The underground economy: What is the influence of the discount factor?

Underground economy is a continuous concern of economists all over the world and finding determinants and factors acting on its size is crucial in the fight to control and stop this negative phenomenon. In this paper, there is investigated a mathematical model founded on the basis of the inter-action between underground economy and official economy. As starting point, it used the logistic model of Verhulst, completed with the effect of the discount factor. Finally, the findings suggest that, at a small growth rate of the underground economy, it is possible not to exist any stable equilibrium points, but excessive size of the underground economy or too high growth rate cause the appearance of stable equilibrium points. This fact may be explained by the assumption that appreciable variations of the underground economy (in size or in growth rate) generate punitive and/or administrative measures from the authorities in order to counteract them.