The Problem with Divestment: Helping Wealthy Investors Instead of Victims








Sloppy Economics and Part-Time Austrians

The economy must have been hit harder than expected, given that so many Austrian Economists have switched to being only part-time Austrians, and otherwise thoughtful economists (whether Austrian or not) have shirked their duties.

What am I talking about? I’m talking about two recent waves of libertarian appeals to poor minimum wage empiricism that would not pass the sniff test in an introductory econometrics class.

The first round:

Kevin Erdmann blog post on the effects of minimum wage on teen employment. Erdmann originally regressed teen employment over time before and after the minimum wage was increased at different times in US history, concluding that there is strong evidence that the minimum wage caused the decrease in the employment trend.

This article was shared by (at least) Steve Horwitz, Peter Boettke, Don Boudreaux, and Mark Perry.

Horwitz introduces the article with

Evidence about the minimum wage harming teen employment you say? Evidence you shall have.

Boudreaux says

These data and these estimates combine with the compelling nature of – and with the central role in economic science of – the law of demand to make an empirically persuasive case that, as employers’ costs of employing low-skilled workers rises, fewer such workers will be hired than otherwise. [emphasis in original]

And Perry tosses in some snarky strikethrough formatting to note that

Marginal RevolutionCafe Hayek and the Coyote Blog are all featuring the chart above and the blog post about the minimum wage law government-mandated wage that guarantees reduced employment opportunities for teenagers by Kevin Erdmann on his Idiosyncratic Whisk blog.

The problem with all of these authors sharing the blog post and praising its conclusion is that the evidence provided is simply useless. One of the most fundamental aspects of science is the idea of controlling for external variables. The original post by Erdmann simply regressed teen employment over time – before and after the minimum wage was increased – without including any controls. However, it is notable that at least some of the periods with minimum wage increases overlap with recessions. And when the two competing theories about why employment has fallen are a minimum wage increase and a recession, my bet is always with the recession.

This is not to say, of course, that I believe minimum wages do not have teen disemployment effects. Rather, my point is that the evidence presented provides no backing for the claim, given the naive data processing performed. Not only can recessions help to explain the trends in employment, but they can also help to explain minimum wage hikes (or at the very least there is a plausible pathway): the economy goes south, so politicians argue for a higher minimum wage to help out struggling families (and win the left-liberal vote). As such, recessions are a classic example of a confounding variable in the analysis.

Yet even if the analysis somehow included the effects of recessions, there would still be too many variables uncontrolled that could be causing the observable effect (Dube also mentions that state-level variation in minimum wages could have an important effect). This is fairly standard Austrian Economics 101 mantra – you can’t control the necessary variables to claim causation (at least in most situations – I believe Imbens et al (1999) to be a tantalizing attempt at empiricism Austrians wouldn’t dislike).  I do not use the word “mantra” disparagingly, as I am strongly influenced by the Austrian position on empiricism and I approach all econometric studies with extreme caution. This case is no different – especially when so little work was done to rule out confounding factors.

The second round:

A Steve Hanke blog post at the Cato blog arguing that data from across European countries shows that minimum wages increase unemployment. Hanke shows a graph of unemployment for countries with and countries without minimum wages. Those without minimum wages have lower unemployment:

This is another piece of fairly useless empiricism. Once again, there are no controls for confounding factors. Is it so strange to think that countries that are more likely to enact minimum wages are also more likely to enact other labor market regulations that weaken the job market? If this is the case, then what we are seeing in the graph could very well be the effect of those other regulations – and we learn absolutely nothing new about the effect of minimum wages. I am not sure whether Dr. Hanke considers himself to be an Austrian, but in either case, the argument is unworthy of being published.

Sadly, the post has been propagated across at least a few websites already (including Boudreaux’s Cafe Hayek).

What could have been said

Once again, I am not disagreeing with the ultimate conclusions of the two posts discussed above. I believe that, if not in the unemployment rate, minimum wage hikes would have impacts in other variables, some seen, some unseen – perhaps job training, perhaps the intensity of the work environment, and so on.

Here’s what the articles could have said, which I would have found not only acceptable but a fantastic argument for their side:

Suppose the correlations in the two analyses ran in the completely opposite direction. That is, minimum wages tended to correspond with higher teen employment in the US over time, and minimum wage countries in Europe tended to correlate with a lower unemployment rate. What would the left-liberals do? They would parade this fact around in victory. Yet the facts are not like that, but the complete opposite. We do not see a corresponding pensiveness and pause on their side as to why the facts might not be so.

In this case, this argument wouldn’t be a critique of the minimum wage policy, but of the opposition itself. This doesn’t make it bad – it points out the dishonesty of loudly parading when the data superficially supports their side, but crickets when it doesn’t.


Austrians should be consistent Austrians: Do not reject empiricism when it disagrees with your policy stances and accept it when it agrees. If an analysis cannot possibly control all relevant variables, the analysis cannot be used to make a causal claim. If an analysis doesn’t even begin to attempt to control variables, then this is not science but toying with numbers.

And if you don’t want to be an Austrian, then at least don’t be a sloppy economist.

Update (2/1/2014): Jonathan Catalán takes on the same study, though he appears more mild-mannered than I am here:

Origins of cooperation and de-facto natural rights in the Hobbesian jungle – Part 1

I love the microfoundations of economics. I love seeing emergent, productive orders arise among individuals who are self-interested and maybe not even fundamentally “good.” That’s one of the reasons why I enjoyed reading David Friedman’s “A Positive Account of Property Rights” [1], which puts forth a theory on how property rights can arise out of the interactions of individuals. I intend to read more of the literature as I have more time.

For now, I’m interested in doing some basic exploration of how it could be possible for cooperation to arise in what I will call the “simple Hobbesian Jungle” – after Hobbes’s understanding of human life as short, brutish, and warlike without the existence of a government.

I wrote most of this post as I was traveling by bus to New York last summer. It began as an attempt to provide microfoundations to fight back against the general belief that humans, left to themselves, could not establish some semblance of peace and stability. As is suggested by the name, the model is very much simplified – meaning it doesn’t encompass the totality of human choices made in the Hobbesian jungle. However, I made the model very harsh to the individual on purpose, so that there would be as little reason to cooperate as possible without outright having everyone destroy everyone else.

As I continued to write, I realized that in its harshness, the world I had created could very well result in stability. Not only this, but this mental experiment led to a realization that it’s possible to explain not only why cooperation arises, but also possibly how the ideas behind morality (don’t kill, don’t steal) get created in the first place. The model also held out some explanatory power for why war could possibly exist and why cooperation fails to arise sometimes. Surprisingly, there are even implications for the question of whether animals have rights.

Let’s dive in.

The simple Hobbesian jungle

Let’s attempt to see how human cooperation could emerge under certain restrictive assumptions that would make it even more difficult than normal for it to emerge. Specifically, why doesn’t everyone suddenly go kill everyone else?

I will model the emergent order through iterated games.

The setup

Imagine a state of existence comprised of atomic, separate, primitive, rational, self-interested men. That is, imagine that we go back in time 20,000 years, and let’s assume away tribes and family relations.

We have a “society” of 50 individuals in a large, closed-off geographical area. These individuals have similar mental capacities, though their physical powers differ in magnitude. At time t=0 they begin by being separated from each other, each owning a certain good or tool that is useful to each of them in varying degrees of magnitude. The items are randomly distributed across the various individuals.

The individuals, by assumption, cannot settle down to create agriculture or establish a division of labor except for in the field of protection services (that’s later). These people, each by himself, roam the countryside at t=0.

There is another assumption – the individuals have omniscience on a limited time horizon. That is, when two people encounter each other, each knows what the outcome of a battle between them would be with 100% certainty. When a battle is concluded, the winner is immediately fully healed and takes the property of the loser. Each possession on the map is valued by all individuals.

At t=0, the individuals may be given an ordinal rank of their fighting capabilities from 1 to 50, with 1 being the weakest, and 50 being the strongest. Each individual is aware that there are 49 other people on the map, and each individual is aware of his ordinal ranking and that of everyone else. The individuals know the rules of the scenario, and go through the following thought process ahead of time: Each person considers every other person and thinks about what would happen in an encounter between them. Let each individual be named as his ordinal rank. In that situation, if 12 were to encounter 17, 12 knows that he would lose in a fight and 17 would win. 17 knows the same information.

Assume away any feelings of morality in these people or any feelings of kinhood. Each individual desires to obtain as many of the goods as possible and also desires to stay alive so that he may make use of the goods. The goods are infinitely durable, and provide a constant level of satisfaction when used in each time step.

Assume that when individuals wander the map they cannot see beyond a limited space around them, and hence may not avoid their peers. People also cannot scout out opponents and cannot escape a battle (although it is theoretically possible that a battle never begins because both parties decide not to fight for whatever reason). In essence, there is a fog of war.

Ready, set, go! First guess

A shallow, first-level analysis of the situation would suggest the following thought process: 50 knows that he can beat any other individual and take his property. 49 knows that he can beat all individuals besides 50. 48 knows he can beat all but two individuals – 50 and 49. This continues until the analysis reaches 1, who knows that he cannot beat any other person on the map and will lose all battles with other people.

Say that 25 meets with 33. What should each actor do in his self-interest? The first instinct might be for 33 to kill 25. After all, it is 100% certain that 33 will gain in the short term without permanent bodily injuries. 25 doesn’t have an option to run, and cannot win a fight in this scenario. It appears that this map is doomed for players to successively kill each other until only 50 is left with all the goods and the highest utility level achievable. Remember that after a given battle is over, the winner is healed immediately by assumption, and hence has no temporary weakness after the battle is over.

Is this what will happen on this map? Remember that individuals by assumption had their omniscience limited to a short time horizon. What is meant is that a person knows the outcome of the coming fight, but does not have perfect information about future social conditions – individuals work under the limited information that we have today in that regard. We may only guess what will happen in the future and support it with evidence. Same goes for them.

A second look

With that in mind, return to the scenario at t=0 between 25 and 33. One obvious outcome is for 33 to win and take 25’s possessions. Are there any alternatives, however? There are. 25 knows that he will lose to 33 in a battle, yet he also knows that 33 would lose to anyone above him. Therefore, it is beneficial for 25 to remind 33 of this fact and to propose an agreement – that they form an alliance for protection. Thus, 25 and 33 agree to not kill each other and to fight together in battle. Why is this beneficial? It is beneficial for 33 because with the help of 25 he can likely take on individuals with a much higher fighting power – say, 37, 42 or even possibly 50. Say that the highest level person they can take on together in battle is 39. Hence, their combined rank is above person 39, but below person 40.

Assume, furthermore, that no person can beat a combination of all of the people below his rank – except for 2, of course (who can always beat 1 in a one-on-one fight).

What social patterns can we predict to emerge?

Let’s look at the lower end of the scale. Individuals below, say, 18, if they encounter each other, know that they stand to gain in the short term by fighting and killing each other off. However, they also know that they might very well be killed soon thereafter by upper-level players. Hence, they have an incentive to band together. If they happen to meet, 12 and 5 might group together, and so would 17 and 16, for example. Players in the middle range, say 18-34, know that they could easily (and with certainty) take on the weaker players and steal their property. However, they also know that people above their rank could kill them and take their property. Hence, it is useful for those players to band together as well. Players in the upper strata of fighting abilities, 35-50, know that at t=0 they are the strongest on the map and that they could take on any individual below them. The lower section of the 35-50 range might fear the upper section, however, so it might decide to group together to protect itself from the very best fighters.

Whenever a person allies himself with someone else, it is less useful for him to ally himself with a weaker person than with a stronger one. However, note that if every player has a personal rule where he decides to only ally himself with a stronger person, then there would be no alliances ever made. In every encounter there is necessarily a stronger player and a weaker player. Hence, while the weaker player may want to ally himself with the stronger one, the stronger one would never want the weaker one under this rule.

We see that for some sort of alliance to come into existence, stronger individuals must ally themselves with weaker ones at some point.

Multiple levels of logic and strategy

Now, two points:

1) It is also clear a person in the 1-17 range, for example, is better off allying himself with a person above his range than a person within the range.

2) A person in the 18-34 range is better off being allied with a person in the 35-50 range than a person in the 18-34 range. Yet even the 18-34 range is better for him than the 1-17 range.

While it might initially appear that people in the 1-17 range will have little use for each other (because they are all relatively weak), these players may also realize that the 18-34 range people have even less use for them. Therefore, 1-17 have a higher chance of an opponent in the 1-17 range allying himself with them than in the 18-34 range. Therefore, it would be useful for people in the 1-17 range to offer each other alliances if they happen to meet. The same goes for 18-34.

Yet what if the initial meetings are from people vastly different in strength from different ranges? For example, what if 12 meets 36? It appears that 36 would not gain very much from allying with 12. However, as was said before, future societal structure is uncertain. 12 might very well employ the following reasoning:

“Sure, 36, you could kill me, because I do not contribute all that much to our joint defense. Yet consider this: Some number of pairs of people, each below 25, have met or are meeting at this very moment. Say that number is X. These people are likely to ally with each other [by the analysis presented previously for people in the same range.] The expected meeting of people in this group is a meeting of players 12.5 and 12.5 (using statistical expectation). Once these people join up, they might be able to take on a player who is ranked 13, 17, or even 20. Therefore, this meeting of the lower ranks increases their power, which shortens the range of variability of power. At time t=1, then, we will have people in lower ranks allying together and bullying people at the lower end of the upper ranks. This lower end, if it meets the growing group of underdogs at t=1, has a chance of joining them, and making an even more powerful group at t=2. As this process slowly wears on, the stronger and stronger players are recruited, and it’s very possible that at t=3 you, 36, will be meeting strong groups of underdogs. Not only this, but you could be meeting people above your rank as well. Therefore, even though I only improve your ranking so that you can beat maybe person ranked 39 or 40, if you do not ally with me, you stand a much higher chance of dying at t=3. We should ally with each other and with any other players that we might happen to meet.” Let this be named argument *.

If 36 buys this reasoning, he will join in. If not, he will kill 12 and take his good. I propose that it is likely for 36 to ally himself with 12.

The tough case

But what if 50 encounters 1 at t=0? The chances of an alliance are much lower. It may even be that 1 offers very little of value to 50, and that 50 decides to kill 1. Remember that fighting has no costs for the group that is predestined to win a given fight (besides the lack of a future alliance).

Hence, the worst-case scenario that we can imagine is that at t=0, 50 meets 1, 49 meets 2, 48 meets 3, and so on with 26 meeting 25. Suppose the cutoff for argument * working is 36 meeting 14. Hence, when players above 37 meet players below 14, * doesn’t work.

What could 1 say to 50 to not have him kill him? Well, note that if 50 kills 1 and 37-49 kill their respective weaklings, that means that in the next round the players left will be 14-50. Furthermore, 14-36 will all have allies (by argument *). Hence, 38-50 are in a very much weakened position at t=1 relative to t=0. Hence, it might be advantageous for 50 to get any help it can at t=0 to protect itself at t=1. [2][3]

Throughout this whole explanation, we must remember that although there are a lot of factors that are constant by assumption (such as knowledge about who would win a battle), the exact social outcome will vary according to the explanatory power of the individuals who bargain with the superiors for inclusion in the “tribes.”

I do not purport to prove that one social arrangement will in fact turn out – it all depends on the powers of the players to convince each other. What I am merely pointing out is various plausible tendencies in the situation. Of course, all of this relies on the individuals realizing that they can call future uncertainty to help them in the first place.

Conclusions for Part 1

In this conclusion section, I will cheat a little bit and point out some of the ideas on which I stumbled after the end of the simple Hobbesian jungle.

The first thing to note is that even in a winner-takes-all, no division of labor or trade, amoral world with no attachments or regret you can have cooperation arise. I have not by any means proved that it will result in sunshine and utopia for everyone. Yet I have shown that uncertainty about future social order could be a driver of social cooperation for the provision of protection.

In future posts, when we strip away some of the assumptions, we will see that different complications introduced in the model will decrease and increase incentives for cooperation – what the net direction will be, we will see (though I expect it will be in the positive direction).

An important note to make is that cooperation was allowed to arise in the model because the players shared a language. If they had no capability to convince each other, they would not have been able to develop this system of mutual protection, but instead would have most likely ended up killing each other, and 50 indeed would have won (although, perhaps, slavery might have arisen instead… That’s another interesting dynamic for another time).

This puts forth a possible explanation for early warring tribes. Without communications, even if they had good intentions, they might not have been able to get them across. Assuming away good intentions and focusing only on self-interest, they still might have been able to develop some mutual protection relationship, yet the language barrier prevented this from happening.

So we see that defense is one of the possible drivers of cooperation. Looking ahead, another driver is tasks that can be completed together more easily than separately (separate from the division of labor). I’m thinking of things like, say, rolling large logs. A man might not be able to do it by himself, yet can achieve the goal with 3 other men. Upon further consideration, defense is in fact a subset of this “cooperative strength.”

The other possible driver of cooperation, we see, will be the division of labor. In our Hobbesian jungle, this was assumed away to simplify the model. Yet upon a first glance, there appears to be a strong case for why the division of labor would be conductive to peace instead of war. Varying levels of talent mean that people have comparative advantages in the production of different goods. Not only this, but specialization allows for an increase in productivity of the laborer. As such, if they can communicate, Hobbesian strangers might prefer to trade instead of to fight.

Taking cooperative strength and the division of labor together, we begin seeing how property rights, at least the concept of self-ownership, might have emerged.

Going back to the importance of a shared language, we can see why cooperation among 1) animals and other animals, and 2) humans and animals is difficult. They have no way to make the case to each other for why they shouldn’t kill each other. Animals cannot make pacts for mutual protection unless it is genetically instilled in them. Humans also cannot face a bear reared on its hind legs and argue for why no, Mr. Bear, you shouldn’t kill me because then you will lose the benefits I can offer you.

The language barrier hinders both the possibilities for cooperative strength and the division of labor. If animals were to wake up tomorrow and be able to communicate completely fluently with each other, we would see more cooperation. If they could also engage in the division of labor, they would start off on the path to creating human-like societies. However, they do not possess these capabilities (beyond their simple abilities to communicate). As such, avoiding conflict and protecting one’s self from animals make having a meaningful society with them impossible. The stronger has always dominated the weaker. Yes, we can keep pets, and even live peacefully and happily with them, but this is only after having “enslaved” them and forced them to fit into our society after extensive “brainwashing” (training) – to put the affair in human terms. The question of animals’ rights extends beyond understanding “don’t hit or kill,” but also to recognizing property boundaries (which will be discussed in future posts). As such, until animals can properly understand these concepts, they remain subordinate to humans and their property (I suppose some select animals, such as some primates, could be excepted).

In future posts, I look forward to making the Hobbesian jungle a little more realistic.

Notes and References:


[2] Another reason 50 might choose to team up with a very weak player is to serve as signaling. While players might choose to team up, they could in theory, at any time, turn on each other. 50 choosing to ally himself with 1 sends a signal that he will restrain himself from killing weaker players and will cooperate well with others. Not a perfect signal – true – but 50 could find a way to make it appear legitimate.

[3] At some point in the discussion, someone might bring up the possibility of everyone teaming up into the same team and being one big happy group. But then, the hypothetical continues, why wouldn’t the best 49 players decide that 1 is useless and take him out? (Another version is that they decide 50 is too powerful by himself and decide to off him). This certainly may happen, yet it’s also possible that 2 will realize that if 1 is killed off, 2 is the remaining weakest player – and the next person on the chopping board. And so he might be agreeing to a slippery slope. So might 49 in the case of killing 50. By backwards induction, more and more players might get killed over time. This would create a disincentive to implement such a “kill the worst (or best) player” policy as long as the players have enough foresight to realize the consequences of their actions.

Concealed Carry License Fees: The Case for Abolition











On the Misteaching of Consumer Theory

A debate was taken up by econobloggers on the usefulness of mathematical economics a few months ago [1]. While their discussion focused on the descriptive and instructional power of mathematics, I’d like to make a note on mathematical formalism at the introductory level of economics – that is, the method of teaching economic principles to undergraduates through mathematical models.

One of the things that have stuck with me from my time studying economics at the University of Maryland is a question a classmate asked in the discussion section in Intermediate Microeconomics: “Is a price floor binding when it’s above or below the market price?” Now, this was in the beginning of the year, and I don’t know how long of a break the student had had since taking the principles level course, yet this led me to wonder where the educational process had gone wrong (remember – these are people who are in a 300-level class in a university which is ranked in the top 25 in the world for economics). The question can easily be restated so that any non-econ major could have answered it: “When the market price for an apple is $10, would a government law that forces buyers pay at least $8 affect the market? What about $12?” [2]

While this specific example doesn’t demonstrate any explicit failure of math in economic pedagogy, it does raise the question of why our future economists can’t answer some of the easiest questions in their field. My contention is that economics professors have failed to provide students with a solid foundation for individual choice theory – that is, how individuals make choices given their incentives and their real-world options.

A problem in consumer theory

One of the basic ideas behind economics is that individuals receive utility, or satisfaction, from the consumption of various goods. Given two types of goods (A and B), different combinations of both of these goods yield different levels of utility for consumers. This is generally recognized by various schools of thought. Mainstream consumer behavior theory then introduces a concept called “indifference curves.” The idea behind this model is that for a given level of utility, there are various possible combinations of amounts of A and B that give a person the same level of utility. For example, 3 apples and 5 bananas may give me as much utility as 4 apples and 4 bananas, and also as much utility as 6 apples and 3 bananas. Taking all of these points (combinations) together, we can draw a curve which graphically shows all the bundles of goods which yield a certain level of utility. We say that a person is indifferent between all of these bundles – she has no preference of one over another. Figure 1 shows an example indifference curve, labeled U1. Another indifference curve shown in Figure 1, U2, represents a higher utility level. That is, all bundles on U2 are preferred over all bundles on U1.

What is the problem with these models? Indifference curves must have a very specific shape to actually describe what is going on (either consciously or subconsciously) in the minds of consumers. The curves have to be bowed in toward the origin, as seen in Figure 1 (like the bottom left half of a circle). Why is this so, however? Couldn’t we draw a bowed out indifference curve (like the top right half of a circle)? The shape of the curve is justified in neoclassical theory by the idea that people like balance – or that averages are preferred to extremes. For example, consider bundles X and Y on curve U1 in Figure 2. If we take the average of these two bundles, we get bundle Z, which is on curve U2. This tells us that Z is preferred to both X and Y, since its indifference curve is higher up.

But what is the justification for this? In the presentation slides for consumer theory in my class, “balance” is listed as an assumption. Underneath, as a bullet, it says “also called convex preference.” What this means is that we are essentially told that the curves are shaped that way – we are told to assume it, without a basis in reality or an explanation why. And the entirety of economic theory is based off of this assumption.

In my Intermediate Macro class we were told a similar version of the assumption – that people like diversity. The professor justified this by waving his hands and saying that people usually like having some of both goods rather than all of one good or all of another. When a student challenged him by arguing that sometimes a person may indeed choose much more of one good and just a little bit of the other, the professor emphatically agreed and stated that we’re just using an approximate assumption that works most of the time. Naturally, he smiled, this is just an assumption.

Before beginning to pick this apart, I’ll note that another (even more mathematical) way of expressing the bowed in shape is to state that the second derivative of the curve is negative. I would definitely not be surprised if there are some professors who, believing that they are being especially rigorous, teach it in this way. Unfortunately, this is no more of a justification of why the curves are shaped that way, but merely a description of the fact that they are.

What was the problem with my Micro professor? She never explained why the curves are shaped as they are. What was the problem with my Macro professor? His explanation left students believing that economists make ad-hoc pseudo-scientific assumptions that may easily be challenged at will. [3]

The alternative?

It’s true that the students in class, if they can remember the assumptions, will likely be just fine on their exams and in higher level classes. However, they will not be able to have a deeper understanding that is the seed of thinking that germinates into the highest level of economics – including Nobel Prize-level economics.

The Austrian school of economics gives a concrete explanation of consumer behavior that is both easily remembered and is a necessary basis for understanding how people actually function. It also gives a clean explanation of the shape of indifference curves, which neoclassicals would do well to assimilate.

Austrians begin by stating that humans act. They act to achieve ends. To achieve these ends, they have to use various means – their time, their labor, their property, etc. The means in the world that we can use to achieve our ends are scarce – we don’t have enough “stuff” to achieve every single thing we might want to achieve. People have preferences, which determine which ends they want to achieve first. Then, in accordance with these preferred ends, people economize, or make the best use of, their means to achieve their chosen ends. An implication of action aimed at achieving ends (as opposed to arbitrary action for no purpose) is that more valued ends (some say more urgent ends) are acted upon before less valued (less urgent) ends.

Taking this information, what can we say about people’s satisfaction (due to achieving ends) relative to the amount of goods they have at their disposal? First off, ceteris paribus – that is, assuming everything else remains the same – the more of a useful good that a person has, the more ends he can achieve. With a loaf of bread I can prevent myself from starving. With two, I can feel pretty full. With three, I can afford to keep a dog as well. And so on. Hence, the more of a good, the higher a person’s level of utility.

Secondly, there is another very useful law of economics we can derive. Notice that, as was mentioned, people act to achieve their most urgent ends first, followed by a little less urgent, then even less urgent, and so on. Well, what does this mean when we have a limited amount of resources? It means that given a certain amount of goods, we use it to satisfy our most valued end first. Next, given some more of the good, we satisfy our next most-valued end. Given yet another increment of the good, we satisfy the third-most valued end. And so on.

Note that with each addition to our stock (or quantity) of the good, we achieve an end that gives us less utility than the previous addition (since it was lower on our value scale). That is, the utility from each additional unit of the good decreases (since we achieve a less-valued end). This utility of the next unit of a good is called the marginal utility. The additional unit of the good is called the marginal unit of the good. The law we just derived in easy-to-follow steps was the Law of Diminishing Marginal Utility. It’s a law in that it necessarily describes how humans work, starting from the simple and uncontroversial empirical fact of humans acting.

How does this means-ends framework help us to understand indifference curves? Let’s begin with a graph of two points that we are told lie on a single indifference curve in Figure 3. This graph will eventually be built up into a whole indifference curve, but for now, we have just two of the points (M and N) from the eventual indifference curve.

Start at point M, which we will say corresponds to using 2 of good A and 10 of good B (the graph is not to scale). We are told that point N is on the same indifference curve, and consists of 3 of good A and 7 of good B. Since they are on the same indifference curve, they provide the same satisfaction, by definition (the consumer is indifferent between them). Moving from M to N, in order to gain 1 of A (while still being as satisfied as before), we were willing to give up 3 of B. What does this mean in terms of preferences and ends? It means that, moving from M to N, the end we can now achieve with 1 more unit of A is valued so highly that it can balance out the ends we will not be able to achieve after giving up 3 of B. The ends we now achieve with one extra A are the most valuable ones remaining that can be achieved with A. The ends that are not any more achieved with the B we lost are the least valued ones that were being achieved with B. That is, when we lose means, we don’t stop doing the thing we value most with them – we stop doing the thing we value least (at the margin). (This is fairly important, so let me restate it – when we gain a unit of a good, we satisfy our next-most valuable end, which, compared to the ends we are already achieving, is the least-valued one overall; when we lose a unit of a good, we stop doing the least valuable thing we were doing using that type of good; these two facts can be understood intuitively if we consider a quick example. If I have 10 units of a good and I am given an 11th one, that 11th one will achieve an end that is valued less than every other end my previous 10 units were achieving. Now, if that 11th one is taken away, I will lose, once again, the least valued end that I was able to achieve.)

So what happens next? How do we put another point of the indifference curve? Well, consider two more possible points – points S and T in Figure 4:

Let’s try to predict which one of the two is likely to be the next point. We know that moving from M to N, we gained 1 A. We know that if we were to gain one more A, we would be able to satisfy another end with A. But this one would be valued less than the previous ones satisfied with A. Furthermore, remember that from M to N we lost 3 of B. We lost the ability to achieve the least-valued things we were able to before with B. If we were to lose even more of B, we would have to start giving up ends that are more and more valuable. So A is becoming less and less valuable, while B is becoming more and more valuable (given the ends we can achieve with each of them). Therefore, if we were offered 1 more of A, we would be willing to give up less of B than we were before.

As a real world example, imagine that A and B are bread and water, respectively. At point M, I was able to eat just a little bit of bread, but I had a lot of water – enough to use water to drink, to flush the toilet, to clean the house, to water my garden, to wash my car, and to use as sprinklers for my little cousins to play in. If someone offered to give me one more loaf bread, I would be willing to give up a bunch of water to gain it, even though I would have to give up, say, the sprinklers and the car wash. If someone were to give me yet another loaf, I would value it less, since I’m less hungry at this point, so I would be willing to give up less water than before. The water I am now giving up is more valuable than the water I gave up before, since now I have to give up washing my house, and washing my house was decently valuable to me. If someone wanted to once again give me one more loaf of bread, I would be even less willing to part with my water, because I am beginning to eat into the water that I would be using to flush the toilet. We see, then, that when I have to trade off bread for water, the more bread I acquire, the less willing I am to part with my remaining water for more bread. Why? Because the bread is satisfying ends that are less and less urgent, and the remaining water I have is satisfying the very most important things to me.

The graph of the indifference curve has to reflect this. So we know that from M to N I got 1 A for 3 B. For the next 1 of A that I gain, I will be willing to give up less than 3 of B. Maybe this time I will give up only 2 of B. Which point – S or T – satisfies this fact?

Here are the points once again in Figure 5, this time with the distances in question emphasized:

If I move from N to T, it is apparent that I will be gaining 1 of A at the expense of more than 3 of B. If, on the other hand, I move from N to S, I will be giving up less than 3 of B. S satisfies the deduction we went through earlier, so S is the next point on the indifference curve. If we connect the points on the same curve, we get the bowed-in shape. Using the same logic, we can deduce that all the points on the indifference curve will form a bowed-in curve, seen in Figure 6:

Now, whether it is very bowed in or not very much bowed in depends on the specific preferences of the consumers, yet the bowed in shape is retained. And this concludes our definitive explanation of why indifference curves are shaped the way they are.

Other critiques

Other critiques of the undergraduate approach to economics include the lack of emphasis on mutually-beneficial terms of trade and on the fact that trade involves goods that are not of equal value.

A voluntary trade being mutually-beneficial (that is, beneficial for both sides) stems from the fact that if it weren’t, then it would never take place. Given that a trade occurs, it can be inferred that both parties expect to benefit.

The second point is that for a trade to take place, a person must value what the other person has more than he (the same person) values what he himself has (this is called an inverse valuation of goods). As such, he is giving away something of lesser value and gaining something of greater value. The same holds for the person with whom he is trading – lesser value for greater value. If this sounds paradoxical, it’s because the subjective theory of value has not been internalized: value is subjective – it is entirely dependent on the individual and what her desires are. As such, it is entirely possible for both people in a trade to be giving away something they want less and gaining something they value more. In fact, this is exactly what happens when a trade is voluntary. As such, trade creates wealth for both sides.

Both of these points do in fact appear in intermediate neoclassical theory. However, they are only minor features of the models presented and can be missed entirely if not pointed out – they are not at all obvious when a student is given two equations and told to solve them. These concepts should instead be front and center in introductory and intermediate courses, and not a mere byproduct of the model. They are, indeed, what drives the model. In favor of appearing to be rigorous by using high-level math, we are neglecting the central ideas in economics. Indeed, when economists Ferraro and Taylor went to a major economics conference and asked a large number of economics students and PhDs an introductory-level question about a concept (opportunity cost) instead of an equation, almost eighty percent of them got it wrong [4].


I have tried to show in this article the importance of the means-ends framework in economic analysis. The mainstream approach of indifference curves deemphasizes important aspects of human action that should instead be underlined. Humans constantly use various means to achieve ends – thereby becoming better off. The occurrence of a voluntary trade implies that both parties are better off, and both parties trade away something they value relatively less than what they gain. Understanding these core principles of economics is vital to grasping the importance and relevance of markets.

References and Notes

[1] “A few words about math” (, “The Point of Economath” (, “Economath Fails the Cost-Benefit Test” (, “My Thoughts on Formalism in Economics” (

[2] To be fair, there is a way to interpret the question so that it actually turns out to be a relatively valid question. Namely, “could non-binding price floors have a general equilibrium effect on equilibrium prices?” It’s easiest to explain what this means through an example. Imagine that the government set the minimum wage at $50/hour tomorrow. If enforced, there would be massive unemployment of every wage earner who produces below that level – since their labor would literally be made illegal. Now, the question is whether this minimum wage would have an effect on wages above $50; for example, on the wages of people who earn $60/hour. The simplest analysis (partial equilibrium) would answer in the negative, pointing out that $60 is already above $50. However, general equilibrium (taking into account all the different markets in the economy) might yield a different result. Since the people who get paid $60/hour rely on the products produced by lower-paid workers as inputs for their own production processes, they would no longer be able to sustain the same level of productivity. As a result, their wages would drop accordingly. For example, a person who cuts and polishes jewels would likely lose his entire wage if all the people who mine jewels were suddenly put out of work. As such, the minimum wage imposed on the other workers lowered his wage, despite it being above the equilibrium price level for his labor market. This is an interesting question to consider, yet, unfortunately, it’s likely not what the student had in mind.

[3] Here I have to give credit to my labor economics professor, who did insist on deriving indifference curves from diminishing marginal utility, although she then didn’t justify DMU – which is an important part of the issue.

[4] “Do Economists Recognize an Opportunity Cost When They See One? A Dismal Performance from the Dismal Science” –