First, the marginal meaning

The marginality of economics refers to the degree to which the dependent variable varies with the change of the independent variable, that is, the amount that the dependent variable changes by a unit and the dependent variable will change. The concept of marginal roots is rooted in the first derivative of higher mathematics and the concept of partial derivative. In economics, according to different economic functions, we can find different margins. Such as marginal cost, marginal revenue, marginal utility, marginal consumption, marginal saving, etc.

Second, the characteristics of marginal analysis and the role of economic development

Marginal analysis was founded by Marshall over two hundred years ago. It tells us that when making decisions, we should use incremental parameters to make decisions in addition to the absolute amount of decision making parameters. This method has the following characteristics: 1. Marginal analysis is a quantitative analysis, especially the variable analysis, the use of this method is to study the number of changes and their relationship. The introduction of this method, so that economics from constant analysis to the development of variables. 2. Marginal analysis is the optimal analysis. Marginal analysis is essentially a study of the extreme value of the function at the marginal point. To study the law of increment and decrement of the dependent variable at a certain point, the function value of this marginal point is the maximum value or the minimum value, the marginal variable Is to make judgments and choose the best point, which can make the optimal decision, it is to study the optimization of the law. 3. Marginal analysis is the status quo analysis. The marginal value is solved directly according to the ratio of two micro increments, which is the amount of variation of the dependent variable caused by the calculation of the new independent variable. This indicates that the marginal analysis is the analysis of the new situation, that is, the status quo analysis. This is clearly different from the total analysis and the average analysis, the total analysis and the average analysis is actually the past analysis, is the amount of all past or all the past. In the real world, due to various factors often change, with the past or the average of the past to summarize the status quo and infer the future situation is unreliable, and marginal analysis is more conducive to the current situation of the emergence of a new situation The resulting effect of the consequences.

Marginal analysis in the 1870s after the first proposed for the effectiveness of the analysis, which established a theoretical basis - marginal utility value theory. The use of this analytical method can be said to have caused the revolution of Western economics, specifically its meaning as follows:

1. The use of marginal analysis has led to a shift in the focus of Western economics research. From the original political economy with a certain "social and historical" significance to purely study how to allocate limited scarce resources to infinite and competitive use for effective use. 2. Marginal analysis created the era of "quantitative" economics. Marginal analysis itself is a quantitative analysis, on this basis, so that a variety of quantitative tools linear algebra, set theory, probability theory, topology, difference equation, and so gradually into economics, quantitative analysis has become the main western economics feature. 3. Marginal analysis leads to the formation of microeconomics. Marginal analysis takes individual economic activity as the starting point, focusing on demand and supply, emphasizing the subjective psychological evaluation, which leads to the birth of microeconomics characterized by "quantity analysis" and market and price mechanism as the research center. Microeconomics is the study of the market and the price mechanism to solve the three basic economic problems, to explore how consumers get the maximum satisfaction, how producers get the maximum profit, how to get the optimal distribution of production resources. 4. Marginal analysis laid the foundation for the optimization theory. On the basis of marginal analysis, Western economics has theoretically introduced a series of conditions and standards which are optimal allocation of optimal resources, optimal income distribution, maximum economic efficiency and the whole society. 5. Marginal analysis leads to significant development of empirical economics. What changes have been made to the whole economy as a matter of change in the study, which provides a basis for studying the empirical economics of the question of what is true and the question of "what" is the economic phenomenon.

From the average analysis to the marginal analysis, it is a major development and transition of the economic analysis method. It is very important. It shows that mathematics has taken a major step in the infiltration of economics. Hicks 1946 "Value and Capital" and 1947 Samuelson's "Economic Analysis Foundation" comprehensive summary and development of the marginal analysis stage of the research work, so that the marginal analysis of the vertex, thus becoming the history of economics two And the development of a complete and complete microeconomic behavioral behavior theory, put forward the general economic equilibrium problem, built a theoretical framework of the general economic equilibrium, the creation of today's consumer theory, producer theory, monopoly competition Theory and the general economic equilibrium theory of the mathematical basis, so the marginal revolution is far-reaching.

Third, the marginal analysis of economic analysis in the two simple applications

1. Application example: the determination of the best yield

(1) Excluding taxation, the optimal yield is determined

Conclusion: Profit reaches a maximum at the level of marginal revenue at marginal revenue. The level of production at this time is called the optimal yield level.

Example 1 The income function R () = 6140-302 (yuan) of the edible oil production plant, the cost function C () = 102 + 60 + 1200 (yuan), which is the weekly production (unit: ton) Good yields and weekly expected profits.

Solution: From the known marginal revenue R '() = 6140-60, the marginal cost C' () = 20 + 60, from the conclusion: 6140-60 = 20 + 60 solution = 76, that is, the weekly optimal yield 76 for tons, the expected profit for the L (76) = R (76) -c (76) = 219040 yuan.

(2) Determination of the best yield after the production tax

Example 2: Under the known conditions in Example 1, if the t yield per ton of production is paid, the best yield and the expected profit per week are calculated.

Solution: Taxes payable by known tons. The profit of the plant is: L () = R () - C () - t

From the previous conclusion can be the best output for the marginal profit of zero when the output. That is, by L '() = 0, solution :.

This yield tax will affect the optimal level of production, of course, also have an impact on the expected profit, and the higher the tax, the lower the optimal yield level.

2. Application examples - determine the shelf life of liquor

Example 3 Assuming that there are 100 tons of white wine, the current price of 8 yuan kg, more than one year can be added value of 2 yuan / kg, storage costs 10,000 yuan per year, due to the accumulation of accumulated funds caused by the opportunity cost of an annual increase of 105p.r, Storage, p is the price of liquor for the year, r is the interest rate, and assuming r = 10%), then how long are these benefits stored?

Analysis: Assuming the best year to be stored, the following functions are known:

(1) Annual increase in the total income function R () = 105 × 2 = 2 × 105 (yuan)

(2) Annual increase in the total cost of storage C () = 10000 + × 105 × 10% [(105 × 8 + 2 × 105) / 105] = 90000 + 200002 (yuan)

(3) Annual net profit function L () = R () - C () = 2 × 105- (90000 + 200002) = 110000-200002

At this point the marginal revenue R '() = 2 × 105, the marginal cost C' (×) = 90000 +40000

Because when R '() = C' (×) when the maximum profit, so there are 2 × 105 = 90000 +40000, that is, 2.75 (years)

As the stagnation of the only, so only when the storage period of 2.75 years, companies can get the best economic benefits, the maximum net profit of 151250 yuan.

From the further analysis of the marginal analysis of this calculus as a tool to economic phenomena as the content of the mathematical analysis method has been deeply integrated into the economics, and become an important part of economics