The first person in the west who applied mathematics to economic problems was Italy's Cheval, who wrote a book on the value of money at 17 1 1. However, the first systematic application of mathematics was 1838, when Frenchman Cournaud studied the pure mathematical principle of wealth, which is generally regarded as the beginning of mathematical economics.
Because the authority of economic theory at that time was not familiar with mathematical reasoning, no one cared. It was not until 40 years later that it was praised by jevons in Britain and Walras in France, and it became famous in the world, and was regarded as the formal origin of mathematical economics and mathematics school. Since then, edgeworth and Marshall in Britain, Fisher in America and Pareto in Italy have further developed mathematical economics.
Cournaud did not use the name "mathematical economics". The title he adopted is not only for theoretical research, but also for using the forms and symbols of mathematical analysis in the research. He believes that the use of mathematical analysis in wealth theory is to explore the relationship between quantities that cannot be expressed by numbers and functions that cannot be expressed by algebra; Even if precise figures are not needed, mathematics is useful as long as it can state problems more concisely, open up research channels and avoid deviating from the subject. It is absurd to refuse mathematical analysis just because you are unfamiliar or afraid of using it wrongly.
Jevons's paper "On the General Mathematical Theory of Political Economy" published in 1862 is the earliest name of mathematical economics. When his main work "On Political Economy" was reprinted in 1879, the bibliography of Mathematical Economics since 17 1 1 was attached, which was equivalent to being made public. He believes that if economics is to become a science, it must be a science that depends on mathematics. The reason is very simple, we must study the complex relationship between quantity and quantity, and we must make mathematical reasoning. Even if algebraic symbols are not used, the mathematical nature of this science will not be reduced.
Jevons's aim is to provide a mathematical explanation for the ultimate value theory and the market rules based on this theory. The center of his theory is that "value is completely determined by utility". He divides the utility of goods to owners into total utility and final utility (that is, later marginal utility), that is, when the total consumption of goods increases, the ratio of total utility increase to commodity increase.
He thinks that with the increase of commodity ownership. The degree of final utility will gradually decrease. Mathematically, it is deduced that the exchange of goods between one commodity owner and another commodity owner can increase the total utility, and the exchange will not stop until the final utility of the two commodities is equal and the total utility reaches equilibrium. At this time, the exchange ratio of the two commodities between the two owners should be equal to the inverse ratio of the final utility of the two commodities after the exchange is completed.
In the book "Outline of Pure Political Economy" published by 1874, Walras thinks that pure economics is essentially a theory of price determination under the assumption of completely free competition system; Price exists because the quantity of goods and useful natural conditions are limited. As long as there is exchange, there will be exchange value.
Exchange value is a measurable quantity and the research object of general mathematics, so exchange value theory should be a branch of mathematics; Mathematical methods are not experimental methods, but reasoning methods. The pure theory of economics, like the science of "physics-mathematics", abstracts the ideal concept from the real concept of experience as the basis, which can be used for reasoning beyond the scope of experience. After the completion of this science, it will return to reality, not for verification, but for application.
Walras's main theory is a general equilibrium theory system based on marginal utility axiology. Although Cournaud also considers that the production, marketing, import and export of individual commodities will adversely affect the income of other commodity producers, it is still limited to partial analysis and fails to take into account the overall situation at the same time. Walras tried to remedy it mathematically.
Edgeworth first studied the economic consequences of bargaining of various commodities, and put forward the concept of indifference curve to avoid using money as a fixed unit to measure marginal utility. Later, it was improved by Pareto and replaced marginal utility as the theoretical basis of general equilibrium. The core of Marshall's theory is that the equilibrium price of goods is the price when the demand price and supply price of goods reach the same when other things are unchanged, so it is also called local equilibrium theory.
Mathematics is more and more widely used in modern economic theory. On the one hand, the theoretical field of using mathematical methods is still expanding; On the other hand, we continue to use more profound mathematical methods to discuss the problems that our predecessors have studied.
Since 1960s, mathematical economics has been combined with calculus, set theory and linear model. At the same time, mathematical methods have been applied to almost all fields of economics. The need of economic life and the invention of electronic computer promoted the rapid development of econometrics related to mathematical economics, and then promoted the development of mathematical economics.
Studying economic problems with mathematical methods is conducive to discovering the essence of economic problems and pointing out the development and change trend of economic problems. Nowadays, mathematical analysis is an indispensable aspect in studying economic problems, and any analysis of economic problems that is divorced from mathematics will be considered unreliable. With the deepening of people's understanding of economic activities, mathematical economics is constantly developing and improving.