# Inverse problems in models of resource distribution

## TL;DR

This paper explores inverse problems in resource distribution models, linking them to complex analysis, and provides conditions for model solvability and compatibility with popular production functions.

## Contribution

It introduces explicit range characterizations for generalized Radon transforms and connects model solvability to rhombic tilings in economic resource distribution.

## Key findings

- Explicit range characterization for a specific Radon transform case
- Compatibility of popular production functions with the models
- Necessary and sufficient conditions for model solvability

## 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.