48

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 ...


36

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 ...


32

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, ...


27

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 ...


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 ...


21

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 ...


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 ...


18

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-...


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 ...


16

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 ...


14

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 ...


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 ...


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 ...


9

"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 ...


8

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 ...


8

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


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).


7

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 ...


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.


5

In my view, it is useful to distinguish two phenomena: individuals have time-inconsistent preferences (this fits your example). There is a huge literature on that. The common practice is to evaluate welfare from the ex ante perspective, thereby assuming that people have well-defined preferences over the long-run, but that their choices might deviate from ...


5

Fair division: from cake cutting to dispute resolution (Brams (1996)) claims that the following text from Hesiod’s Theogony (sometime in 750 and 650 BCE) is the earliest recorded example of an envy-free (but not regret free!) fair division problem: For when the gods and mortal men had a dispute at Mecone, even then Prometheus was forward to cut up a ...


5

In case you want to go into Dynamic Stochastic General Equilibrium models, the book "Dynamic General Equilibrium Modeling" 2009 (2nd ed.) by B. Heer and Al. Mausser is a very useful companion. For econometrics I would also suggest "Probability Theory and Statistical Inference: Econometric Modeling with Observational Data" 1999, by A. Spanos. It provides ...


5

In addition to the notes from @Ubiquitous, I'd recommend these excellent and free/open resources from a number of academics. These are all posted freely and openly by the authors, and are all high-quality (and all at the "graduate level"). John Cochrane's Time Series for Macro and Finance monograph pdf John Stachurski's intro grad textbook, online Michael ...


5

Read Hal Varian's textbook "Microeconomic Analysis". It's brief, yet a standard text in a 4th year or graduate course in advanced micro. Then grab a good book on mathematical economics that's actually well written, and includes suggestions on how to develop good mathematical intuition, not just a bunch of recipes on how to solve problems. For example, you ...


5

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 ...


5

Your friend is right that GDP and similar measures are flawed—or, at least, incomplete. But this isn't exactly news to economists! For example, Richard Easterlin was arguing in the 1970s that GDP is a poor measure of national well-being. The specific issues with GDP that you point out in your question (failure to account for the value of innovations or for ...


5

In a standard cheap-talk setting, a sender (S) has better information on a state of the world and wants to communicate this information to a receiver (R) who then takes an action. However, S and R prefer different actions conditional on the state. Importantly, S is free to send any message independent of what she knows. That is, she cannot commit to a signal ...


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