1 Economics enables people to learn to increase the total amount of happiness, after all, mathematical models based on reason can make better guidance for life. However, it should be noted that this is statistically true, that is, for a large number of people who choose this method, a larger proportion of the population can have a better life than other methods, but for individuals who strictly follow the principles of economics, there is no such guarantee, after all, even if the probability is low, misfortune can happen. But it only makes sense that the probability will decrease, such as the probability of misfortune from 5% to 1%. Economic thinking is essentially the way smart people think, a map that can guide the path to happiness, but it does not necessarily ensure that everyone will reach their destination.

Any theoretical system needs to be abstracted, and then a grand system is constructed on top of these abstract concepts, and this axiomatic embodiment has unparalleled power in past practical proofs, such as Euclidean geometry and non-Euclidean geometry. Economists abstract the concepts of commodities, values, prices, currencies and so on according to the situation of the real world, and sort out various special relationships like theorems through the construction of certain mathematical relations, and then continue to construct more complex relationships on the basis of these relations, so as to form the final theoretical system.

To a certain extent, we can understand it from a mathematical point of view: assuming that there is such an objective function, it can make the choice of gain and loss at the lowest cost in exchange for the maximum benefit, that is, to obtain an extreme value. Therefore, the quantification of various concepts is the most important, such as Bentham's utilitarian utility measurement, which quantifies happiness and pain, and uses money as a measure of measurement, which greatly promotes the development of economics. It's a bit one-sided, but it's valuable. Other disciplines need this kind of quantification to go further. So on this basis, specific phenomena can be regarded as a series of decisions, and the choice behind the decision can be understood as a variety of possible games, such as in the choice of work mode, walking, cycling, driving or taking the bus, to consider: actual expenses, driving time, waiting time, comfort level, etc., people according to their preferences to different characteristics to assign weights, and to compare different travel schemes, that is, optimization, and finally determine the mode of travel. This is based on the assumption of linearity, and further study will reveal that these weights are dynamically variable and interrelated, i.e., nonlinear.

Of course, the world is complex, and different theories are only valid within a certain range, and utility theory is supplemented by marginal theories outside the scope of its application, such as diminishing marginal returns, that is, in a certain period of time, under the condition that the consumption of other goods remains unchanged, with the increase of consumers' consumption of a certain commodity, the utility increment that consumers get from each consumption unit of the continuous increase of the commodity will decrease. This tendency is as pervasive as the natural attenuation of radioactive particles. This time function that considers increments is a kind of differentiation on which we can construct complex relationships in the same way that calculus does.

Commodity value is a subjective psychological phenomenon that expresses people's perception and evaluation of the ability of goods to satisfy people's desires, and value is both derived from utility and conditioned by the scarcity of goods, which considers the relationship between aggression and demand. The labor theory of value proposed by Ricardo believed that labor is the source of value, but this is incomplete, and the marginal utility school believes that cost determines supply, and supply determines the final degree of utility, and utility determines value.

From this point of view, calculus can be used as a powerful mathematical tool (margins = derivatives) to build the edifice of modern economics based on mathematics. The maximization of the value of the utility function guides specific decisions, and although different individuals have different weight allocations in specific situations, we can be sure of the truth that the decisions made by each individual are always the utility maximization after the subjective weight allocation. That is, we can't be sure why people make a particular choice every time, but we believe that it is an optimal choice relative to that individual, a local optimality. But it's not optimal overall, after all, there are a lot of factors to consider, but not everyone is so smart.

2 Of course, people are not as ideal as the rational people who can fully live up to economics, and more often decisions are based on irrational emotions, habits, preferences, and so on. In most cases where it can be calculated, people are more sensitive to loss than they were to estimate the value of what they lost than they were to get the same. Therefore, the importance of psychology in concrete decision-making is self-evident.

Our specific valuation is not completely based on complex calculations, but will form certain expectations in our minds, and this is measured according to certain standards, which is a psychological complement mechanism.

The irrationality of the crowd is the formation of positive feedback, and a typical example of the formation of this bubble economy is the Punch scheme.

Therefore, behavioral economics adds the psychological aspects of the individual, which is a modification of the rational person hypothesis of neoclassical economics, and makes the theory closer to reality. However, in any case, the rational component still occupies a greater weight, so economic theories based on the assumption of rational people can provide a boundary for our decision-making, and our complex behavior will not necessarily fit the theory exactly, but at least fluctuate around the theory. After all, we are able to perpetuate, according to Darwinism, that it is always better from generation to generation, which requires us to adopt the right strategy, which is to use a smart approach.

3 From macro to micro, there are the core concepts of microeconomics such as demand elasticity and consumer surplus: when the price falls or rises, the quantity of commodity demand will increase or decrease accordingly, and the degree of demand change is smaller than the price change, that is, the demand elasticity is small; otherwise, the demand elasticity is large, if the two are equal, the demand elasticity is uniform. In other words, the so-called elasticity of demand refers to the degree to which demand and price are interdependent. The magnitude of the elasticity of demand depends on the degree to which the quantity of demand changes as the price changes. That is, when the supply is constant, the price depends on the demand, and depends on the buyer's desire and purchasing power. When the supply increases, the price falls, and when the supply decreases, the price rises. This is similar to the targeted treatment of our biological research, such as the relationship between leptin and obesity, which allows us to lose weight by injecting leptin.

However, the relationship between supply and demand is dynamically changing, and a certain complex structure such as positive/negative feedback can be formed, such as theoretically drug prohibition will reduce the supply of drugs, further reduce the demand for drugs, and naturally reduce drug-related crimes, but the reality is that drug addicts' demand for drugs is inelastic, and drug trading is closely related to the country's anti-drug efforts, so the supply elasticity is larger. In the case of constant demand and reduced supply, the price of commodities will continue to increase, so that some people will take risks driven by high profits. This corresponds to the regain of weight after leptin weight loss, and the possible mechanism is a decrease in the feedback or sensitivity of the leptin receptor.

Price discrimination is essentially a means of classification, which can distinguish between price-sensitive and non-sensitive people, so as to maximize the purchase intention and purchase price points, that is, to maximize the overall profit, which is consistent with the theory of utility maximization, and can achieve a better balance between price and sales. There is a difference between the price that consumers are willing to pay and the market price, and this difference is called consumer surplus, which is also a core concept in economics. This is the basis of a pricing system.

The essence of consumption is to obtain satisfaction, and these satisfactions are also hierarchical, the lowest level is physiological satisfaction, such as maintaining the survival of the individual, then psychological satisfaction, such as the envy that luxury goods can bring, and finally the realization of high-level satisfaction, such as the embodiment of personality and so on.

In my current view, value is intrinsic, price is based on the selective expression of value (it can be high or low relative to value, depending on the utility and willingness to pay), value is the condensation of labor (this kind of pay is cost), and price is a measure of utility and scarcity (can evaluate value in turn), the former is more abstract and difficult to grasp, the latter can be measured in the form of money, this kind of index that can be observed and calculated, derived from various mathematical methods of today's microeconomic system.

4 At an ideal level, any decision can be seen as choosing an equilibrium point between benefits and costs. Of course, in specific cases, it can be further subdivided, and the benefits and costs can actually be converted into each other.

Capital is highly rational, and we can think of it as a truly rational person at this level, because the flow of capital makes fuller use of all the information available to human beings, like the potential difference of osmotic pressure, which can flow quickly to the place where profit exists. Of course, there is a high probability that there will always be some capital that will die halfway, which is a natural metabolism.

Being able to combine labor, capital, land and other factors of production is an enterprise, which is profit-oriented, and obtains rewards that are profits by providing a certain utility to society. When the marginal profit is 0, supply and demand reach equilibrium, and the increase in income by increasing one unit of output is equal to the marginal cost, that is, reaching an extreme value. Excess profit of 0 means that no new enterprise is willing to infiltrate this market, but the enterprise will have a positive accounting profit, that is, the profit brought by land, capital, and labor is not zero. The concept of marginality, described in calculus, can guide us in predicting possible future developments.

In the market, the price of commodities is often the result of the interaction of many factors, these factors include, at least: the potential value of the product in the minds of customers, the supply and demand situation, the company's production and management costs, competition and substitute prices, bargaining power, etc., that is, the equilibrium of a series of games.

5 The market, as an invisible hand, is actually the final equilibrium of the dynamic game between various complex forces, and all kinds of complex seemingly unrelated relationships are actually the emergence of patterns, like the various theorems of the axiomatic system. We believe that if everyone does their part well, then they can bring positive benefits to the macro whole of society, so that our human civilization can continue to be a fragile but brilliant organism. This fundamental driving force gives rise to a complex market system, which we abstract as the "invisible hand" (the achievement of equilibrium) for the sake of understanding. The allocation of resources in a market economy is realized through the price system. The realization of the price takes full account of the information that we as human beings cannot understand, but which the huge organism of the market can quickly transmit. After all, all changes in the market are interrelated, and we may not be able to find these specific relationships, we need to take into account that changes in price and quantity in one market will affect the supply and demand of other markets, this nested structure is undoubtedly extremely complex, from a simple linear relationship to a complex feedback structure or even a chaotic state (chain effect).

Because of the interaction between the various markets, individual markets can only be in equilibrium if all markets are in equilibrium. So theoretically equilibrium is unstable. When the prices of all commodities are in equilibrium, there is no oversupply or undersupply of each commodity. If such a set of prices exists. This state is then called general equilibrium. This is also only a theoretical one, which can be proved by calculus and a large number of simultaneous equations, and of course later there is Shizuo Kakutani's fixed point theorem on set-valued mappings that proves the existence of general equilibrium (Nash equilibrium is derived from Brouwer's fixed point principle). There are even experiments that have proven the existence of equilibrium. In a controllable experimental environment, this kind of experimental economics can observe the behavior of experimenters through the method of controlling the changes in experimental conditions, and use this method to test, compare and improve economic theories.

6 The professional explanation of opportunity cost is that a producer gives up the maximum income that can be obtained from using the same factors of production in other productive uses. The simple understanding is that when we choose one thing, we must give up another thing that can bring the greatest benefit, and the benefit of giving up is the opportunity cost, which can be used as a mechanism to constrain individual behavior.

Schumpeter's theory of entrepreneurship based on the idea of innovation believes that "innovation" is an economic process in which the original factors of production are rearranged and combined into new modes of production in order to improve efficiency and reduce costs. In Schumpeter's economic model, those who succeed in "innovating" survive diminishing profits, and those who are unable to recombine factors of production are the first to be eliminated from the market. It is a natural selection. Innovation is the "recombination of factors of production", which can be understood as a change in the weight of the linear combination of different factors of production, and this may bring a certain amount of risk, and the leader is the bearer of the risk. Real entrepreneurs consider innovation, grasp the limited development opportunities of the times, and achieve dynamic development.

In general, Darwin's theory of natural selection can be applied to the field of economics: so-called innovation corresponds to biological variation, i.e., genetic mutations, the recombination of factors of production corresponds to mating within the group level, and finally individuals are diverse. Then in the multi-level competition game: with the environment, within the population, and between the population, there will be adaptive screening, survival of the fittest, and then multiplication from generation to generation.

7But where there is freedom, there must be oppression, and vice versa. Because the reality is a dynamic equilibrium, different components can and must exist until an equilibrium is reached, that is, the marginal benefit is zero, as in today's advocating free trade, there are also international treaties that restrict the freedom of trade. All this is due to the existence of comparative advantage due to differences between individuals, which leads to the existence of the final relative utility, so that the exchange can bring about an increase in absolute utility for both parties. Of course, the consumption of resources is absolute.

Lerner's theorem: Prohibition of imports = prohibition of exports. This is the result of the natural flow of benefits from the concept of economics. In this regard, the principle of conservation of interests follows the principle of conservation, if the level of productivity of the whole remains the same, then the interests of the whole are limited, and the profits of any group will inevitably bring losses to other groups, as in the famous joke "10,000 new jobs occupy the headlines of the newspapers, while the loss of thousands of jobs goes unnoticed." A case in point. However, the emergence of interest groups can grab huge benefits, but this is the result of the loss of interests of other small individuals, that is, the transfer of interests. The power-law distribution of the network, with its low marginal cost, is able to collect the long tail. For example, the automobile makes society prosperous and comfortable, but at the cost of burying the lives of a thousand people every year, which is the result of statistics, and it is actually only a small change in the probability of subdividing each individual, until it can be ignored.

The advantages and disadvantages of free trade and trade protection can be dynamically transformed. Therefore, different strategies for specific regions in a particular historical period can maximize the benefits of the whole. This is consistent with the benefit-cost considerations when we make decisions together.

8 The absolute state of free competition or monopoly is a theoretical equilibrium state, but the reality is based on the compromise of these extreme cases, but a complex state in which multiple situations coexist. In addition to perfect competition and complete monopoly, there are many intermediate stages in the market, including at least oligopoly and monopolistic competition. After all, individuals always have a tendency to maximize their own interests, which is a prisoner's dilemma. But it is also the existence of competition that makes efficiency constantly improving. This corresponds to the development of innovation, which makes the whole society more dynamic. Capital is essentially adding fuel to innovation, and innovation can lead to social transformation.

9 In the face of such a complex organism as the market, any measure taken may not necessarily achieve the set goals, and inhibiting the market according to specific changes, such as government intervention in the market to protect the interests of consumers, may not solve the problem once and for all, but at best prolong the development of the problem, and more often than not, it may be counterproductive, such as the government's decision to tax luxury goods, with the result that the lives of the poor are worse instead of getting better.

The government is a powerful force for economic prosperity, but excessive government intervention will undermine economic progress. Only by maintaining a reasonable level can there be the greatest benefits and the least disadvantages. After all, the variety of effects and secondary effects that can be produced by daring to complex systems is far beyond people's imagination. As F.A. Hayek said, the road to hell is usually paved with good intentions, such as a minimum wage that leads to an increase in the supply of labor and a decrease in demand, which in turn leads to unemployment. Such a guarantee system, designed to reduce poverty, not only does not contribute to poverty reduction, but distorts the allocation of resources;

Therefore, there are enough factors that need to be taken into account when the intervention is just right.

10 Economic thinking is about making decisions and understanding the world based on a simple cost-benefit analysis. The main reason for the abolition of slavery in the United States, for example, is that the cost of protecting the system has exceeded its net benefits. - Ram Bazel, professor at the University of Chicago, USA

Theoretically, the market economy system can solve all problems, because the price mechanism can perfectly regulate the demand of consumers and the production of enterprises. But this is based on the assumption that consumer demand and business production are rational, and when we stop taking it for granted, then a whole system of economic theory will be shaken. Just like quantum mechanics subverts and innovates traditional physics. Ronald Coase is digging deep into the production within the enterprise and opening the black box of the company's production. The cost of evaluating and quantifying the work determines the adoption of the hourly wage system and the piecework wage system. The transaction cost determines the various behaviors of the enterprise, and the transaction cost is the time, energy and money to reach a transaction, which covers almost all aspects of economic life, including the cost of information, the cost of negotiation, the cost of drafting and implementing the contract, the cost of defining and controlling property rights, the cost of supervision and management, and the cost of changing the institutional structure. In the past, the production of enterprises was based on the assumption of zero transaction costs, just like the physical frictionless assumption, which is an ideal situation, and the positive transaction costs can be taken into account to be closer to reality. According to Coase's theory, the root of the existence of a business is to save transaction costs. This is one of the costs of the market price mechanism, and the boundaries of the firm are determined by the internal administrative costs of the firm compared to the market costs, the margin of which is 0 when the firm stops expanding.

Transaction costs are multi-layered: management and monitoring costs, expenses for market research, taxes, PR, advertising, and so on. Since the transaction has a cost, the division of labor will not be infinitely subdivided, it stops at the degree of division of labor where the marginal benefit of the division of labor is equal to the marginal cost of the transaction, so as long as the division of labor can reduce the transaction cost, the division of labor will be further refined.

Solution to the Total Benefit-Total Cost Problem:1 Marshall established the idea of general equilibrium by simplifying the problem with valid assumptions. 2. Yang Xiaokai uses the Kuhn-Tucker theorem to exclude some non-optimal possible solutions, so as to greatly narrow the range of the optimal solution, such an analysis is called supermarginal analysis (like pruning in wide/deep search?)

11 The real world is a world of information asymmetry, and the previous market assumptions were based on the rapid transmission of information (like the zero-friction assumption, but there is also a cost to obtaining information), while the real situation is delayed, which leads to more complex situations such as fraud. Because of information asymmetry, buyers lack the evaluation of the real quality of second-hand goods, they can only continue to lower the price, and finally those high-quality second-hand products have to withdraw from the market, leaving more and more defective products, and eventually even the market does not exist. This positive feedback mechanism is a kind of prisoner's dilemma. Therefore, the power of the brand lies in the constant release of high-quality signals to maintain the fear caused by the asymmetry of information.

If marriage is understood as a transaction, the matching of various information is the most important, but there is also an information asymmetry, which will eventually lead to marital instability.

12 Game theory, Nash understands the existence of non-cooperative games and their equilibrium, thus revealing the intrinsic relationship between game equilibrium and economic equilibrium. The profit of all parties in the game is exactly zero. The result of competition is stable, i.e. a "Nash equilibrium".

Have each bidder write down the highest price they are willing to make on a piece of paper, put it in an envelope and seal it, and when the bidder's offer is announced, the highest bidder gets the lot, but only pays the next highest price. It may seem like a minor change, but it proves to be the theoretically optimal auction mechanism, as it encourages everyone to bid their true bid, and the result of telling the truth is more favorable to them than the result of lying.

Neoclassical economic theory holds that the pursuit of individual self-interest will eventually increase the social welfare of the collective, but according to the outcome of the prisoner's dilemma, the opposite is true, the person will only choose the strategy that is most beneficial to himself, without considering the interests of social welfare or any other opponent, but the result of self-interest is often to the detriment of others and not to himself. This is because the competing interests are multi-layered, and the so-called prisoner's dilemma also requires the prisoner as a whole to play with the interests of the whole society, and the society can obtain greater benefits through the Nash equilibrium. Therefore, the design of the system is crucial.

13 Specific interventions are actually incentives for individual behavior, and good incentives can enable us to achieve the desired results. And the determination of property rights is a good way. When people are able to transform the fruits of their labor into private property, they strive to improve their skills and work smarter, and private property rights encourage smarter management. Smith argues that property rights and trading systems can eliminate irrationalities in distribution.

The core idea of the Clark mechanism is that if a subject's reported preference changes the final choice of the whole, it must contribute a sum of money equal to the loss it inflicts on the other agents. In such a system, you can lie, but it won't do you any good, and it's better to tell the truth than to do it yourself. The idea of the Clark mechanism is that when a person's actions cause damage to others, the injured person should be compensated.

14 Externalities indicate the impact of an economic agent's activities on the welfare of bystanders. "Externalities" refer to the non-market effects of the activities of producers or consumers on other producers or consumers in actual economic activities.

Appropriate "penalties" should be imposed on polluting activities that affect the public environment, known as the "Pigou tax", and if bad externalities are taxed and punished, good externalities should theoretically be compensated, but the costs of measuring externalities are higher than the benefits they may bring. The final idea is to avoid more serious losses from the perspective of overall social costs and welfare. Coase's approach, on the other hand, is to grant specific rights, such as the right to pollution, to one of the perpetrators and victims, so that they can negotiate a final benefit-cost equilibrium. Coase pointed out that if property rights are clear and transaction costs are zero, social costs can be minimized and social welfare maximized by allowing A to harm B or B to harm A. Because A and B can maximize resource allocation through voluntary negotiation, the two parties can internalize externalities through voluntary negotiation and the transaction cost is zero.

Coase's theorem: As long as legal ownership is clearly defined and freely exchangeable, if the transaction cost of ownership is zero, then the equilibrium state resulting from the market mechanism is in the most efficient state, regardless of how ownership is initially distributed. It's a great way of thinking that upends the naïve idea that one should be punished for causing the damage (which is reflected in various aspects of reality, such as symptomatic treatment in medicine, and the promotion or inhibition of the expression of a gene protein in biological research), and in fact, everyone can take action. Coase's theorem states that external influences lead to improper allocation of resources due to unclear property rights, and that some external influences would not occur if property rights were clear and fully protected. Of course, there are transaction costs to consider.

The questioning of the "Pigou tax" by Coase's theorem has led to the rejection of traditional customs, and the elaboration of property rights has changed the perspective of people's observation of the problem. Coase's theorem tells people the importance of clarity of property rights and the importance of institutions in economic activities.

15 The system is the essence of the development of our human society, and it is a norm with good guiding significance that we have paid or are paying the price for. This is the sublimation of all previous economic concepts and the guarantee of the market. Institutions can be seen as living organisms that follow Darwinian natural selection, evolve and influence decisions made in the real world, and those decisions can in turn change the specific institutions of the world. Taking the lead in institutional innovation, just like taking the lead in adopting advanced machinery and equipment, can obtain social returns that exceed the average profit. Moreover, the system has a self-reinforcing function. Institutions can continue to reproduce and replicate in a certain direction, that is, historical development will have inertia, that is, path dependence.

A good system must be able to encourage people to tell the truth. A good system should also be able to promote the welfare of society as a whole.

16 There is also a game between the contradiction between efficiency and fairness, and a certain equilibrium needs to be reached. If everyone pursues efficiency, then society will not be efficient. If everyone pursues fairness, then there will be no fairness in society.

Pareto's Law: 20% of the population owns 80% of the property.

Pareto optimal: If you can find a way to resourcing resources that makes some people better off when others don't get worse, then this is a Pareto improvement until no improvement exists.

Olson's research has come to a highly controversial conclusion: rational, self-interested individuals generally do not contribute to the collective good, and collective action is not easy to achieve. This is consistent with the situation that the Nash equilibrium is easy to achieve in the game, but it is not easy to achieve a plan that is more beneficial to both sides of the game.

Arrow's rigorous proof tells people the paradox that if we want the whole society to be rational, then there will inevitably be a dictator, but if there is no dictator, then the social choices made are often irrational. Arrow's impossibility theorem is like Gödel's incompleteness theorem, that is, slightly more complex theorems will contain indeterminate propositions that can neither be proved nor negated, which means that there is no such a unified system that can prove or deny all propositions in mathematics, and all logical systems have propositions that cannot be proved or denied, that is, all logical systems are "incomplete", and the final solution is beautiful, but it cannot be realized.