53

Instead of proposing specific equations, I will point to two concepts that lead to specific equations for specific theoretical set ups: A) Equilibrium The most fundamental and the most misunderstood concept in Economics. People look around and see constant movement -how more irrelevant can a concept be, than "equilibrium"? So the job here is to convey that ...


40

I find that the essay "The New Astrology" by Alan Jay Levinovitz (an assistant professor of philosophy and religion, not an economist) makes some good points. ...the ubiquity of mathematical theory in economics also has serious downsides: it creates a high barrier to entry for those who want to participate in the professional dialogue, and makes checking ...


34

What is a reason to be against mathematics in economics? The danger that any tool creates: to impose itself on the tool-user, diluting and narrowing its view of the world. It is a matter of Human Psychology why this happens, but it certainly does, and the aphorism "to he who holds a hammer everything looks like a nail" expresses this phenomenon, which has ...


33

As has already been said, the MOST fundamental equation is surely: $$\text{MB}=\text{MC}$$ EDIT: This equation is fundamental in terms of the way economists think. As pointed out in the comments below, in terms of fundamental equations of economic models, the most fundamental equations describe equivalences between the uses and supplies of items (money, ...


26

I would like to point out that the question is not whether we should have math in economics, but why some people attack mathematical economics. A lot of the recent answers seem to try to answer the first question. Now then, to cover all bases like a good incumbent in a differentiated product market, I will also post an answer with points that economists have ...


22

Most of intro econ is intersecting lines. Specifically, $$MB = MC$$ * Equilibrium is achieved when Marginal Benefit is equal to Marginal Cost* $$\dfrac{MU_x}{p_x}=\dfrac{MU_y}{p_y}.$$ Marginal Utility per unit cost should always be equal Economics is about the logic of human behavior, how we make decisions in a world of scarcity. These equations describe ...


19

I think one of the most important equations (at least within macroeconomics) is: $$E\left[ m R \right] = 1$$ This equation has been used to derive many foundational results. This equation motivated the Hansen–Jagannathan bound. It is fundamental for asset pricing as well. Also, something interesting I saw from once from Tom Sargent. If you use the ...


19

I once heard Roger Myerson talk about why he thought Economics has, as a Social Science, been so successful in applying (or has so readily incorporated) mathematics. He suggested that perhaps it was due to some of the fundamental linearities within the world. Two examples would be the flow-balance constraints of scarce goods (commodity constraints) and no-...


19

Why hasn't JPE formally retracted Oster (2005)? In this case there simply is no reason to retract the paper. Academic papers are typically retracted for one of the following reasons: Retraction for error: For example, if paper claims that if $3+x=15$ then $x=10$ and such error significantly changes conclusions from the study (usually the mistake has to be ...


18

I think there are two important criticisms or limitations. Limit 1: The first, overlapping with what many others have said, is that all mathematic economics are reduced-order models of very highly complex relationships between monumentally complex actors. As Einstein is alleged to have said (approximately) "Insofar as the truths of mathematics relate to ...


17

Although I agree with Jyotirmoy Bhattacharya that the most interesting ideas in economics are not always best expressed through equations, I still want to mention the Slutsky or compensated law of demand from consumer theory $$ (p' -p) \Big[ x\big(p', p' x(p,w)\big) – x\big(p,w\big)\Big]^T \leq 0,$$ where $p',p \in \mathbb{R}_{++}^n$ are any two price ...


17

I disagree that: a) The core curriculum should not include things that are relevant only for those pursuing graduate school. b) A university degree should necessarily focus only on career outcomes for students. c) There are only two relevant careers and therefore the only thing worth teaching is how to handle different types of data. The core curriculum ...


15

I think that the opposition to mathematics in Economics mainly has to do with the obstacles it poses to indoctrination. A proposition expressed in terms of a mathematical/logic system is susceptible of objective verification, whence the inconsistencies of a proposition are more visible than where a rigid framework is missing. Moreover, mathematical ...


13

I was recently amazed to discover instances of computational social choice in The Nine Chapters on the Mathematical Art, the Chinese counterpart of Euclid's element, written by several generations of scholars from the 10th up to the 2nd century BCE. The core issues in social choice theory is the question of fair allocation, or fair collective decision. Once ...


12

I don't think there are any economics equations with the same status as, say, Maxwell's equations in physics. In its place we have concepts like the equimarginal principle, competitive equilibrium or Nash equilibrium which are at the core of the "economist's approach". But I think that the real worth of economics is not even in these ideas themselves but in ...


12

As long as the main results/conclusions of your paper don't rely solely on the non-economics literature you cite, you should be okay. In other words, it's perfectly fine to use non-economics literature to motivate or even as part of the support for your thesis, as long as you also include proper economic arguments, i.e. theoretical models or econometric ...


11

"All models are wrong; some are useful." The title is really all one needs, but to put a few more words behind it, mathematics is very good at deriving detailed results from very specific premises. It is very easy to make a mistake in the premises and obscure the consequences with language. A major issue in macroeconomics is that every policy decision ...


10

Firstly, for basic introductory econometrics, the following is quite good: "Introduction to Econometrics" by Stock and Watson. It is light on technical details, and heavy on intuition. This might not appeal to you if you are a math major, but it's the most important thing to get straight if you are interested in applying the empirical methods rather than ...


10

I second/third/whatever the objection to the "ideal careers" put forth here. Data Analyst - Most of these jobs will go to comp-sci graduates, especially as artificial intelligence and machine learning methods become more widely adopted. Tools such as deep learning, generative adversarial networks, and reinforcement learning explicitly require no or little ...


9

Game Theory in the Talmud by Robert J. Aumann discusses a bankruptcy problem and a variety of fair division problems of a contested sum from the Talmud, a document written roughly between 200 and 500 CE. For example: A fascinating discussion of bankruptcy occurs in the Babylonian Talmud 2 (Ketubot 93a). There are three creditors; the debts are 100, 200 and ...


9

A bit late to the game, but I'm surprised no one has named the equation to calculate OLS estimates: $$ \hat\beta=(X'X)^{-1}X'y $$


9

For me, one of the most important ones is the budget constraint. It might seem too obvious but a lot of laypersons (though maybe not physicist) don't get it! $p⋅x \leq w$


9

I recommended familiarity with the following topics: partial differentiation and optimization of multivariate functions study fixed point theorems. Kakutani and Brower are good ideas. Set theory is very important analysis (especially sequences, sub-sequences, convergence of sequences, etc.) Topology (basics is good enough. For example, understanding ...


8

Whilst not as foundational as, for example, the Slutsky equation, the condition on the Lerner index that a profit maximising firm with price $p$, cost $c$, and price elasticity of demand $\eta$ has $$\frac{p-c}{p}=-\frac{1}{\eta}$$ is an important equation in industrial organisation. This is not only an elegant formulation of the solution of the firm's ...


8

Adding to previous answers ... The basic Solow model is an example of a class of long-term macroeconomic models in which output is a function of inputs of two or more factor inputs and the ratios of the inputs may vary over time or between countries. Other examples include: The Mankiw-Romer-Weil model which treats physical and human capital as separate ...


8

There seem to be two things: The first is that "perceived value" is not something that directly corresponds to something economists usually study. It might be related to, say, marriage patterns and household incomes, political power, or whatnot. If you can show that it is an important aspect of a problem that falls within the (vague) boundaries of ...


7

It is already written but Euler equation in continous time yields $$\frac{\dot{C}}{C}=\sigma(r-\rho)$$ where $\sigma$ is intertemporal elasticity of substitution, $r$ interest rate and $\rho$ is the discount rate (impatience level).


6

The foundation of intertemporal economics is the net present value equation. That is, the net present value of a future income stream is the yearly incomes divided by an appropriate discount factor, based on the prevailing interest rate, r, taken to the nth power, where n is the number of years.


6

People have argued that if $P \neq NP$ then efficient markets are impossible and certain equalibria may not exist. However, they may hold approximately, so I'm not sure if this qualifies. Additionally, if it turns out that $P=NP$ then certain economic optimization problems (e.g. in logistics) become easily solvable. On the other hand, if $P \neq NP$ then it ...


6

Disclaimer: My academic coming of age was in an environment where behavioral economics played only a minor role. My research is theoretical, both "behavioral and non-behavioral", economics. I believe it is incorrect to say that game theorists (or economists) in general are not convinced by behavioral economics. You can easily see it is considered ...


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