An economic system of Arrow Paradox should have two social goals.

Most generally, people put forward that an economic system should have two social goals. We should start with welfare economics.

Welfare economics has experienced three milestones since it was put forward.

The first milestone is Pigou's Economic Welfare, which is called the old welfare economics. It contains two basic propositions: first, the greater the net output value of national production, the greater the social and economic welfare; Second, the more equal the national income distribution, the greater the social and economic welfare.

The second milestone is the new welfare economics named after Pareto optimal state. The essence of the largest welfare state they put forward is the largest efficiency state, which is manifested as follows: in economic operation, if the status quo is changed, at least one person's welfare will be improved, and this change is beneficial; If at least one person's welfare is reduced, this change is unfavorable; However, if one person's welfare is improved and another person's welfare is reduced, it cannot be said that this change is necessarily favorable or unfavorable. However, at this time, it has reached the Pareto optimal state.

Economists have proved through strict reasoning that under the condition of perfect competition, if consumers pursue the maximization of utility satisfaction, producers pursue the maximization of profit, and the owners of production factors pursue the maximization of income, they will certainly reach the Pareto optimal state of maximizing social welfare without economic external effects.

The third milestone is the school of social welfare function represented by Bergson and Samuelson. Social welfare functional school thinks that because different income distribution will have different effects on consumption and production, welfare economics should not exclude income distribution. Pareto optimal state only solves the problem of economic efficiency, but not the problem of rational distribution. If a person monopolizes the world's mountains and rivers, there will still be a corresponding Pareto optimal state. They believe that economic efficiency is only the greatest necessary condition for social welfare, and the reasonable distribution of product income is the greatest sufficient condition for social welfare. Only by solving the problems of efficiency and fairness at the same time can we achieve the only optimal state of social welfare.

Therefore, they try their best to find the social welfare function. Based on the similarity between political voting and monetary voting, they proposed to construct social welfare function through political voting.

But unfortunately, Arrow deduced the paradox of voting with strict mathematical logic, and proved in a formal way that it is impossible to produce a unique social welfare function acceptable to everyone by voting. This makes the fair assumption of social welfare functional schools go to ruin.

However, the paradox of voting mentioned by Arrow Paradox triggered a profound crisis of economic theory. In the deepest sense, Arrow Paradox can be understood as: in any case, there must be contradictions between individual private interests and the overall interests of society, and it is impossible to logically draw the conclusion that all individual private interests can be satisfied as well as the overall interests of society.

Arrow paradox destroyed the achievements of welfare economics for many years. At the same time, we should further see the profundity revealed by paradox. Because, according to Adam Smith's "invisible hand", that is, the concept that the market economy leads to the optimization of resource allocation in the whole western economics is based on the premise that personal interests are satisfied, which will automatically lead to the overall optimization of resource allocation in the whole society. Imagine that when the form of political voting is changed to the form of currency voting, the seriousness of the problem is highlighted. Because Arrow's paradox has been divorced from the specific content, it is proved in an axiomatic form that it is absolutely impossible to draw a conclusion from the above premise. In this way, the whole architectural foundation of western economics will be overthrown, and the ready-made conclusions of market economy will be overthrown.

The reason is profound, the thought is profound, the challenge is severe, and the situation is very severe. But where is the problem?

The problem is that when theorists subconsciously understand Arrow paradox, they equate people's political voting behavior with people's monetary voting behavior. This also includes Arrow himself. He wrote: "Voting and market methods are ways to combine many different personal interests to make social choices." "Similarly, the market mechanism cannot produce reasonable social choices." "Any social welfare function is either imposed or autocratic." An economic society always has its own production resources, such as land, capital, labor and so on. With these production resources, how to configure the elements according to the method described by Pareto, so that they can be produced most efficiently? And how to achieve the most efficient Pareto state by consuming the products obtained in production?

Generally, two people, two products and two factors of production are used to explain the problem intuitively with Edgeworth's block diagram. Although boxplot of edgeworth can only clearly explain the Pareto optimal state distribution in the case of 2×2×2, Arrow-Debru theorem has comprehensively proved the Pareto optimal state distribution of any individual, any product and any production factor. Therefore, the qualitative use of edgeworth and boxplot to illustrate the problem does not affect the accuracy of the conclusion.

This is a two-person society, with two factors of production, namely, L-quantity labor and K-quantity capital. To produce two products, X and Y..l-quantity labor and K-quantity capital constitute two sides of edgeworth's box diagram, which shows the limitation of production factors. At this time, according to the technical level of the society at that time, we can draw the equal output curve family of X and Y products.

The yield curve from the origin o, q, q, etc. Similarly, from o[, y] to the left, the number of two production factors used to produce Y product is calculated, and there is an equivalent output curve of Y output.

Obviously, the distribution of labor and capital at point A of figure 1 to produce X and Y products is not a Pareto optimal state. Because, along an equal output curve of X or Y, moving down the dividing point between labor and capital can increase the output of another product without reducing the output of this product. The adjustment process can be performed until the curve is tangent to the hyperbola. For example, points b and c in the figure 1. The use efficiency of production factors at point B and point C is the most efficient Pareto state. Because at this time, if we want to increase the number of X products, it will inevitably lead to a decrease in the number of Y products, and vice versa.

All the tangents of the production lines of X and Y products like B and C form a new curve in edgeworth boxplot, which is called the production contract curve. It starts from o[, x] in the lower left corner and extends to o[, y] in the upper right corner. The allocation of production factors on this line has reached Pareto optimal allocation.

When the output of X and Y obtained along this line is recorded at the same time and converted into a new coordinate system, that is, the product quantity coordinate system, the combination curve of the maximum output of X and Y and such a fixed limit of L and K can be obtained, which is called the production possibility curve.

The production maximization state corresponds to a certain point on the production possibility curve in fig. 2. If we take point D in Figure 2, then point D is the maximum number of common products obtained by both parties ... So, how do they get the maximum utility from the product of X and Y represented by point D?

This can be made according to their indifference utility preference curve. The origin O in the lower left corner is the origin to measure the utility of A, and the point D on the production possibility curve, that is, the point in the upper right corner, is the origin to measure B. Their indifference preference curves are i[, A 1], i[, A 2] and i[, A 3], i[, B 1], i[, B 2] and i[, respectively. In Figure 2, i[, A 1] of A and i[, B 2] of B intersect at point E, which represents a distribution method of the product of X and Y between two people, but point E is not a Pareto optimal point. Because, after moving to the lower right along the indifference curve of any one person, the utility of another person will increase. Only at the G or F point, further exercise will reduce another person's utility. Observing point G and point F, the indifference preference curves of two people are just tangent.

When all pairs of tangents of two indifference preference curve families are found, the Pareto optimal state curve expressed by consumption-the exchange contract curve connecting the two origins o-d is obtained.

While moving along the curve of exchange contract, record the utility changes of two people. If the change of two people's utility is transferred to the utility coordinate system representing two people, the total utility change curve of two people can be obtained.

This curve only shows the change curve of the total utility of Party A and Party B, which is marked at point D of the production possibility curve in Figure 2. Therefore, it can be seen that the current total utility change curve is the largest expression of the consumption that two people can get after producing a specific number of X and Y product combinations with established L and K production factors.

Every point on the production possibility curve is a possible point to maximize the output of two people. And the maximum x and y product corresponding to each point can find the total utility change curve formed by two people with different distribution. Therefore, countless total utility change curves can be made. The outermost envelope formed by all the curves of total utility change is the possible curve of total utility. For curves, see the dotted line at the outer edge of Figure 3.

The total utility possibility curve is the situation that both parties can obtain Pareto optimal state after eliminating all possible changes in the quantity of X and Y products, that is, eliminating intermediate variables. At this time, they have both the highest production efficiency and the greatest consumption welfare.

The total utility possibility curve mentioned above can be understood as the maximum flight radius of the aircraft, and any point above is an airport that can land. However, the economic operation result obtained only from the above is still an unconstrained result, or a result with too few constraints. Therefore, people cannot know an exact answer.

What is missing here? Without the intervention of distribution.

People naturally ask, can the distribution of economic operation be decided naturally? Or can we choose according to people's wishes?

The answer to this question immediately triggered people's fair view and behavioral thinking about using political voting to decide economic choices.

If we operate according to the "nature" of the market economy, the economy will also have its "natural" solution. However, the "natural" solution of the economic system is the result of the role and constraint of nature on people. Because it is derived from the production function, the distribution function can be derived and the products can be distributed according to the marginal productivity of various production factors as the distribution weight. Accordingly, according to the role of production factors in production, the quantity of production factors provided by each person can be allocated to the final product.

Is such a solution unique?

It is unique. Because according to the distribution function, the distribution share of production factors with marginal decreasing trend such as labor and capital is determined by their marginal productivity. Distribution caused by technological progress, risk and monopoly. Is determined by the production of products, in addition to the above factors such as labor and capital. In a set of equations, the distribution determined by the above items is immutable and unique.

However, the "natural" operation scheme of market economy has one of the most nerve-racking side effects, namely "Matthew effect". The "natural" operation scheme has a positive feedback process and result, which makes people's income and means of production more and more unbalanced, resulting in the polarization result that the rich get richer and the poor get poorer.

People have reflected and questioned this. Because the factors of production provided by nature to human beings should be regarded as being provided to all mankind, not to some people or some people. From this point of view, it is not satisfactory and acceptable for any individual or part of people to use or "occupy" the factors of production provided by nature and occupy an inappropriate share in distribution.

This is the problem that welfare economics sees, and they also refine the solution to the problem: why can't we add another way on the premise of maintaining "natural" distribution, instead of completely distributing products with the "natural" marginal productivity model imposed by nature? Or in layman's terms, it is to redistribute social products through secondary distribution.

From this point of view, they introduced the voting method to decide the distribution of products among people.

Voting mode, from the most fundamental point of view, is the way for members of human society to choose and decide the internal affairs of human society. It is this form of choice and decision-making that ignores the necessary premise of human existence: that is, the overall existence of human society depends not only on the subjective will of internal members, but also on the nature of human society.

The voting decision of welfare function, in a sense, means that people want to get rid of the forced distribution function of nature through production function and derived distribution function, and distribute people's income internally through consultation and coordination between people. However, such a decision is likely to be unconstrained, or to be precise, it is a decision with too many degrees of freedom. Different people have different opinions, and it is not difficult to understand that there is no unique result. Just as the Pareto optimal state can't get a unique solution without distribution function, people see the same problem on its opposite side: in voting, people can't get a unique solution of fair distribution, that is, a fair solution that doesn't exist in everyone's satisfaction at the same time.

Looking back, from the perspective of economic analysis, we can see the real role of currency votes. It not only directly arranges and solves the interest relationship between people, but also indirectly arranges and solves the relationship of how people get benefits from nature. Currency voting has the same three marginal substitution rates, which not only solves the coordination relationship within human society, but also considers the interaction and influence mechanism between man and nature. Therefore, the choice of currency voting is by no means equal to the choice of political voting.

The emergence of Arrow Paradox lies in the lack of sufficient constraints, that is, when natural constraints are absent, the unique solution of human affairs cannot be reached.

This is the deep mechanism root of Arrow Paradox.

The contradiction between fairness and efficiency is an application aspect of Arrow paradox.

With this understanding of Arrow's Paradox, looking back to analyze the contradiction between fairness and efficiency, the problem suddenly becomes clear.

From the "Great Harmony" society in ancient times to the "Utopia" society in modern times, and then to the practical socialist society in modern times, there is always a main line running through the standard of testing social and economic conditions, that is, "fairness". However, where the measure of "fairness" comes from has been ignored by people until welfare economics turns to efficiency for serious study.

In fact, in utopian communism, the measure of "fairness" comes from people's ethical thinking. When the theory of scientific communism was established, because the theoretical system of Das Kapital only focused on the inequality of wealth distribution caused by the inequality of social members' possession of means of production, the scale of "fairness" derived from it was also the scale formulated within human society. For such a "fair" scale, Arrow paradox always exists. In other words, the conflict between the private interests of individuals and the overall interests of society is always inevitable, and it is always impossible to get a "fair" scale that everyone agrees with at the same time.

But at the same time, when people are pursuing a better life, they always find that it is not enough to measure it only by the measure of "fairness", and the measure of "efficiency" must be introduced to supplement it. What is measured by the scale of "efficiency" is no longer entirely the internal affairs of human society, but inevitably involves the demand and interest relationship between man and nature.

The double object of "fairness" measure-"efficiency" measure has been accurately introduced since Pareto, and has been used by western economists to test social and economic conditions. However, judging from the development results of welfare economics, the scale of "efficiency" must not be all-inclusive, and its implementation must also be supplemented by the scale of "fairness".

This is the paradox of "efficiency" and "fairness". When the "efficiency" scale is emphasized, the "fairness" scale will be introduced; On the contrary, when emphasizing the "fairness" scale, the "efficiency" scale will be introduced. Insist on either one, and you will drag the other one in. They can't seem to have it both ways, but they must take care of each other. The two can neither be separated nor integrated, which seems to be the opposite of contradictions in reunification.

The historical facts in academic circles also show that when voting or other means are used to determine a fair distribution model, great disadvantages are also introduced. Since the production process is also a reproduction process, people must also make decisions between current consumption and future consumption. It is found that the distribution determined by people's internal consultation or voting not only changes the distribution of current consumption among people, but also changes the compensation ratio of production factors, that is, the appropriate relationship between current consumption and future consumption determined by the "natural" mechanism. Because the living environment of human beings is no longer pure nature, but artificial nature. This artificial nature can only be maintained by the constant maintenance and improvement of people. Maintenance and improvement are directly related to the regression of production factors. The result of the distribution vote will definitely change the return of production factors. What is really fatal is that such changes always make the next round of reproduction deviate from the Pareto optimal state. This means that while cutting the produced cake fairly, it will make the copied cake smaller.

Then, can we draw the conclusion that "efficiency" and "fairness" should be given consideration from the internal operation of the economic system? Because, we see that only considering "efficiency" can not get the unique solution of economic operation, and only considering "fairness" can not get the unique solution of economic operation. Considering both, is there a scheme that can meet the criteria of "efficiency" and "fairness" at the same time, that is, to maximize efficiency while achieving the best fairness?

Sure! Because we have seen that once we join the constraints of nature on the existence of human society, we will inevitably get the only result because of the new constraints. As for the proof of this conclusion, please see other papers to be published by the author. There, it will give a conclusion that efficiency is the highest and fairness is the best under the constraint of keeping nature at all times. This makes it possible for us to have a coordinate system with both "efficiency" and "fairness" when evaluating the operation of any real economic system, so that people can judge and measure the deviation of the actual economic operation from these two ideal scales.

But unfortunately, this kind of natural constraint has appeared in an all-round way, making people live in a "fair" and "efficient" society, but it only appeared in human childhood-primitive society. At that time, due to the extremely low productivity, any deviation from the "fair" distribution would make some people not get enough food and die. The existence of nature is to use cruel means to force people not only to produce efficiently, but also to distribute fairly.

However, when productivity increases and people have surplus products, the freedom of distribution increases and the natural constraints are no longer so severe, which makes Arrow paradox have room for survival not only in terms of efficiency, but also in terms of fairness.

The establishment of socialist market economy is the application of the dictatorship conclusion of Arrow Paradox.

The logical result of Arrow's voting paradox is shocking: social decisions are either imposed by the outside world or made by authoritarian governments.

Half of what he said is right and the other half is in doubt. Half of them are right. The decision must be imposed by the outside world, that is, by factors other than people, which reflects the reset of natural constraints. It proves that people living in Sri Lanka have an inescapable nature, just as people can't escape from the earth without grasping their hair. The other half is worth pondering, that is, decision-making must be dictatorial. We have to admit this conclusion on the premise, because there are indeed results that all people can't get by rational voting, but authoritarian decision-making can get. But if this half sentence is abused, it will have extremely serious and disastrous consequences.

However, after understanding the source of Arrow paradox, we will have a deeper understanding of the decision mechanism of social decision-making. Because, in any case, social decisions are made within society, although it still needs to reflect natural constraints, such as when using currency tickets. However, currency tickets are only a way of social decision-making. Although it is an extremely important way, there is still a problem in social decision-making that monetary votes cannot be used to determine the content. However, judging from Arrow's paradox, the decision-making in these contents can never rule out the factors of dictatorship. So, what is the relationship between the dictatorship and the external constraints of nature? This is the consideration of transaction costs caused by the establishment of socialist market economy in China.

Since Langer and others analyzed how to implement the optimal allocation of the socialist planned economy, people have clearly realized that the operation of the economic system is not cost-free, and the allocation of resources and the distribution of products require costs. However, how such costs and expenses enter the field of economic analysis depends on the "transaction cost" proposed by Coase. Coase thought deeply about how to conduct and obtain the transactions neglected by predecessors, and found that there must be a kind of cost in market transactions-transaction cost. From the glimmer of this gap, a vast new world was discovered.

Under the guidance of this beam of fluorescence, after long-term exploration, people finally realize that the reason why the human form of existence has evolved into a market price system is that it can be used to solve the information transmission, production cooperation, resource allocation and commodity exchange between people in human social existence, thus solving the most efficient demand of human beings for the whole nature, because the market price system is the system with the lowest cost and, in mechanical terms, the system with the lowest friction coefficient.

Starting from the transaction cost, the new institutional school extends its research and demonstration to the superstructure such as property rights, social ideology, law, government and democracy, and finds that all social activities running for the economic system have costs.

Therefore, the new institutional school restored the political economy in social research from the materialistic point of view. This also confirms the advantages of Marxist economics from another aspect. However, in contrast, it is even more materialistic than classical Marxist economics. Because Marx's classical economics starts with the labor theory of value, analyzes the social relations between people formed by the connection of economic relations in society, and focuses on social relations, from which the study of superstructure is derived. However, due to the limitation of premise, it cannot be included in the optimal allocation of resources that must be involved in the basic research of economy. This is its theoretical blind spot. In this sense, the research of the new institutional school complements the deficiency of Marx's classical economics, and truly demonstrates that the emergence and existence of the superstructure serves the economic base from the economic base. At the same time, it is these economic foundations that support the operation of the superstructure and have transaction costs.

Knowing this, we will have a more solid materialistic thinking cornerstone for the decision-making behavior of human society.

A good "dictatorship" decision should not only make people's production and consumption reach the largest marginal area, but also ensure that the normal operating expenses within society are minimized. Only by breaking through the "source" section and "flow" can we get the so-called highest efficiency state of personal capital, or the Pareto optimal state after considering "friction"

Making such a decision will never happen overnight. Sometimes, in order to get such a "dictatorship" decision, it takes a long time, even expensive and painful exploration.

After the founding of People's Republic of China (PRC), with the end of the revolutionary war, the surging class struggle will also be slowed down, and it is imperative to solve the national economy with low living standards and backward development and build a modern and powerful country. However, the party's central work has long deviated from the goal of developing the national economy. After the "ten years of turmoil" ended, China * * * began to realize clearly that the party's central work must be unswervingly put on economic construction without any interference. It was this decision that laid the ideological foundation for China's economic take-off.

Taking economic construction as the center solves the direction problem, and what kind of system is used to realize economic construction is the way problem. On this issue, China has also experienced a long exploration. From abandoning the traditional planned economy to implementing a planned market economy, and then proposing the combination of planned economy and market economy, the socialist market economy was not established until the 14th National Congress of the Communist Party of China. This process took about 15 years.

The production subject of market economy is enterprise. How to implement public ownership in enterprises was clearly put forward by the 15th National Congress of the Communist Party of China after long-term theoretical debates and practical experiments. If this process is counted from 1992, it will take about five years. In fact, the implementation of the contract system can be traced back to 1984.

Generally speaking, it took nearly half a century to realize that market economy is an economic system with the highest efficiency and the lowest operating cost, and finally decided to adopt market economy as a means to implement the rapid development of modern China.

In addition, reducing the cost of social operation is not carried out under the guidance of clear consciousness and theory, but China is a mature ruling party and its political leaders are wise. He was quite aware of the civil strife, poverty and weakness in China's modern history, and learned a lesson from the Cultural Revolution, so he could think about China's economic transformation from the perspective of political stability.

Compared with Russia, the cost is too high because they rashly adopt the so-called "shock" therapy to transform the economic system. There is a consistent understanding that while maintaining political stability, we should establish and maintain the legal system of market economy and make a gradual transition.

Although these decisions are not the result of a referendum, but the political decisions of the ruling party, they reflect the urgent desire of the people and the binding role of nature on mankind. This is also the embodiment of China's superb theoretical thinking level and mature political decision-making.