Continuous and Discontinuous Piecewise-Smooth One-Dimensional Maps

Positive welfare effects of trade barriers in a dynamic partial equilibrium model

“…A particular, yet quite natural nonlinearity may arise if one considers capacity constraints, as is the case, for instance, in the discontinuous cobweb model of Kubin and Gardini (2013). As determined by Avrutin et al (2014), discontinuous maps may give rise to intriguing dynamic phenomena. Moreover, it may be interesting to relax the assumption that commodities in the two regions are homogeneous by allowing for some imperfect substitutability between these products.…”

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

“…The three steady states in our model are located at the point 3 All three steady states in our model can be derived directly from the exponential replicator dynamics (9). For n t−1 = 0, π t−1 =π and n t−1 = 1, the number of active firms comes at rest, i.e.…”

Market Interactions, Endogenous Dynamics and Stabilization Policies

“…This implies that the evolutionary model where firms make entry decisions on the basis of past profits becomes a piecewise (one-dimensional) nonlinear map. These types of maps have been studied extensively in recent years (see Avrutin et al 2018, for a general introduction and Commendatore et al 2014, 2015, and Tramontana et al 2010, 2013 for economic applications) and it turns out they typically give rise to an even richer set of complicated behaviors than smooth nonlinear maps already do. Schmitt et al (2017a) study the complications that emerge through the kink in the profit function.…”