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How to establish mathematical economics model
, find the problem; Second, it is meaningful to make sure the problem you want to study; Third, don't read the literature, write your own model first; Fourth, summarize your model; Fifth, make mistakes and then modify them; Sixth, look for literature to see if your model has hit others (if you are a graduate student, the tutor can tell you directly); If there are no obstacles, present your research.

The subject's question should stay in the third stage, and the previous answers have given good answers. I am a relatively failed example and can be used as a negative teaching material.

My graduation thesis is about theoretical model and technical progress. The general steps for me to make a model are to have a good idea first, then form my own story, read the basic model and start writing my own model, or express my own story in mathematical language. Generally speaking, this model has a core mechanism, such as Acemoglu's task-based model, and its core mechanism is Ricardo's comparative advantage principle. For another example, the core mechanism of adverse selection model is information asymmetry. Except for the core mechanism, other parts of the model are the basic principles of economics, such as some basic characteristics of a perfectly competitive market and some basic characteristics of a monopoly market, but the solution of the whole model is centered around the core mechanism. I haven't figured out the core mechanism of my model until now, so I made some mistakes in the process of building the model (the mistake of understanding the perfectly competitive market led me to introduce some wrong conditions), but fortunately, my intuition is strong enough to guide the model to a less wrong result. Of course, these mistakes were corrected by me in the end, and I added some stronger assumptions, which I couldn't correct. My model is too complicated to get a simplified solution.

Therefore, looking back on my model building process, my only success is that my model has always been loyal to my story, so I feel that when building a model, I must remember my own story well and not be biased by other people's research. Failures: First, the basic theory is not solid, and the understanding of the perfectly competitive market is biased, which leads to the model almost falling short. Second, there is no good understanding of the basic model for reference (why the assumptions introduced by others help the model to solve), and a brand-new assumption is rashly replaced, which leads to the model being too complicated.

Therefore, I don't think you should modify the assumptions of other people's models before you figure out the mechanism. You can write your own model according to the story you want first, because this will ensure the consistency of your model and won't make your model look like four elephants. Then go to the literature to see if your model has hit someone else's model.

I feel it is not difficult to make a model. For example, with martial arts, the basic principle of economics (rational people, profit maximization and even complete market competition) is internal strength. After practicing internal skills, I created some moves to overcome the shortcomings of other sects' martial arts. But without internal skill, all moves are fake. And their own moves are also displayed according to the operation mode of internal skill, otherwise fighting with people is very fatal. If you want to break other people's moves, you must know how they play, why they play like this, and where the flaws are. Of course, if you study the defects of others all day, there is no future. Some people will learn a set of martial arts directly and create their own internal skills, some people specialize in internal skills, and some people study whether their understanding of internal skills is correct. Eventually there will be different sects.