Side effects of nonlinear profit taxes in an evolutionary market entry model: abrupt changes, coexisting attractors and hysteresis problems

In order to demonstrate that nonlinear tax systems may have surprising and potentially undesirable side effects, we develop an evolutionary market entry model in which firms decide on the basis of past profit opportunities whether or not to enter a competitive market. Our main focus is on the case of a proportional tax on positive profits. Such a piecewise-linear tax scheme induces a kink in the profit functions of firms' strategies, and may lead to abrupt changes in a market's dynamics, coexisting attractors and hysteresis problems. Since these phenomena can also be observed in more general models, a proper understanding of their basic mechanism may be helpful to explain the intricate behavior of many economic systems.