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The aging of European societies is reshaping their population pyramids. The increase in life expectancy and the decrease in the fertility rate lead to an increasing share of the elderly population. This leads to rising age-related expenditures, especially public pension expenditures to GDP. Consequently, economies are reforming their pension systems to make them more sustainable. Next to the aging-related challenges, the new EU members, eleven post-socialist economies: Bulgaria, Croatia, the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia, and Slovenia share a similar history of restructuring of their pension systems and establishment of a multi-pillar system. The objective of this article is to examine the similarities and differences between the pension systems of the selected post-transition economies of the European Union to establish the basis for further research, simulations, and assumptions on the impact of future pension reforms. For that purpose, we apply Ward’s clustering methodology on three variable groups in three selected years: 1996, 2006, and 2016. The idea of clustering economies in three years with a 10-year gap is relevant since it reveals how the cluster structure is changing over time. Additionally, three periods represent three different phases in the pension systems’ development. Three groups of variables were used for cluster analysis. First, pension systems’ characteristics include average effective retirement age, pension expenditure, and replacement rate. Second, demographics encompass fertility rate, life expectancy at the age of 65, net migration rate, and old-age dependency ratio. Third, the macroeconomics and labour market variables refer to the GDP growth rate, real labour productivity, labour force participation rate, and the unemployment rate. Results of cluster analysis show that the composition of the countries in the extracted clusters changes significantly, both throughout the observed period and when looking at different variable groups. Our results revealed that the pension systems of economies with later retirement proved to be more sustainable, during the three observed periods, due to lower pension expenditures that are in turn positively reflected in the favourable economic conditions and their labour market.

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 work is licensed under aCreative Commons Attribution-NonCommercial 4.0 International License.

Background: Duality in the microeconomic theory enables us to represent consumers’ preferences and production technology with various dual functions satisfying certain regularity conditions. Objectives: Since the basis for the application of duality in the microeconomic theory is the price taking behaviour, this paper takes the challenge of applying principles of duality to a monopolistic case where a single producer has an influence on the price which it charges for its product. Methods/Approach: The standard approach of deriving the profit function for the monopolist from the production function and the defined pseudoproduction function is accompanied by an alternative approach in which the starting point is the pseudocost function. Starting from the derived profit function, the pseudoproduction function and the pseudocost functions are recovered and a version of Hotelling’s lemma is given. Results: The structure of the profit maximization problem in a monopolistic case was made similar to the structure of the profit maximization problem in the perfectly competitive case and it is shown that all starting functions can be recovered back from derived functions. A version of Hotelling’s lemma is illustrated, which brings us indirectly from the profit function to the supply function. Conclusions: By introducing the pseudoproduction function in the profit maximization model of a monopolist, the structure of the problem becomes similar to the perfectly competitive case and duality results can be applied. The profit function is derived from the pseudoproduction and the pseudocost function, and all starting functions are recovered back from the derived profit function.

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.

This paper analyzes the mark-up of the price of a product over marginal costs for a monopolist using Appelbaum’s theoretical model. The profit maximization model of an industry that uses the monopolist’s product as its input is formulated. Our goal is to express the monopolist’s mark-up as a function of the elasticity of substitution for the respective industry and to analyze how changes in the elasticity of substitution affect the mark-up ratio. Consequently, the CES production function along with its substitution parameter is chosen. An analytical description of changes in the elasticity of substitution and its influence on the monopolist's mark-up is given. All scenarios are supplemented by geometrical illustrations, economic interpretations and numerical examples.

The problem of setting the reservation price in terms of a two-part tariff requires, subject to new prices, reducing the difference between minimum expenditure for the starting level of utility and nominal consumer income. This difference in expenditure can be translated into the area below a compensated demand curve. The compensated demand curve is not directly observable, so the reservation price in this paper is approximated by a change in the consumer surplus. For the case of heterogeneous consumers, a number of reservation prices exist. This paper will address error estimation in setting prices of a capital good and a service. The results obtained are demonstrated using a numerical example.

In the Stackelberg leadership model the follower firm acts like in the Cournot model and for the given level of production of the leader firm determines its own production level which maximizes economic profit. The leader firm chooses quantity knowing that the follower firm will react to it according to its reaction function. Many economic phenomena have Stackelberg model structure and in this paper the relationship between the client and the producer of embedded sofware is modeled using this approach. The product quality affects the likelihood of product safety and the consumers' utility but depends on the invested effort. The goal is to find an equilibrium in the Stackelberg model where the client is the leader, and the producer is the follower. In the first step, the producer chooses the number of units of labor for the given price of a product in order to maximize the expected profit. In this way the producer indirectly affects the software quality. In the paper the effect of the product price change on producer's reaction is analysed. The comparative statics results confirm our intuition. The higher the product price, the greater the level of labor units employed by the producer and the better the product. Increase in labor costs has opposite effect on the producer's decision. In the second step the consumer determines the product price in order to maximize his or her expected utility. This decision is affected by the producer's reaction or the price effect on the product quality. The consumer's utility and the software quality are usually directly related in the existing literature. In this paper, this relationship is complemented by the probability of product safety. Theoretical optimization models which are solved by the client and the producer are illustrated numerically and the total welfare in the Stackelberg and the cooperative equilibrium is compared. The effect of the change in relationship between the employed labor units and the software quality on the given results is analysed. According to our numerical example, the more favorable this relationship is, the higher is the client's and the producer's welfare in the Stackelberg equilibrium. Even though fewer workers are employed, produced software is better. The total welfare loss is smaller due to more dominant effect of more favorable relationship between employees and the software quality in the Stackelberg equilibrium than in the cooperative equilibrium. Given the sensitivity of the results, future research should be devoted to examining the functional relationship between given variables in specific phenomena. The cost of software maintenance could also be taken into account.