资源分配模型中的反问题
Inverse problems in models of resource distribution
摘要：
我们继续研究生产要素替代的建模问题，这是由于需要可计算的经济学数学模型，可以用作应用开发的基础。这个问题已经被研究了几十年，并且已经建立了与复分析和几何学的若干联系。我们描述了几种资源分布模型，并讨论了由这些模型产生的广义Radon变换的逆问题。我们给出了一个简单的显式范围表征的一个特定情况下的广义Radon变换，我们应用它来表明，最流行的生产函数与这些模型是兼容的。此外，我们还以适当矩问题的形式给出了模型辨识问题可解的一个必要条件和一个充分条件。这些条件是制定在菱形平铺。
英文摘要：
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.
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