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The article presents a dynamic model of exchange, production, and consumption. In a dynamic world, complicated predictions often have to be made. Thus, in this article, the classical exchange model is expanded with a dynamic model specifying the intermediate states toward a static equilibrium, which may or may not be reached. A price mechanism was necessary to develop in order to describe these changes over time. The model is illustrated with two examples of the emergence of division of labor. The robustness of the dynamic model is tested with sensitivity analysis.

This paper develops a simple model of division of labor under perfect competition. The model shows under that the division of labor is compatible with perfectly competitive markets if coordination costs are increasing with the number of teams. We also show under what conditions interior solutions for the division of labor exist under imperfect competition.

After the COVID-19 pandemic, the whole world will operate remarkably differently over its global production chain. This paper develops a general equilibrium model with endogenous industrial cluster and endogenous industrial network based on the division of labor and specialization to formalize and explore the interrelationship and rules of industrial cluster, network of division of labor, the economies of specialization and agglomeration under the new era of post-pandemic global economy. The model suggests that institutional efficiency of mutual trust, and competition among countries and industries will facilitate important circular effects, which will propel and shape the arrangement and allocation of industrial clusters, the position located at the production chain, and consequently the status of economic growth. In particular, the improvements in institutional efficiency of mutual trust over economic and technology systems will expand the demand for transactions and network size, which in turn will determine the development of cluster and network scope, as well as the position of the network. It offers a partially economic explanation of the current concern of de-globalization, decoupling and de-risking after the pandemic.

Motivated by the study of social insects, we introduce a stochastic model based on interacting particle systems in order to understand the effect of communication on the division of labor. Members of the colony are located on the vertex set of a graph representing a communication network. They are characterized by one of two possible tasks, which they update at a rate equal to the cost of the task they are performing by either defecting by switching to the other task or cooperating by anti-imitating a random neighbor in order to balance the amount of energy spent in each task. We prove that, at least when the probability of defection is small, the division of labor is poor when there is no communication, better when the communication network consists of a complete graph, but optimal on bipartite graphs with bipartite sets of equal size, even when both tasks have very different costs. This shows a non-monotonic relationship between the number of connections in the communication network and how well individuals organize themselves to accomplish both tasks equally.

The division of labor (DOL) and task allocation (TA) among groups of ants living in a colony is thought to be highly efficient, and key to the robust survival of a colony. A great deal of experimental and theoretical work has been done toward gaining a clear understanding of the evolution of, and underlying mechanisms of these phenomena. Much of this research has utilized mathematical modeling. Here we continue this tradition by developing a mathematical model for a particular aspect of TA, known as age-related repertoire expansion, that has been observed in the minor workers of the ant species Pheidole dentata. In fact, we present a relatively broad mathematical modeling framework based on the dynamics of the frequency with which members of specific age groups carry out distinct tasks. We apply our modeling approach to a specific TA scenario, and compare our theoretical results with experimental data. It is observed that the model predicts perceived behavior, and provides a possible explanation for the aforementioned experimental results.

Response threshold models are an important tool to model division of labor in social insects and to investigate the underlying principles of self-organization. In this article response threshold models which incorporate dynamic environments with varying demand for work and their influence on division of labor are studied. In their natural habitats, social insects are always exposed to dynamic environments, however, the effect that such environments have on response threshold models has rarely been investigated. In the course of this article it is shown that overworking and underworking, i.e. working more or less than the ideal amount, over a certain time is a colony-size dependent effect in dynamic situations. By adjusting the number of possible learning steps, which correspond to changes in the maximal threshold values relative to a colony's size, the performance of colonies in dynamic environments can be increased. A setup inspired by repeated migration behavior is also investigated. It is shown that these different learning rates affect a colony's ability to maintain an activity onset for a reappearing task.

There were three anomalies in Japan in the 1990s: low output growth, declining asset prices, and widespread rollover of bad loans. In this paper, a model of multiple equilibria is presented in which these three anomalies emerge when too many firms become insolvent simultaneously as a result of a macroeconomic shock, such as a collapse of an asset-price bubble. A key factor is the role of debt contract as a commitment device for a debtor. Once a bad debt is rolled over, the debtor firm's commitment becomes untrustworthy, and the transactions among firms are disorganized. It is also shown that banks rationally roll over bad loans if too many insolvencies occur simultaneously.

This paper presents a simple general equilibrium model of economic performance through time. The model incorporates four main determinants of economic performance: technology, capital investment, the division of labor and quality of institutions. It demonstrates that growth is not automatic even with technological progress. In order to maintain economic growth, it is important to continuously implement new technologies through capital investment. It also shows that institutional improvement promotes the social division of labor, which is an independent source of economic growth.