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

If you ask yourself how much a potential employer would have to pay you to convince you to work for him, the answer is probably something like "at least as much as I could earn by doing the same job for another employer". So, provided there are several employers competing to hire workers, you can think of employers as bidding against each other for the best ...


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, ...


30

Because there is no indication in your question that you are a student or practitioner of economics, I am writing an answer for a lay audience. Let me know if you would like more technical detail. A fairly general prediction from economic models of competition between firms is that the price that maximises their profit is higher the less sensitive is demand ...


30

Yes, customers who were exposed to day-ahead wholesale market prices were paid to use electricity. It is a combination of several different factors that make the day-ahead wholesale electricity market special. Firstly, very few electricity consumers participate in it directly. So the demand side is very illiquid, with very low short-run elasticity - and it ...


29

My favorite example is the initial formulation of Arrow's impossibility theorem in the first edition of Arrows' "Social Choice and Individual Values" (1951). In the first edition, Arrow claimed that, together with 4 other conditions, the following domain condition ``The domain $\mathcal{D}$ is sufficiently extensive so that there exists at least one free ...


27

I completely agree with denesp's answer, however I think you can make it even simpler. On a very small scale, it's certainly true that if I gain, somebody else might lose. If I take away my brother's chocolate, then he will lose it, and will most probably not get anything comparable. OK, let's say I prefer chocolate to wine gums and my brother likes ...


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 ...


22

Kydland and Prescott's seminal paper on RBC theory uses a log-log specification on consumption-leisure preferences, arguing it is the only one that matches long-run constant share of working hours (one of the Kaldor facts). This is false. In fact, there's a whole class of additively-separable utility functions (King-Rebelo-Plosser, which were discovered (...


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

Suppose you have a differentiable function $f(x)$, which you want to optimize by choosing $x$. If $f(x)$ is utility or profit, then you want to choose $x$ (i.e. consumption bundle or quantity produced) to make the value of $f$ as large as possible. If $f(x)$ is a cost function, then you want to choose $x$ to make $f$ as small as possible. FOC and SOC are ...


19

Very influential paper by Angrst and Krueger (1991) used quarter of birth as an instrument for effect of schooling on earnings. Since compulsary schooling stops when you reach a certain age (so many dropout when they can). However it turned out that quarter of birth is not a good instrument, correlated with family background and thus also earnings. http://...


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 ...


17

Let's put the succinct answer by @TheAlmightyBob into an abstract model: We want to model the labor market. Markets' structure assumptions: goods market and labor markets are perfectly competitive. All participants are "too small" economically, and they cannot affect equilibrium price through their quantities demanded/supplied - they are "price takers". ...


17

A classic example is to consider the question Why doesn't Tiger Woods mow his own lawn? Woods is an excellent golf player. But he also may be excellent at mowing. Still, if he devotes time to mow the lawn he sacrifices time playing golf, in which he is much more productive. A gardener who is skilled at mowing lawns but not at playing golf sacrifices ...


17

I suggest to learn more about the Economics of Superstars. Within the economics field, the "superstar" term is "...used to refer to extreme wage outliers (Adler, 1985; Rosen, 1981). These outliers are such that in a labor market there appears to be a convex relationship between wages and skills (Lucifora & Simmons, 2003). There are two main competing, ...


16

This is a fundamental question which economics can answer quite well. I'll rephrase your question a little bit- Is economics a zero sum game? The answer is no. Certainly some transactions are, but for the most part, no. It can be proven a little bit more rigorously and denesp has alluded to that by linking the fundamental theorems of welfare economics. I'll ...


16

Check out sunk cost. Although this might seem completely counterintuitive, the investment you have made should be irrelevant to your decision to stay or quit, if this investment has already been made and cannot be recovered. What matters is whether the benefits you are yet to incur outweigh the costs (that you are yet to incur). So the decision should be a ...


15

In a 1929 paper, Harold Hotelling introduced what became the standard model of spatial competition. Two firms position themselves on an interval, which induces a certain demand structure, and then compete in prices. The model was influential and widely taught. The message was that firms diferentiate minimally, both locate in the center. But in 1979 (!) ...


15

There is a good Planet Money episode on ticket scalping; I recommend it. The reason for banning ticket scalping has nothing to do with economic harm, and everything to do with making the arts (or sports, whatever) accessible to people of more-modest means. Consider the fact that artists could, if they wanted, just auction off all the seats to their shows, ...


15

Opportunity Cost of the Seats Once the movie is made the cost of production is sunk and irrelevant to the proper pricing of tickets. Only the marginal costs of serving an additional customer and the opportunity cost of showing a different film would enter into ticket pricing. Since cinemas should be setting the number of screens for each movie so that the ...


14

The main difference between partial and general equilibrium models is, that partial equilibrium models assume that what happens on the market one wants to analyze has no effect on other markets. Therefore in partial equilibrium models one only considers a market for one good and assumes that the price of every other good or the wealth one has does not ...


14

Following up on the excellent MWG diagram in Amstell's answer, the fundamental observation needed is that holding $p$ fixed, $e$ and $v$ are inverses of each other. $e$ tells us the amount we need to spend to get a certain amount of utility $u$, while $v$ tells us the maximum amount of utility we can get from a certain expenditure $w$. Whenever we want to ...


14

This is freebee, but I'm gonna grab it: Reinhard and Rogoff (2010, AER pp) argued that there is critical level of government debt-to-gdp ratio at around 90%, arguing that countries that cross this level of leverage typically grow less. Ignoring the whole point of correlation versus causality, UMass student + coauthors [reference needed] showed that this ...


14

As a complement to the great answers already here, let me give an even simpler small scale example in which you win and no one else loses: Suppose you have a broken fan at home. Scenario A: you relax on your couch then go to sleep. Scenario B: you take your fan apart, figure it's just a loose screw, tighten it, put it back together again, and it's fixed. ...


14

This is called the Alchian–Allen effect. The Alchian–Allen effect was described in 1964 by Armen Alchian and William R Allen in the book University Economics (now called Exchange and Production). It states that when the prices of two substitute goods, such as high and low grades of the same product, are both increased by a fixed per-unit amount ...


13

I strongly suspect that an emerging important area for applications of measure theory will be in approximate dynamic programming techniques. Approximate dynamic programming (aka "reinforcement learning" in the computer science literature) has been the direction of research work in the last ~10-20 years of the dynamic programming literature. Economics is only ...


13

Not sure how much this will help, but the diagram in Mas-Colell p.75 is something I always have in mind when deriving these functions. I'm not sure what books you're using, but Microeconomics by Mas-Colell et al. is the go to graduate resource. But I prefer Microeconomic Analysis by Varian. Much easier to read and still has the important content needed ...


13

Yes, if there were more competition then net neutrality would not be such a big issue. Any throttling would cause an ISP to lose customers to competitors. Competition is a main assumption behind why markets work. However, in this case an ISP has market power which breaks the assumption. The market power allows them to easily put smaller ISPs out of business....


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