived a class of measures, which are then exemplified.

No abstract received.

External habit formation explains why welfare states can be expected to exhibit increasing dependency over time expressed in the share of the population receiving welfare transfers. At the same time, the average number of hours worked decreases. Under plausible parameter values, the rate of taxation and the welfare expenditure share of national income monotonically increase over time and asymptotically approach a steady state. A positive interactive feedback loop between slow-moving external habits and welfare policies makes the extent of redistribution a “moving target”. Consequently, setting arbitrary redistributive goals may never satisfy redistributional demands in future periods. Technological progress may mask the underlying dynamic effects of the welfare state.

After outlining what appears to be the central principle unifying the literature of the division of labour that has been expanding during the last two decades, I highlight a set of selected research topics, which appear to me to be of particular significance and therefore deserve much further exploration.

In the paper we study a general equilibrium model with specialization and division of labor. The function of the market is not only to allocate resources for a given structure of division of labor, but also to coordinate all individuals' decisions in choosing their patterns of specialization in order to utilize positive network effects of division of labor net of transaction costs. We establish the equilibriuni existence theorem, the first and second welfare theorems, and the core equivalence for a family of general equilibrium models with both possible increasing returns and transaction costs. Using an analytical framework with consumer-producers, economies of specialization, and transaction costs, the spirit of the classical economics of the division of labor is resurrected in a modern body of mathematical formalism.

This paper investigates Allyn Young's two important doctrines concerning the division of labor and roundabout production. First, apart from advancing the state of knowledge, the progressive division of labor that can occur within a given population encourages the adoption of more specialized, differentiated intermediate goods in the production process. Second, the level of division of labor and the extent of the market depend on each other. Using a general equilibrium model with increasing returns to specialization, economies of complementarity between intermediate goods, and transaction costs, we demonstrate that the level of division of labor and the number of intermediate goods increase concurrently as transaction conditions are improved.

In the popularly used ranking method of peer rating, the exclusion of the evaluations/marks given to oneselves is intuitively appealing and has been actually practiced, since a person/university/country typically is biased in favor of itself. This short paper shows that this apparently reasonable principle of self-exclusion may give unacceptable rankings. In particular, it may rank B over A despite the fact that everyone including B ranks A over B. An impossibility theorem (in two versions) is proved, showing that, if the self-awarded marks are excluded, no method of ranking can satisfy some compelling conditions like monotonicity, neutrality, and weak unanimity. Some proposals to overcome the difficulty are discussed. While no ideal proposal has been discovered, some may be practically acceptable in most cases.

We show in this short note that the thesis in Tullock (1994) about how the environment coordinates the division of labor in non-human societies can be formulated by the fixed-point argument. As such, both what maybe called the Tullockian environmental coordination and the conventional Walrasian pricing coordination in economics turn out to be special cases of a more general principle, into which further exploration remains to be made.

Summary In pursuing their plans economic agents regularly have to adjust their pacing of orders, production, and deliveries in unanticipated ways. Information constraints turn many of these adjustments into myopic reactions to accelerations/decelerations observed in the activity level of suppliers and/or customers. For analyzing the resulting dynamics, this note suggests a macroeconomic model derived from the idea of representing the adaptive interdependencies in terms of a system of integrated service channels. It sheds new light on what happens in stages of strained/exhausted production capacity and implies the possibility of cycles in aggregate output due to imperfectly synchronized production processes.

A general equilibrium model with increasing return to labour specialisation and economies of transaction agglomeration is developed to address the residential land-rent escalation associated with the urbanisation process, which is in turn endogenised as a result of the evolution of the division of labour. The interplay among the geographical pattern of transactions, trading efficiency and the network size of the division of labour plays a crucial role in our story of urbanisation. We show that: as transaction conditions are improved, the equilibrium level of division of labour and individuals specialisation levels increase; the urban land-rent increases absolutely as well as relative to that in the rural area, the relative per capita lot size of residence in the urban and rural areas decreases; the diversity of occupations in the urban area and the population share of urban residents increase; and the productivity of all goods and per capital real income increase.

Summary. In empirical studies concerning comparison of economic structures and/or structural changes of economies, it is quite useful to employ an aggregate index to describe the structural difference (similarity). This paper offers an axiomatic characterization of the measurement of structural difference between economies that leads to some difference (similarity) index which is practically useful in empirical studies.

This paper develops a formal model with transaction costs and economies of specialisation to address the size of the firm and the level of social division of labour. It is shown that the increase of the level of social division of labour and the decline of firm size may concur, and that the size of the firm crucially depends on, among other things, the relative transaction efficiency of the labour market with that of the markets for intermediate products.

This paper develops two models of the lobbying of interest groups to examine the effect of the number and size of interest groups on rent dissipation. In cases where individuals ignore the effect of the lobbying activities on the rent size, the number of groups is negatively related to rent dissipation and there exists an inverse relation between the extent of egalitarianism of within-group rent sharing rules and the total rent dissipation in the symmetric setting. Model two examines the case where each individual in each group takes into account the effect of lobbying activities on the total “pie”, of which she/he competes for a share through within-group and between-group interaction. The relation between the number of symmetric groups and the total rent dissipation is shown to be an inverted “U”-shape, contrary to the conventional wisdom that holds a monotonous relation between the two variables.

An interactive Markov chain model of multilevel substitution process is presented and discussed briefly. An upper triangular matrix, whose elements on and above the main diagonal are the transition probabilities arranged in some order, is proposed as a criterion matrix for the monotonicity of the transition matrix.

We develop a framework, extending the conventional duopoly model by replacing the Hotelling line with a simplex in high-dimension spaces, to study the competition and access regulation of multiple networks. We first characterize the competitive equilibrium when the substitutabilities of the networks are not too high, or the access charges are nearly cost-based. We then analyze how the equilibrium market shares respond to marginal variations in the access charges under various regimes of access regulation, and thereby examine the efficiency implications of such regulation regimes. In particular, we analyze the asymmetric scenario in which some networks are incumbent and some are entrants. It is shown that some existing results of the duopoly do not extend to a multi-firm setting, largely because regulation of multiple networks is structurally far richer.

In this short paper, we investigate the behavior of the age-dependent value of a statistical life (VSL) within a lifecycle framework with a finite maximal possible lifespan. Some existing results, obtained under the unrealistic assumption of an infinite life expectancy, are reversed. In particular, we show that when the market interest rate is equal to (or less than) the sum of age-specific mortality rate and the discounting rate in time preference at any age over the remaining lifetime, then VSL declines. We also show that an inverted-U shape of VSL profile over the life cycle emerges under realistically plausible circumstances. An innovation is that we characterize the changes in optimal consumption and instantaneous utility with age, showing that such changes are proportionate to the difference between the sum of age-specific mortality rate and the discounting rate in time preference and the market interest rate, which may prove to be useful in addressing other issues related to VSL.

This paper analyses the effects of inter-market and intra-market income heterogeneities on output and social welfare under uniform pricing and differential pricing regimes by considering a finite number of markets. We first derive the linear demand curve in each market under plausible conditions, and then show that more markets (and consumers) are excluded under uniform pricing the higher are the inter-market income differences. We also show that adding markets, even of lower income levels than those of existing markets, helps to decrease prices and thus cause more markets to be served. Implications of intra-market income dispersion are also explored., Cet article analyse l'effet des disparités de revenu inter et intra-marché sur le produit et le bien-être social, sous des régimes de prix uniformes et différenciés en considérant un nombre fini de marchés. Il calcule la courbe de demande linéaire de chaque marché dans des conditions plausibles et montre ensuite que plus les différences de revenu inter-marché sont élevées, plus les marchés et les consommateurs sont évincés dans des conditions de prix uniforme. Il montre aussi qu'en ajoutant des marchés, même à des niveaux de revenus inférieurs, cela tend à diminuer les prix et ainsi à satisfaire plus de marchés. Nous explorons aussi les implications de la dispersion de revenu intra-marché.

Nothing New under the Sun? Pieces up to Adam Smith Classical Political Economy Marshallian Economics The Austrian Insights.