Does the Graduate School of Economics Exam require high mathematics? This is a question that students who consult Japanese economics graduate school are more concerned about, today we will talk about it~
Among the basic disciplines of economics, microeconomics, macroeconomics and econometrics have relatively high requirements for mathematics, while economics-related directions, such as economic history and literature review, are more related to the accumulation of knowledge and the broadening of knowledge.
The degree of mathematics required in the graduate school of economics, such as finding limits, finding derivatives, finding integrals, differential equations, series, and median theorems, is almost mandatory every year. From this, we can see that the knowledge of calculus and limits occupies a relatively important position in economics.
What is the difficulty of mathematics in Japanese economics equivalent to domestic mathematics?
Let's look at the assumptions of a model of firm reoccupation related to industrial organization.
The following are the basic settings for model variables:
(Mizuno Ethics, Industrial Organization Theory)
It can be seen that in such a problem, it is a problem that can be solved by this model to maximize the profits of enterprises 1 and 2 under the production volume (equilibrium production) that both parties are satisfied with (equilibrium production).
Therefore, how to explain the maximization problem and how to find the best advantage has basically become a problem that needs to be continuously discussed in macro-microeconomics.
In economics, it is emphasized to find the optimization condition of the target variable when the control characteristic coefficient and other variables are unchanged. In optimization theory, the optimality condition refers to the sufficient and necessary conditions for the objective function and constraint function of the optimization problem to be satisfied at the best advantage.
Then we can deduce a capacity point that satisfies the condition through the optimal conditions, which is the most advantageous. Most of the optimal conditions used in the current examination are the optimal conditions of the equation constraint.
➤How to define such optimality conditions?
Let's take a look at the basic definitions and derivation ideas.
For example, we need to solve a minimization problem (e.g. expense minimization problem).
The optimality condition and solution method of this problem have been theoretically solved in calculus, which is the Lagrange theorem and the Lagrange multiplier method. So let's take a look at what happens in the local advantage x*.
This is the well-known first-order condition. （First-order condition）
So what is the actual application, let's review the problem of corporate profit maximization above. Taking enterprise 1 as an example, we can get the equilibrium production obtained in the first-order condition:
I believe that after the above explanation, everyone has an understanding of the most fundamental optimization problem solved in economics.
As a candidate who is about to take the Graduate School of Economics Examination, what mathematical concepts are included in the knowledge points of Japanese economics?
In macro-microeconomics, in addition to the optimization problems mentioned throughout the knowledge points, another important component is game theory.
There is a word "GTO" in Texas Hold'em:
GTO, or GameTheory Optimal, translates to Chinese should be called "Game Theory Optimization." This means that in a game or game behavior, while you choose your best strategy, your opponent is also choosing the best solution for you. And the most well-known theory in economics is the Nash equilibrium.
Nash equilibrium, also known as non-cooperative games.
The theory was proposed by the famous economist, founder of game theory, Nobel Prize winner John Nash, that is, the prototype of the male protagonist of the movie "A Beautiful Mind".
The theory is that in non-cooperative games, there is a combination of strategies such that each participant's strategy is the optimal response to the strategy of the others.
If the strategy currently chosen by the participant forms a "Nash equilibrium", then unilaterally changing his or her strategy will not bring any benefit to any one participant. One of the more well-known examples is the prisoner's dilemma.
Under the premise of no prior communication, the criminals will choose to confess the least harm to themselves between the choice between both parties confessing guilt, one denying the guilt of the other, and both denying it. In this way, regardless of whether the other party admits guilt or not, the benefits obtained by themselves are the greatest.
Nash equilibrium is the theoretical basis of general equilibrium in microeconomics, industrial organization correlation and other knowledge, and different equilibrium models under different game models derived from this are also a combination of game theory and economics.
It can be said that the cornerstone of microscopic theory is based on game theory and information asymmetry. Therefore, the study of game theory is also crucial.
In addition to optimization and game theory, linear algebra and probability theory are mostly used in statistics and econometrics.
However, if you are not a student of econometric theory, you usually do not need too professional knowledge of linear algebra, because the design model itself is a relatively cutting-edge research, and the goal that needs to be achieved at the monk stage is to be able to understand its principles and use these tools.
For example, the Markcroft process occupies an important position in the dismantling of statistical and econometric models, and the application of these empirical aspects is also applied to macro models and financial model analysis.
Therefore, not every mathematical knowledge needs to master and penetrate the principle, on the contrary, studying various papers while learning in research can make mathematics more conducive to their own research.
How to solve mathematical problems when you have zero foundation, or a weak mathematical foundation, how to cope with the examination in graduate school?
First of all, we need to encourage everyone that a weak foundation in mathematics will not affect the study of economics. In the process of learning mathematics, it is much more important to grasp the definition, understand thoroughly and understand the process of derivation than to directly brush the questions or directly listen to the pre-examination sprint of some domestic postgraduate examinations.
We can see that most of the questions in the Japanese graduate school exam can be obtained by simply the four rules and derivation operation, or differential operation.
Therefore, when you put aside the fixed problem-solving mode and really learn to use mathematics as a tool, then learning mathematics will no longer be painful.
Seeing this, do the students have a basic understanding of the difficulty of mathematics in the graduate school of economics? If you have the need to apply for the exam, please contact Xiaoyuan quickly~ We will carefully plan the examination plan according to the specific situation of each student, and do our best to help students pass the dream school!