Model of world technological and economic efficiency frontiers

Анотація

The model generalizes the classical concept of the world's technological frontier. The article is devoted to the theory of comparative analysis of the efficiency of national economies using the non-parametric method of data shell analysis (DEA). The proposed model summarizes the classical concept of the world's technological frontier. Algebraically, it is the solution to the well-known linear programming problem, which determines the countries that use the best combinations of capital and labour to produce a unit of output. Geometrically, it is the envelopment of the states of the studied countries in the plane of relative volumes of factors of production ("technological plane"). Authors add to this problem three other problems and the classical equation of nominal national income distribution between the factors of production. The first of these problems identifies countries that have the best combinations of real labour and capital prices. Analogously, the geometric solution to this problem authors defined the world economic frontier. It is the envelopment of the states of countries in the plane of real prices of production factors ("economic plane"). The other two frontiers consist of countries with the best combinations of parameters of the national function of product price distribution and product volume distributions between labour and capital. The economic frontier, built by the envelopment method of the price distribution function, can be depicted on the technological plane as an envelopment of the worst technological conditions. Similarly, the technological frontier, built by the envelopment method of product distribution functions, can be depicted on the economic plane as the shell of the worst economic conditions. Approbation of the model on data from 13 countries in 2017 revealed a geographical axis in the direction of "northwest-southeast" on the European continent.

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