Title: Inverse problems in models of resource distribution,
Abstract: We continue to study the problem of modeling of substitution of production
factors motivated by the need for computable mathematical models of economics
that could be used as a basis in applied developments. This problem has been
studied for several decades, and several connections to complex analysis and
geometry has been established. We describe several models of resource
distribution and discuss the inverse problems for the generalized Radon
transform arising is these models. We give a simple explicit range
characterization for a particular case of the generalized Radon transform, and
we apply it to show that the most popular production functions are compatible
with these models. Besides, we give a necessary condition and a sufficient
condition for solvability of the model identification problem in the form of an
appropriate moment problem. These conditions are formulated in terms of rhombic
tilings.