Four Studies in Theoretical Spatial Economics

In what follows, four research topics in theoretical spatial economics are presented, topics which have been worked on recently. They start with two so-called "Tinbergen-Bos Systems" (TBS) analyses. The first is a check on the empirical presence of "Tinbergen hierarchies" in Dutch microregional data; the hypothesis is not rejected. The second develops two theoretical aspects: the computation of non-allowable TBS (supply of some goods and/or services being absent) and the solution via continuous linear programming (CLP) of Tinbergen-Bos metricised systems. This CLP approach can be found back in an essay, the third one, on the maximal flow capturing problem, for which a solution in those terms is presented. Coming back to TBS, it should be mentioned that spatial interdependence via transportation costs is a central idea in the analysis; this idea is applied again in an optimal control set-up with potentialised partial differential equations (PPDEs), for which a - once more potentialised - framework and an explicit solution are proposed.