European Union (EU) is facing large migration flows, whose distribution and volatility in the observed period between 2006 and 2015 across the EU member states, among other factors, were affected by the financial and economic crisis. This paper examines how the homogeneity of the EU member states was changing with respect to economic performance and migration statistics indicators. Consequently, the non-hierarchical cluster analysis by using k-means method was conducted based on the average values of the selected variables in four time periods: the pre-crisis, crisis, and post-crisis periods. The fourth period is year 2015, the beginning of massive immigration in the EU area due to world migration crisis. Our results indicate relative stability of the number and structure of clusters of EU-28 member states in the selected time periods on the bases of observed variables. There are few exceptions, however, related to countries that were heavily influenced by the financial and economic crisis, and Germany which stood out with decreasing unemployment rates and increasing net migration values in the post-crisis period.

In this article we analyse the short run profit maximization problem in a convex analysis framework. The goal is to apply the results of convex analysis due to unique structure of microeconomic phenomena on the known short run profit maximization problem where the results from convex analysis are deductively applied. In the primal optimization model the technology in the short run is represented by the short run production function and the normalized profit function, which expresses profit in the output units, is derived. In this approach the choice variable is the labour quantity. Alternatively, technology is represented by the real variable cost function, where costs are expressed in the labour units, and the normalized profit function is derived, this time expressing profit in the labour units. The choice variable in this approach is the quantity of production. The emphasis in these two perspectives of the primal approach is given to the first order necessary conditions of both models which are the consequence of enveloping the closed convex set describing technology with its tangents. The dual model includes starting from the normalized profit function and recovering the production function, and alternatively the real variable cost function. In the first perspective of the dual approach the choice variable is the real wage, and in the second it is the real product price expressed in the labour units. It is shown that the change of variables into parameters and parameters into variables leads to both optimization models which give the same system of labour demand and product supply functions and their inverses. By deductively applying the results of convex analysis the comparative statics results are derived describing the firm's behaviour in the short run.

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Recent macroeconomic and demographic trends have resulted in new challenges for pension systems. One of these challenges is to create a sustainable pension system while simultaneously providing adequate pension benefits for current and future pensioners. This research explores how similar are pension systems of eleven European Union countries by using hierarchical cluster analysis for year 2016. Variables representing pension systems, as well as demographic, macroeconomic and labour market data were used to cluster these economies. Three clustering solutions were generated using hierarchical clustering approach, one for each variable group. Given the number of observed countries, only two cluster solutions were considered. According to the characteristics of the pension systems, countries that have greater problems of unsustainability are recognized. A similar group of countries also forms the cluster characterized by unfavourable demographic trends that make it more difficult to maintain sustainability. Romania stands out from other economies, based on macroeconomic indicators, as it recorded faster economic growth, greater labour productivity growth and lower unemployment rate in 2016. The findings of this study provide a guideline for future pension reforms, since they indicate which countries' experience could be valuable in defining certain policy measures.

This paper examines a two-way relationship between convex analysis and microeconomic theory. Motivation for this paper are the observed similarities in the structure of the theory of consumer behavior and production theory. The fact that the behavior of variables is not determined by their nature but, rather, by their relationships is best illustrated and explained by using convex sets and convex analysis, which occupy central place in microeconomic theory. This paper is the result of efforts to make complex results of convex analysis and its application in microeconomic theory more transparent. Starting with the well-known economic phenomenon of profit maximization the authors derive in a novel way general results within the framework of convex analysis. From those results follow, directly and indirectly, the conclusions of the theory of consumer and producer behavior. The authors show that applying the Fundamental Theorems of Calculus opens up a new perspective in which the marginal cost curve can be interpreted as the marginal profit curve. This enables the derivation of Hotelling's lemma in a new way. Using the new interpretation of Hotelling's lemma, the authors reconstruct the cost function and confirm the Conjugate Duality Theorem of Legendre-Fenchel transformations. Relaxing the assumption of differentiability by describing the graph of the cost function as the envelope of its tangents, the authors rederive the properties of Legendre-Fenchel transformations and show that they hold in general. The path from the well-known economic facts to completely general conclusions of convex analysis is continued by applying the Conjugate Duality Theorem of Legendre-Fenchel transformations to the profit function. The essence of the dual characterization of technology by the profit function is illustrated by the graphical representation of linear homogeneity of the profit function. It results in the possibility to reconstruct the production function while using only the First Order Conditions to rederive Hotelling's lemma. It is this inductive-deductive approach used to examine the properties of Legendre-Fenchel trasformations and their application in the theory of consumer and producer behavior that establishes a two-way relationship between convex analysis and microeconomic theory.