I. Menger's View of Economics

Unlike the popular view at the time, which regarded economics as a tool for guiding social policy, Menger believed that economics studied universal economic laws, which existed independently of the will of man. As he wrote in his book: 
"Whether a thing is useful to me or not, whether it is a good or not, whether it is an economic good or not, whether it has any value to me and how much it is worth, whether an economic exchange will take place between two economic individuals and, if it does, in what range the price will be determined - -These and many other questions are entirely independent of my will, just as any law of chemistry is independent of the will of the practicing chemist. ...... economic theory is concerned not with the practical rules of economic activity, but with the conditions under which people engage in finely tuned activities designed to satisfy their needs.”
Menger emphasized that economics studies the behavior of people and how they make choices to satisfy their infinite needs under conditions of limited resources.
Commodities and Economic Commodities
Menger distinguishes between “commodities” and “economic commodities”:

• Commodity: refers to anything that satisfies human needs.

• Economic commodities: refers to those commodities that are limited in quantity and need to be obtained through economic activities.

He pointed out that the economic properties of a commodity are not intrinsic to it, but depend on its relationship to human needs. When the quantity of a commodity is sufficient in relation to the demand, it does not have economic properties; conversely, when the quantity of a commodity is not sufficient to satisfy the demand, it becomes an economic commodity.

For example: 
"Suppose a village depends on a mountain stream for its water supply, whose normal flow is 200,000 barrels of water per day. However, when heavy rains come, and in the spring, when the snow melts on the mountain, the flow rises to 300,000 barrels. During the driest periods, the flow would drop to only 100,000 barrels of water per day. Suppose further that the inhabitants of the village, for drinking and other purposes, would normally require 200 barrels of water per day, and that a maximum of 300 barrels would fully satisfy their needs. ...... In this case, it is clear that not only is it guaranteed that all demand for the commodity will be met, but that the economic individuals will only be able to partially utilize the quantities available to meet their needs. ...... On the other hand, those goods which are naturally available in quantities that exceed demand may also acquire economic properties for their consumers if a powerful person prevents other members of the economy from freely acquiring and using them.”

III. THE THEORY OF VALUE
According to Menger, value is subjective and depends on how important an individual is for a good to satisfy his or her needs. He proposed the law of diminishing marginal utility, which states that the marginal utility of a good (i.e., the additional satisfaction from each additional unit of the good) decreases as the quantity of the good a person owns increases.
“If we ask, for example, why, in general, a pound of drinking water has no value to us, while a minute quantity of gold or diamonds usually exhibits a high value, the answer is as follows: diamonds and gold are so rare that all the diamonds available to all mankind could be put in a box, and all the gold in a large room. This is a conclusion that can be reached by a simple calculation. On the other hand, drinking water is so abundant on earth that it is difficult to imagine a reservoir large enough to hold it all. Thus, people can only satisfy those most important needs that are served by gold and diamonds, and they are usually able not only to fully satisfy their need for drinking water, but also to let a great deal of it go to waste because they cannot use up all the amount available. ...... Thus, in general, if people are unable to dispose of a certain amount of drinking water, no human need is left unfulfilled. On the other hand, in the case of gold and diamonds, even the least important fulfillment, guaranteed by the total amount available, remains of relatively high importance to the finicky. Thus, specific quantities of drinking water are usually of no value to the finicky man, but specific quantities of gold and diamonds are of high value.”
Menger rejected the labor theory of value and argued that the determinant of value is not the amount of labor expended in the production of a good, but the importance of the good to an individual in satisfying his or her needs.

IV. Exchange Theory
According to Menger, exchange is a voluntary activity between two parties in order to obtain greater utility. He analyzed the mechanism of price formation under three market structures: isolated exchange, monopoly and competition.
“The most general form of relationship leading to human trade is as follows: an economic individual A owns a certain commodity which is worth less to him than another commodity owned by another economic individual B. B's estimate of the value of the same quantity of commodities is reversed, and the second commodity is worth less to him than the first commodity owned by A. The second commodity is worth less to him than the first. ...... It is clear that A will receive a value of x from the transaction, while B will receive a value of y. In other words, after the exchange, A will find himself in a position as if he had added to his wealth a commodity of value x to him, while B will find himself in a position as if he had added to his wealth a commodity of value y to him.”

V. Monetary Theory
According to Menger, money originated from the need for a more efficient medium of exchange. Due to its highly marketable nature, certain commodities gradually evolved into money. He emphasized that money itself is a commodity whose value also depends on supply and demand.
“We find, therefore, that in order for a commodity to circulate freely, it must be marketable in the widest sense to every economic individual through whom it is handled, and to each of them it must be marketable not only in one, but in all four of the respects we have discussed above.”

VI. Summary
The Principles of Economics is the founding work of the Austrian School, and it has had a profound impact on the development of economics. Menger's ideas of subjective value theory, the law of diminishing marginal utility, and the analysis of the market mechanism are still important in the study of economics. His theory emphasizes the central role of individual choice and subjective judgment in economic activities, providing a new perspective for understanding the operating mechanism of market economy.

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Menger's Unique Insights into the Theory of Value and Its Impact on Traditional Economics

Karl Menger's most important contribution to the theory of value was the formulation of the theory of marginal utility and its integration into the theory of value and price. His ideas had a profound impact on traditional economics and challenged the dominant classical economic theories of the time.

1. subjective theory of value.

Menger's most revolutionary insight was that the value of a commodity is determined not by its cost of production or labor input, but by its importance to an individual in satisfying his needs. He argued that value is subjective and depends on an individual's assessment of the utility of a good, rather than being objectively present in the good itself.

He proposed the law of diminishing marginal utility, which states that as the amount of a good a person owns increases, the additional utility (i.e., marginal utility) from each additional unit of the good decreases. This means that the value of a good depends on its least important use, i.e., its “marginal utility.

2. Relationship between demand and scarcity.

According to Menger, the economic characteristics of goods depend on the relationship between demand and scarcity. When the demand for a good exceeds the quantity available, the good has an economic character and therefore a value.

He categorized goods into economic and non-economic goods. Economic goods are scarce, their quantity is less than the quantity demanded and therefore have value. Non-economic goods are abundant, their quantity exceeds the demand and hence have no value.

3. Hierarchy of values of commodities.

Menger introduced the concept of hierarchy of value of commodities, arguing that the value of a commodity is determined by its contribution to the final consumer good (i.e., the first level of goods). He called the intermediate goods and factors of production necessary for the production of final consumer goods as higher level goods, which derive their value from their contribution to the production of final consumer goods.

4. Contributions to price theory.

Menger analyzed the process of price formation in depth, distinguishing between monopoly and competition. He argued that prices are formed in the bargaining process between buyers and sellers and ultimately depend on the interaction between demand and supply.

He also provided a seminal analysis of bilateral monopolies, pointing out the complexity and uncertainty of price formation in such cases.

Menger's theories have influenced traditional economics in the following ways:

Spurred the marginalist revolution: His subjective theory of value and the law of diminishing marginal utility became the basis of neoclassical economics, replacing the labor theory of value of classical economics.

Contributed to the development of microeconomics: His analysis of price formation, monopoly and competition laid the foundation for the theoretical framework of microeconomics.

Influenced the formation of the Austrian School: Menger was one of the founders of the Austrian School, and his theories had a profound impact on the school's core ideas, such as subjectivism, methodological individualism, and market process analysis.

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Menger's explanation of commodity exchange and the mechanism of price formation

Motivation for commodity exchange

People exchange goods because exchange allows them to better satisfy their needs. Exchange may occur when a good owned by one person has less utility to him than a good owned by another person, because exchange allows both parties to obtain a good with higher utility.

As the economy grows and people become more aware of the importance of their own economic interests, they will tend to exchange their goods for goods that are easier to sell, even if they don't need them for a while. This behavior is motivated by economic interests and does not require any agreement, legal compulsion, or public interest considerations.

Origins of Competition

Monopoly is usually an early and primitive phenomenon, while competition is a later phenomenon. Every artisan who opens his business in a particular locality is in a sense a monopolist if he is the only person in the locality practicing that trade.

Over time, other artisans may move to that location and offer similar goods or services, thus creating competition.

Mechanisms of Price Formation

In isolated exchange

In an isolated situation where only two people are exchanging, the price is formed between the limits of both parties' valuations. For example, if A has a horse that B is willing to exchange for a maximum of 30 bushels of wheat and A accepts a minimum of 20 bushels of wheat, the price of the horse will be formed between 20 and 30 bushels of wheat.

In the case of a monopoly

When a seller has a monopoly, the price will be determined by the most willing buyer. The seller will choose the buyer with the highest bid to make the transaction. The price will be formed between the limit of the highest bidder and the limit of the next highest buyer's valuation.

In the case of bilateral competition

When there is competition between buyers and sellers, the price will be formed between the limits of the valuations of supply and demand. Those buyers who value the commodity less or are less competitive will be excluded from the transaction.

The emergence of money

With the development of trade, some commodities, especially those that were easiest to sell, became generally accepted as mediums of exchange. These commodities are called “money”.

The emergence of money was not the product of a state or law, but the result of a natural evolution. The first forms of money were probably commodities such as livestock, which later evolved into metal money.

The use of money simplified the exchange process and made transactions more efficient. People could use money to measure the value of goods and store wealth more easily.

Important Concepts

Demand: Refers to the amount of a good that people want. Demand is influenced by the utility and price of a good.

Competition: The competition between multiple economic agents for limited resources.

Monopoly: A situation where there is only one seller in a market.

Money: refers to a universally accepted medium of exchange.

Menger's theory emphasizes the role of subjective value in the exchange of goods and price formation. He argued that the value of a commodity depends on the valuation people place on it, which in turn depends on their expectations of its utility.

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The Importance of Karl Menger's Discourse on the Origin and Role of Money

Carl Menger's account of the origin and role of money is of great importance to economics, especially the Austrian School. From an individualistic and subjective value theory perspective, it explains how money spontaneously arose from the dilemma of bartering and the key role of money in facilitating transactions, reducing transaction costs, and increasing economic efficiency.

Here are a few important implications of Menger's argument:

A naturalistic explanation of the origin of money: Menger argues that money is not created by the state, but is the result of the spontaneous evolution of the market. When people have difficulty in bartering, they naturally seek more marketable goods as a medium of exchange. Initially, some commodities were widely accepted because of their own utility, such as livestock and shells. Over time, those commodities that were most saleable, such as gold and silver, evolved into universally accepted money. This naturalistic explanation challenges the prevailing statist view of money and emphasizes the role of market forces and individual choice in the origin of money.

A profound analysis of the functions of money: Menger elaborated on the three main functions of money: medium of exchange, measure of value, and means of storing value. He pointed out that money, as a medium of exchange, can greatly reduce transaction costs and facilitate the exchange of goods and services. Money, as a measure of value, can provide people with a common reference to facilitate their valuation and comparison of different commodities. Money as a means of storing value allows people to preserve their wealth for future use. These functional analyses remain the basic theoretical framework for money in economics today.

INSIGHT INTO THE NATURE OF MONEY: According to Menger, money is essentially a commodity whose value depends on market supply and demand. Although money can exist in the form of coins, the coins themselves are not money, but only a specific manifestation of money. This insight into the nature of money helps us to understand phenomena such as fluctuations in the value of money and inflation.

IMPLICATIONS FOR MONETARY POLICY: Menger's theory of money provides a theoretical basis for sound monetary policy. He emphasized the importance of the market mechanism in the evolution of money, hinting at the possible negative effects of government intervention in the monetary system. His theory also provides theoretical support for monetary systems such as the gold standard, emphasizing the importance of stability in the value of money.

In conclusion, Menger's account of the origin and role of money is a milestone in the history of economic thought. His theory not only profoundly explains the phenomenon of money, but also provides an important theoretical basis for our understanding of the modern monetary system and the formulation of sound monetary policy.