The influence of the utility function on the dynamics of the underground economy ALINA BADULESCU Department of Economics University of Oradea 1, Universitatii Str., 410087-Oradea ROMANIA abadulescu@uoradea.ro http://steconomice.uoradea.ro V. A. CAUS Department of Mathematics and Informatics University of Oradea 1, Universitatii Str., 410087-Oradea ROMANIA vcaus@uoradea.ro http://stiinte.uoradea.ro Abstract: In this paper we are investigating a mathematical model founded on the basis of the inter-action between underground economy and official economy. As starting point we are using the logistic model of Verhulst, completed with the effect of utility. Key-Words: utility function, underground economy, definitional approach, behavioural approach, equilibrium solution, Lambert function 1 Introduction The underground economy is subject of many scientific debates. Its consequences on economic growth have been studied by many authors. The underground economy (or shadow economy, unofficial economy, hidden economy, informal economy, non-observed economy etc.) is a reality – in different proportions and sizes – of all countries over the world and a subject of research in the same time. The literature on this issue focuses on several directions. The first one regards gathering statistics and information in order to estimate as accurately as possible its magnitude, size and components. The second direction investigates the causes and factors influencing its extension. This issue is particular important in the perspective of the measures, punishment methods and policies to control and limit its spreading. There is a quite large literature dealing with these aspects (and others). We can mention, not exhaustively: Frey and Pommerehne [1], Thomas [2], Lippert and Walker [3], Johnson et al. [4], Pedersen [5], Schneider [6] etc. The goal of this paper is to investigate the influence of the utility on the existence of the equilibrium points in the dynamics of the underground economy. In section 2 we briefly overview the basic approaches of the “underground” economy, in sections 3 and 4 we present a mathematical model built on the basis of the interaction between the underground economy and the official economy. The construct starts from the logistic model of Verhulst, completed with the effect of the utility. Section 5 concludes. 2 “The underground economy” – brief overview As known, there is no general agreed definition of the so-called “underground economy”. There are different opinions related to the definition and coverage of different activities, which can mainly be classified in two basic approaches: First, there is the definitional approach, describing the „underground economy” in terms of simply unrecorded economic activities. Second, there is the behavioural approach, considering that the „underground economy” is better defined in terms of behavioural characteristics. The main reasons of the existence of the „shadow economy” are resuming by Schneider [6]: RECENT ADVANCES in MATHEMATICS and COMPUTERS in BUSINESS, ECONOMICS, BIOLOGY & CHEMISTRY ISSN: 1790-2769 99 ISBN: 978-960-474-194-6