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O pewnej implikacji

100%
PL
The purpose of this paper is to show how the process of provinga theorem in different ways or proving generalized versions of the theorem,after learning one its proofs, influences the development of the skills of provingtheorems and analysing proofs by the students of mathematics. Toillustrate this process we use an elementary theorem about numbers and itsgeneralizations, giving fourteen proofs. Proving theorems we use methodsand facts which are available to high school students.
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The Janus Face of Homeownership-based Welfare

80%
EN
This paper reflects on the different faces of asset-based welfare from both a theoretical and an empirical perspective. It shows that asset-based welfare can be perceived as a lever for welfare state restructuring but also as an instrument for poverty eradication. In most countries, asset-based welfare policies focus on stimulating home-ownership. The general idea is that by becoming a homeowner, households build up equity that can be released for care and pension purposes in old age. However, there are signs that such policies increase inequality between homeowners (depending on the location of the dwelling and/or the period in which it was bought), but particularly so between homeowners and tenants. We therefore contend that home-ownership based welfare policies need a clear and fundamental specification of the role of the government: how to deal with housing market risks and how to prevent politically unacceptable levels of inequality and exclusion?
EN
Research background: Income inequality and poverty attract a lot of attention among politicians, activists as well as scientists, who are trying to find a solution to these socio-economic problems. State intervention is commonly expected in this field, however, there is no agreement about the most efficient methods and instruments, as well as about the scale of public expenditure for the purpose of limiting poverty and inequality. Purpose of the article: The aim of the paper is to specify efficiency of government social spending in reducing problems of poverty and income inequality in the EU countries. Moreover, the attention is paid to changes in the efficiency in a period of the 2007 crisis occurrence and its overcoming and to sources of the changes. Methods: To fulfill the main goal of the paper, the DEA method is used, which enables to compare the social efficiency of the EU countries. The Malmquist index is also calculated and decomposed to identify changes in the efficiency and their sources in the crisis period. Data used in the analyses were obtained from Eurostat and OECD databases and cover the period from 2007 to 2016 year. Findings & Value added: The main findings of the paper shed some light on the differences in social efficiency of government spending in the EU countries. Generally, the countries with a higher level of social spending are also those with lower efficiency in inequality reduction, however, the relationship doesn?t appear for poverty alleviation. Thus, the research suggests some substitution between the scale and the efficiency of social spending, at least for the inequality dimension. Moreover, some differences in a social model can be found between the countries of the  South and of the North: the countries of the South focus their social policy mainly on inequality reduction, while the Scandinavian countries as well as some other affluent societies direct their public support mainly on poverty alleviation. The research also shows that in the crisis period decreases in efficiency concerned mainly the poverty dimension. It reflects the fact that the poor were the losers of the crisis in favor of the middle classes. The efficiency losses were induced by negative changes in the current usage of public sources, while institutional reforms positively influenced the efficiency.
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Critical Housing Analysis
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2020
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vol. 7
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issue 1
103-113
EN
This article sets out a theoretical framework for the political economy of the private rental sector, with a particular focus on the question of inequality. It brings together three existing bodies of research. First, macro-accounts of social stratification and wealth inequality. Second, Marxian critiques of the antagonism between accumulation and social reproduction. Third, qualitative accounts of tenants’ experiences of housing inequality. The article synthesises these three literatures to put forward a political economy approach which can capture the multi-dimensional and multi-scale nature of both ‘housing’ and ‘home’ in the private rental sector. In so doing, it contributes to recent research on ‘generation rent’, in particular the related class and generational inequalities, as well as wider debates on the political economy of housing.
EN
Although influence of reference population on assessment of individual position is well recognized on the ground of sociology, its impact is rarely taken into account in economic analysis of inequality. Few analyses that are concerned with issue of reference groups in the context of inequality and relative deprivation measurement deal, however, with single reference group. The aim of the paper is consideration on how concept of reference populations of different kind (reference groups and reference categories) may be applied to assessment of aggregated complaint that results from inequality in income (wealth) distribution.
EN
The article deals with the unequal treatment of company shareholders. The analysis is conducted from the perspective of minority shareholders and their interests. The author uses a research method that presents the position of minority shareholders in companies on the basis of the agency theory. Szewc-Rogalska shows the influence of dominant shareholders and top managers on the market value of companies (in light of both Polish and foreign empirical studies), along with a review of ways to limit inequality among shareholders. The analysis reveals that the position of minority shareholders can be threatened by agency conflicts that occur in companies. In companies with concentrated ownership, these conflicts are different than in companies with scattered ownership. After a dominant shareholder exceeds a certain level of ownership, the company is likely to face problems resulting from the shareholder’s desire to pursue their own interests at the expense of other shareholders. Inequalities among shareholders cannot be eradicated completely, and there is no single fully efficient mechanism to protect minority shareholder rights. A diverse range of activities is needed, including improved information transparency of companies and better corporate supervision, in addition to increased activity of minority shareholders and the creation of legal mechanisms to protect their interests.
EN
Research background: In Economics, the concept of inequality aversion corresponds with the concept of risk aversion in the literature on making decision under uncertainty. The risk aversion is estimated on the basis of subjective reactions of people to various lottery prospects. In Economics, however, an efficient method of estimating inequality aversion has not been developed yet. Purpose of the article: The main aim of this paper is to develop the method of estimating inequality aversion. Methods: The method is based on two income thresholds which are subjectively assessed by surveyed respondents. Given the level of household income, just noticeable worsening of household welfare is perceived below the first threshold, whereas just noticeable improvement of household welfare is perceived above the second threshold. The thresholds make possible effective calculations of the parameter of the Arrow-Pratt’s constant inequality aversion utility function. In this way, an individual utility of income becomes an empirically observable economic phenomenon. Findings & Value added: In this paper, two theorems are proved which provide the guidance on how to identify a proper version of the above function. The proposed method is tested on the basis of statistical data from the archival survey conducted among Polish households in 1999. The statistical analysis of those data reveals the appearance of convex utility functions as well as concave ones. Nevertheless, the prevailing part of the Polish society exhibited inequality aversion in the year 1999. Another result of this paper is that inequality aversion diminishes as income increases.
Nowa Krytyka
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2016
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issue 37
119-140
EN
The aim of this paper is to present a few contemporary social theories concerning inequality against the background of Karl Marx theory. The author is interpreting work of the Dahrendorf, the Piketty, the Standing and the Stiglitz, showing their contribution to understanding our present time, as well as indicating their weak points. Moreover such authors are being mentioned as Therborn, Merrifield or Caparrós. The main question is: can we talk about the class global society? The author is answering that we are dealing today with next “primitive accumulation”, and we can expect the new class struggle in the future.
EN
The paper deals with the relation between income inequality, innovation processes, economic development and income convergence within the European Union. The presented results suggest a non-linear relation between the economic development and the income inequality. There is also visible the significant influence of innovation activity and technology diffusion on the economic growth. We could observe strong and stable innovation-related polarisation into two different groups of countries in the European Union, as well as a phenomena that countries considered as technological followers imitate the innovation leaders very quickly. The real convergence occurs on the international scale, but not at the regional level. It seems that the latest tendency will remain in the future.
EN
The most common measure of inequality used in scientific research is the Gini index. In 2007, Zenga proposed a new index of inequality that has all the appropriate properties of an measure of equality. In this paper, we compared the Gini and Zenga indexes, calculating these quantities for the few distributions frequently used for approximating distributions of income, that is, the lognormal, gamma, inverse Gauss, Weibull and Burr distributions. Within this limited examination, we have observed three main differences. First, the Zenga index increases more rapidly for low values of the variation and decreases more slowly when the variation approaches intermediate values from above. Second, the Zenga index seems to be better predicted by the variation. Third, although the Zenga index is always higher than the Gini one, the ordering of some pairs of cases may be inverted.
EN
Research background: Income inequality has risen sharply since the 1990s, despite the increase in the average size of redistribution in countries representing different welfare state models. The problem of increasing income inequality is currently a challenge for the EU economies, not only with well-established liberal traditions, but also with conservative and social-democratic ones. Therefore, it is worth conducting research on the redistributive effects of fiscal policy. Purpose of the article: The article aims to show the redistributive effects of fiscal policy, paying particular attention to the most characteristic trends in redistribution, which are responsible for the growing income inequality. An overview of the fiscal instruments ? mainly personal income tax and benefit systems ? along with an empirical research on their potential impact on income inequality, allows for conclusions to be drawn about the effectiveness of redistributive policy in the EU countries. Methods: Both descriptive analysis and panel data analysis is implemented to examine the effectiveness of redistributive policy in tackling income inequality in the EU?28 countries in years 2005?2017. Findings & value added: Based on the panel analysis, it has been found that social transfers were much more effective than direct taxes in combating income inequality. In addition, the largest increase in income inequality ? as previously assumed ? was observed in the liberal welfare states, while the smallest in the social democratic welfare states. The empirical analysis extends the existing knowledge on main weaknesses of fiscal welfare state, indicating the required changes that may improve both its equity and efficiency.
EN
In 1996 Latvia became one of the first countries in the world to adopt the notional defined-contribution (NDC) pension system. The authors have been studying the distribution of old-age pension benefits in Latvia and its dynamics over recent years. They conclude that the Latvian pension formula practically lacks any redistribution mechanism, pension benefits do not have any upper limits, and the minimum level is set as inadequately low. Pure NDC systems are not adequate for countries with a relatively large gap between the rich and the poor (as is the case of Latvia); material stratification is not evened out in old age, and combined with low replacement rates it leads to massive poverty among the elderly. Latvian authorities have recently recognized the need for NDC pension system improvement, and elaboration of the basic pension concept in Latvia should start in 2015. The authors provide a brief comparison with the situation in neighbouring Estonia, where the distribution of pension benefits is much more even.
EN
Tax systems are useful indicators of the economic and political conditions which concur to shape them. With respect to developing countries, an analysis of the tax burden can help to understand how the process of modernization is sustained through fiscal extraction from different social classes and productive sectors. This paper presents statistical evidence on the distribution of taxes in Japan around the time of World War I, which was a pivotal moment for both economic growth and political change. Sources indicate that government officials had a clear perception of inequality and its structural causes; the surveys examined here can therefore be considered a starting point for reform of the tax system, as discussed in the next twenty years.
EN
The aim of this paper is to obtain a sample from the world income distribution (WID). We assumed log-logistic form of countries’ income distributions with unit means. This implies that such distributions are fully described by their corresponding Gini indices. Gini estimates came from Deninger-Squire, WID2, and other databases for 119 countries in the years 1990-2005. We generated random sample for every distribution and multiplied its values by GDP/capita. Sample size was controlled by sequential ratio test. The world sample consisted of country samples weighted by population shares. We have found that WID is bimodal with diminishing inequality and poverty during analyzed period.
EN
The problem of calculating the Gini index in the presence of negative inputs may be overcome by decomposing the quantity at stake into “positive” and “negative” parts, which, by definition, include only non-negative values. For such constructed sources, concentration indexes may be calculated and their influence on the overall inequality evaluated. In the paper we present the methodology of such an assessment and illustrate it with the example of Italian income data.
EN
The Zenga index of inequality is a new proposal of measuring this phenomenon. The properties and empirical applications of Zenga index (and the underlying Zenga curve) have been recently widely investigated. Its advantages (and differences, as compared to other existing measures) have been pointed out. However, one of the possible problems associated with the use of the Zenga index has not yet been appropriately addressed.Namely, the Zenga index assumes different values depending on whether it is applied to grouped or ungrouped data. As it may seem that due to contemporary computers power it is not necessary to group data, the problem still exists as a conceptual one. Moreover, in some situations – such as applying equivalence scales – avoiding grouping of the data is not possible even in principle. The problem is stated, illustrated by simple numerical examples and briefly discussed in this paper.
EN
We study the evolution of income and wealth inequality in an economy undergoing endogenous structural change with imperfect labor mobility. Our economy features two sectors: services and manufacturing. With faster TFP growth in manufacturing, labor reallocates from manufacturing to services. This reallocation is slower due to labor mobility frictions, which in turn, raises relative wages in services. As a result, income inequality is higher. Moreover, we study the impact of structural change on wealth inequality. Its economic intuition is more ambiguous. On the one hand, increased income dispersion implies increased dispersion in the ability to accumulate wealth across individuals. On the other hand, younger workers who hold the least assets are the most mobile across sectors. Their incomes are improved, which boosts their savings, which works towards equalizing wealth distribution. The consequence of these changes can only be verified with a computational model. To this end, we construct an overlapping generations model with two sectors: manufacturing and services. Our model also features heterogeneous individuals. With our model, we are able to show how the structural change affected the evolution of income and wealth inequality in Poland as of 1990.
EN
The study investigates whether economic growth in the Balkan countries was pro-poor in the most recent period. We also try to establish to what extent various measures of pro-poorness of economic growth produce consistent and comparable results. Firstly, concepts of pro-poor growth are defined and corresponding approaches toward measuring pro-poor growth are presented. We distinguish between measures based on a general class of pro-poor indices and a dominance-based techniques. In the empirical part of the study, we verified whether economic growth in six Balkan countries (Greece, Bulgaria, Romania, Slovenia, Croatia and Serbia) was pro-poor in the 2012–2017 period. The analyses is based on the latest available panel data of the European Union Survey on Income and Living Conditions (EU-SILC). Growth was pro-poor in Croatia, Romania and Slovenia during the whole analysed period. The growth pattern was non pro-poor in Bulgaria, Greece and Serbia in certain years, mainly during periods of economic downfall. Various measures of pro-poor growth patterns do not produce consistent results in all instances. The results of the conducted comparative analysis suggest that the level of social benefits does not directly influence the pro-poor nature of the economic growth.
EN
This article investigates the rise of populism in Poland, applying an interdisciplinary method, with political, social, and economic factors as the compound reason for the turn from liberalism towards populism. The methodology of the study is the exploratory analysis of research, historical materials on Poland`s transition to capitalism, and calculation of the selected empirical data of household incomes, linked to election results, in the regional cross-section. The household economic condition was validated by a report on deprivation and the presented growth of households’disposable income, exposing regional differences between the selected voivodeships. The populist party Law and Justice (PiS) won the two last elections, with the majority of votes in low-income regions, which proved the hypothesis that economic inequality, amplified by globalisation and transition disparities were the main reasons for populism’s prevalence. The democratic backsliding has not changed party-political scenery for very long, which revealed that for the majority of Polish voters, economic upgrading counted more, despite the violation of democracy. Therefore, the advance of knowledge about measures to reduce the in-country socioeconomic disparities between regions has become more important.
EN
Financial inclusion has been one of the key pillars of Colombia’s development strategy for a number of years. Financial inclusion policies have aimed at channeling microcredit to poor, spreading formal banking system usage, fostering electronic payment acceptance, and making financial services more affordable. Using simulations from a general equilibrium model it is possible to identify the most binding financial sector frictions that preclude financial inclusion of enterprises, and study the effects on growth and inequality of efforts to remove these frictions. The study finds that lowering contraints on collateral promises higher growth while inequality is better tackled through measures that lower the financial participation cost
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