## Who Was Leonid Vitaliyevich Kantorovich?

Leonid Vitaliyevich Kantorovich was a Russian mathematician and economist who won the 1975 Nobel Prize in Economics, along with Tjalling Koopmans, for his research on the optimal allocation of resources. His 1959 book, *The Best Use of Economic Resources*, described optimal ways to address problems of centrally planned economies, such as planning, pricing, and decision making. He also made important contributions to functional analysis, approximation theory, and operator theory, and he originated the technique of linear programming.

### Key Takeaways

- Leonid Vitaliyevich Kantorovich was a Russian mathematician and economist.
- Kantorovich won the 1975 Nobel Prize in Economics for his research on the optimal allocation of resources.
- Kantorovich published
*The Best Use of Economic Resources*in 1959, which described the optimal allocation of resources. - Many of Kantorovich's mathematical and economic findings were used to help manage the Soviet economy.
- Kantorovich's contributions to mathematics and economics include linear programming, price and production theory, and resource allocation.

## Understanding Leonid Vitaliyevich Kantorovich

Leonid Vitaliyevich Kantorovich was born in Russia in January 1912. After the death of his father, Vitalij Kantorovich, in 1922, the 10-year-old budding mathematician was raised alone by his mother, Paulina.

Kantorovich enrolled in Leningrad State University at the age of 14 and graduated at the age of only 18. As Kantorovich noted in his autobiography, he first began delving into the more abstract fields of mathematics during his second year of university. He noted that his most significant research during that time period centered around the analytical operations on sets and on projective sets as well as solving N.N. Lusin problems.

Kantorovich went on to report his findings to the First All-Union Mathematical Congress in Kharkov, Russia, in 1930. While at Congress, Kantorovich collaborated with other Soviet mathematicians, including S.N. Bernstein, P.S. Alexandrov, A.N. Kolmogorov, and A.O. Gelfond.

He became a full professor in 1934 and received his doctoral degree in 1935 while working at Leningrad University and at the Institute of Industrial Construction Engineering. Kantorovich later went on to work as the director of mathematical economic methods at the Siberian Division of the Soviet Academy of Sciences and as the head of the research laboratory at the Institute of National Economic Management in Moscow. He also received the Order of Lenin in 1967.

Kantorovich was married to a physician named Natalie in 1938. The pair had two children, both of whom entered the fields of mathematics as adults. Kantorovich died in 1986.

## Contributions

Kantorovich himself noted that much of his work coincided with Russia's expanding industrialization; as such, many of his mathematical findings were used to help manage the Soviet economy, which focused on state ownership, collective farming, and industrial manufacturing. The Soviet economy was a planned economy focused on the allocation of resources by the state as opposed to a free-market economy where the market determines resource allocation.

### Linear Programming

While consulting with the Soviet government's Laboratory of the Plywood Trust, Kantorovich was assigned to devise a method for distributing raw resources to maximize output. As a mathematician, Kantorovich saw the problem as to how to mathematically maximize a linear function subject to many constraints. To solve this problem, he developed a method known as linear programming.

### Price and Production Theory

In his 1939 book, *The Mathematical Method of Production Planning and Organization*, Kantorovich argued that his mathematics of constrained optimization could be applied to all problems of economic allocation. Similar insights were developed as part of neoclassical production theory and price theory by economists John Hicks in Britain and Paul Samuelson in the United States. In Kantorovich's models, he showed that the coefficients on certain variables in the equations could be interpreted as input prices to coordinate the allocation of resources.

### Resource Allocation

Kantorovich further developed his theory in the book, *The Best Uses of Economic Resources.* He showed that the implicit relative prices of inputs from his models were critical even in centrally planned economies where no actual markets operated to generate market prices. He also argued that this included the implicit price of time in trade-offs between present and future production and consumption plans, which corresponds to the market interest rate in a capitalist economy. He asserted that planned economies should use interest rates as capitalist economies do.