The goal of this publication is to provide basic tools of differential topology to study systems of nonlinear equations and to apply them to the analysis of general equilibrium models with complete and incomplete markets. The main content of general equilibrium analysis is to study existence, (local) uniqueness and efficiency of equilibria. To study existence Differential Topology and General Equilibrium with Complete and Incomplete Markets combines two features. First order conditions (of agents’ maximization problems) and market clearing conditions, instead of aggregate excess demand function. Then, the application to that “extended system” of a homotopy argument, which is stated and proved in a relatively elementary manner. Local uniqueness and smooth dependence of the endogenous variables from the exogenous ones are studied using a version of a so-called parametric transversality theorem. In a standard general equilibrium model, all equilibria are efficient, but that is not the case if some imperfection, like incomplete markets, asymmetric information, strategic interaction, is added. Then, for almost all economies, equilibria are inefficient, and an outside institution can Pareto Improve upon the market outcome. Those results are proved showing that a well-chosen system of equations has no solutions. \ud \ud The target audience of Differential Topology and General Equilibrium with Complete and Incomplete Markets consists of researchers interested in Economic Theory. The needed background is multivariate analysis, basic linear algebra and basic general topology

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The collection of municipal solid waste (MSW) is a public service with notable effects on the environment and public health. The objective of this study was to evaluate the impact of selective collection and recycling of MSW on the performance of municipalities in providing MSW services. By employing the data envelopment analysis method, the efficiency and eco-efficiency scores for a sample of 298 municipalities in Chile were analyzed and compared. The efficiency estimation focused on the economic performance of the municipalities in the provision of MSW services, whereas the eco-efficiency assessment also integrated the environmental performance. The results indicated that the selective collection and recycling of MSW had a significant impact on the performance of the municipalities in providing these services. The percentages of efficient and eco-efficient municipalities were very low (4.70% and 4.36%, respectively), thus demonstrating the large room for performance improvement by Chilean municipalities in the management of MSW. The efficient and eco-efficient municipalities were heterogeneously distributed throughout the country, revealing the lack of collaboration between municipalities at the regional level. Finally, exogenous variables to the management of MSW carried out by the municipalities, including the population served, population density, tourism and waste generated per capita, all had an impact on the efficiency and eco-efficiency scores. The results and conclusions of this study are of great relevance for policy makers at the regional and local levels to improve the management of MSW in the context of a circular economy.

In European countries, wastewater treatment service is often provided by utilities, which have to comply with environmental laws and, at the same time, should control costs in order to restrain tariff growth and earn profits. By applying a conditional order-m efficiency method, this study provides some insights to the operational variables affecting the efficiency of 137 plants owned by a water utility operating in Tuscany, Italy. These performance drivers are categorized as: 1) wastewater features, 2) plant technology, 3) other plant features, 4) output quality, and 5) sludge disposal method. Starting from some controversial results from prior literature, this paper provides some useful insights on the best policies that could be adopted by a utility to catch cost savings

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