The paper deals with models of household economy with infinitely many agents classified into a finite number of types. The notions of competitive equilibrium, core and quasi-core are examined with special emphasis on their mutual relations.

Public Employment Services (PES) are identified as important institutions in the process of improving the match between supply and demand in the labor market, which, despite their importance, still do not achieve the desired efficiency. The indicated problem is partly due to the lack of appropriate evaluation methods for the applied labor market policy instruments. This paper aims to verify the possibility of using the two-stage Data Envelopment Analysis (DEA) method in measuring the efficiency of public sector entities. The authors focused on 39 PES operating in Mazovia province, Poland in 2019. In the first stage, the model of technical efficiency of local PES included six variables (four inputs and two outputs). Only seven PES obtained full efficiency. The inefficiency of analyzed PES varied from about 1% to 80%. In the second stage, the attention focuses on the relationship between true unknown efficiency and its determinants (five environmental variables, both demand and supply oriented). Then, the regression coefficients and confidence intervals showed that three out of five variables influence the efficiency results, the share of the long-term unemployed, the share of the unemployed under 30, and the share of the unemployed over 50 in the total number of unemployed.

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The aim of this study is to evaluate and compare the financial and managerial efficiency of healthcare inpatient systems in one country. The research question is: What factors give rise to efficiency variations within the regional healthcare system (hospitals)?A two-step approach proposed by Simar and Wilson has been applied. The first step applies the Data Envelopment Analysis to estimate the unit (i.e., a Polish region in our research) efficiency scores, which is followed by truncated regression with double bootstrapping to examine the impact of uncontrolled variables on efficiency scores.The efficiency scores obtained in 16 regions from the output-oriented model with non-increasing returns to scale indicate a full effectiveness of five regions. The DEA scores of the other regions exceed the value of 0.8 and do not differ significantly.The bootstrap-corrected DEA scores do not considerably change the efficiency assessment. The direction of the impact of the ‘percentage of people above 65 years of age’ variable and the ‘growth rate of total liabilities on efficiency’ variable is opposite to that observed for the ‘average salary’ variable.The results obtained suggest that the regional healthcare system efficiency can be affected by the ageing population, pay pressure, and liabilities.

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