25. Hyperbolic Discounting

Note: This post is the twenty-fifth in a series. Click here for the full listing of the series.

"The first beast that will appear
will entice us with money and fame.
If you listen long enough
you'll forget there's anything else.
Tie me to the mast
of this ship and of this band.
Tie me to the greater things
the people that I love."



The prototypical hyperbolic discounter was Odysseus. Ahead of time, he knew that he preferred being alive to hearing the song of the sirens, but he knew that once he heard the siren's song, his preferences would switch and he would be lured to his death by their singing. The only way to hear their song and not fall into their trap was to take preventative measures, tying himself to the mast and instructing his shipmates not to set him free.

Here is how Wikipedia defines 'hyperbolic discounting':

"In behavioral economics, hyperbolic discounting refers to the empirical finding that people generally prefer smaller, sooner payoffs to larger, later payoffs when the smaller payoffs would be imminent. However, when the same payoffs are both more distant in time, people tend to prefer the larger outcome, even though the time lag from the smaller to the larger would be the same as before."

As always, an example is helpful.

Say I offer you a choice between $50 now, and $100 one year from now. A lot of people will take the $50 now.

Now say I offer you $50 in five years or $100 in six years. A lot of the people who took the $50 now instead of $100 one year from now, will decide in this case to wait the extra year for the extra $50, choosing the $100 in year 6.

Even though the difference in the payout ($50) and the difference in time (one year) is the same, people have different preferences depending on how imminent the choices are.

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It's generally accepted that given a choice between getting something sooner vs. later, sooner is better - after all, you could die before later comes! (plus, a bird in the hand is worth two in the bush). This process of putting less weight on things that are further into the future is known as 'discounting'.

Where there is disagreement is in the pattern of preferences - i.e. how people discount. It has been typical to model people's discounting using an exponential distribution.

In this model, the amount you discount for a certain size of time period always remains the same, regardless of how far into the future that time period is. So if I discount something that happens one year from now vs. something that happens now by 5%, then I will discount something that happens 10 years from now by 5% vs. something that happens 9 years from now (because in both cases, there is a one year time window between the two choices).

This type of discounting is so common (particularly in the world of finance) that it's sometimes a surprise to realize that there is any other way to do it.

However, experience with, and experiments on, people have demonstrated that many people actually employ a 'hyperbolic discounting' model (just ask the CEO of Money Mart!). The difference with the hyperbolic model is that you place a much higher discount rate on time periods that are near, and a lower discount rate on time periods that are far. One of the interesting consequences of this type of discounting is that ahead of time, when two potential events are at a distance, you may prefer one to another (going for a run, vs. eating a bag of potato chips, for example). However, once the events get closer in time, the short term payoff from the bag of chips may come to outweigh the longer term gain from going for a run. If you are self-aware enough to know your vulnerabilities, it may be possible to, like Odysseus, take preemptive measures (e.g. prayer - 'Lord, lead us not into temptation', or, more practically, not buying chips while at the grocery store).


Mathematically, the exponential function reads as: y = e^-rt

(note that isn't just any old e, it's this e)

t represents time and as it gets bigger, the negative exponent gets larger, meaning the value of the function gets smaller - this is the mechanism through which the future payoffs (with a larger t value) are valued less than more current payoffs (with a small t value).

r represents the rate at which the future payouts shrink in importance - the higher the r value, the more you value the present vs. the future.


The hyperbolic function looks like this: y = 1 / (1 + rt)

t again represents time, this time in the denominator of a fraction, so again as t gets bigger the payout gets smaller.

It's easier if you see both curves plotted on a chart.



Note how the hyperbolic function drops off suddenly and then levels out, while the exponential function is much steadier. It is the sharp change in slope of the hyperbolic function which leads to the pattern where you do something in the short term (when the curve is steep, and you just need to do something now and damn the consequences) but come to regret it later once you are no longer on the steep part of the curve.

On the off chance that anyone actually made it to the bottom of the post, you might be wondering what this has to do with ethics. If so, thinklink back to the model of rational behaviour that David Gauthier sketched out where whatever a person decided to do must be rational, given that that was their preference. Hyperbolic discounting muddies the waters considerably since it means that not only will a person's preferences not be stable over time, but they will be predictably unstable. I know that there are actions I can take ahead of time to prevent myself from falling victim to temptation or short term thinking.

Furthermore, it seems that ethics often seem connected to this type of behaviour. What is patience but an attempt to place more weight on the future instead of the present? What is courage but an attempt to place more weight on the distant future instead of the very near future? What is procrastination but a failure to place more weight on the future than the present? Unlike Gauthier, we can't simply dismiss this running battle between the present and the future in any consideration of ethics.


Note: Lots more reading on the topic here.

24. Morals by Agreement: The Lockean Proviso

Note: This post is the twenty-fourth in a series. Click here for the full listing of the series.

This is the sixth and final (for now, anyway) post on the book Morals by Agreement, by David Gauthier.

Gauthier summarizes his argument in chapter 7, of Morals By Agreement as follows:

"If you seize the products of my labour and then say 'let's make a deal', I may be compelled to accept, but I will not voluntarily comply. We are therefore led to constrain the initial bargaining position, through a proviso that prohibits bettering one's position through interaction worsening the position of another. No person should be worse off in the initial bargaining position that she would be in a no-social context of no interaction. The proviso thus constrains the base from which each person's stake in agreement, and so her relative concession and benefit, are measured. We shall show that it induces a structure of personal and property rights, which are basic to rationally and morally acceptable social arrangements."

As best as I can tell, Gauthier's argument is effectively the same as in the previous chapter. That is, if people are going to set up a society based on cooperation, chapter 6 argued that people who break their agreements wouldn't be accepted in such a society, since they would make it impossible for people to make agreements 'rationally'. In chapter 7, the argument is that cooperative society also needs to exclude people who better their own position at the expense of others, since people who act this way make it irrational for people to participate in that sort of society.

He notes that another way of expressing this is to say that, within a cooperative society, people have the 'right' not to be coerced or deceived into doing things they would not do voluntarily.

Of course, the history of just about every piece of land on the planet is a history of people having taken it by force at some point and then made any future agreements starting from that position, so Gauthier does make one concession to reality in noting that people will acquiesce to a deal that benefits them, even if that deal is unfair because it represents past acts of coercion - if the deal is better than nothing. So, for example, in South Africa it was not required to undo every act of colonialism before apartheid could be ended.

He also notes that where some people have a large technological advantage over others, it won't necessarily be rational for them to cooperate with the others, as opposed to simply coercing the others to do what they want. He ends the chapter by arguing that this means that the proviso applies only in relations between equals.

Presumably the reason for the distinction is that, in a battle between equals, the retaliation back and forth would leave both parties worse off than a cease fire, whereas in a one-sided battle, the victor is likely to come out ahead, even after allowing for their costs of coercion. Gauthier doesn't (as far as I see, anyway) consider whether this notion has any implications for the behaviour of the government, which, as the only legitimate source of force in society, is in a similar position vis-a-vis its subjects as the technologically superior party is to the inferior. In other words, Gauthier's argument seems to imply that it is 'rational' for the government to coerce people in ways that it is not rational for individual citizens to do.


One thing that was unclear to me was why Gauthier seemed to insist that the prohibition against violating the proviso only applied before the establishment of cooperative society, rather than remaining in force all the time, even after society was established. Perhaps he simply assumes that, once cooperative society is established, refraining from the sort of coercive behaviour that would violate the proviso is already taken care of by the the fact that people come to voluntary agreements (as described in chapter 5) and abide by those agreements (as described in chapter 6).

* Note that it is called the 'Lockean' proviso because John Locke was one of the first philosophers to set out this sort of notion that people had the right to do what they wanted as long as they didn't make others worse off in the process.

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Finally, if you would rather get someone else's (more concise) perspective on Morals by Agreement, one of the most interesting internet links that I found summarizing it was these philosophy class notes, written by Dick Arneson

23. Morals by Agreement: Constrained Maximization

Note: This post is the twenty-third in a series. Click here for the full listing of the series.

This is the fifth of what should be a few posts on the book Morals by Agreement, by David Gauthier.

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In the Seinfeld clip above, Jerry Seinfeld arrives at the car rental agency only to find that although they have his reservation they don't have a car for him. He then explains that they don't understand the concept of a reservation - anyone can take a reservation, the trick is holding the reservation.

Similarly, in David Gauthier's philosophy based on people who maximize their self-interest, it's easy enough to explain why people might make agreements to co-operate (as explained in chapter 5) but the hard part is to explain why people would hold to their agreements. This is the task of chapter 6 of Morals by Agreement, where Gauthier attempts to explain why people who are self-interest maximizers would keep to their agreements when breaking those agreements might be more beneficial to them than keeping them would be.

Gauthier notes that in Hobbes' book, Leviathan, Hobbes creates a character known as 'the Foole' who argues the case for breaking your agreements where this is beneficial to you. Hobbes' solution is the creation of the sovereign. A government that will ensure that it is in your interest to keep your agreements by punishing you harshly if you don't. He also points out that Hobbes' solution dispenses with the need for morality (understood as a constraint on pursuit of self-interest) by simply re-aligning self-interest with the good of society via the sovereign's presence.

Gauthiers introduces the terminology 'Straightforward Maximizer' to be someone who, like the Foole, does what is in their best interest even if they have previously agreed not to and 'Constrained Maximizer' to indicate someone who foregoes their self-interest in situations where a fair co-operative solution will yield them a benefit over what they would get if everyone pursued their self-interest.

The Constrained Maximizer will cooperate if he expects others to do so, but if he suspects that the people he is dealing with are straightforward maximizers, he will do the same to avoid being taken advantage of.

In the terms of the Prisoner's Dilemma, the Constrained Maximizer will not confess if he thinks that the other Prisoner is also a Constrained Maximizer, but if he thinks the other prisoner is a straightforward maximizer, he will confess to avoid being taken advantage of.

Gauthier explains that the Constrained Maximizers will achieve better outcomes than the Straightforward Maximizers in the case where everybody knows which type of person everyone else is (i.e. if Constrained Maximizers had to wear 'CM' sweatshirts and Straightforward Maximizers had to wear 'SM' sweatshirts.) This is only logical - the Constrained Maximizer changes his strategy based on who he is dealing with whereas the Straightforward Maximizer doesn't, so naturally it is in the interests of the Constrained Maximizer to want everybody to be easily identified in one role or another.

Sadly, of course, in real life it is not always obvious who you can trust.

This (I think) is why Gauthier later says that,

"Failing to exclude straightforward maximizers from the benefits realized by co-operative arrangements does not , and cannot, enable them to share in the long-run benefits to co-operation; instead it ensures that there are no benefits to share."

In other words unless you kick out the straightforward maximizers, co-operation will fail.

Gauthier argues that Constrained Maximization is not simply another way to pursue maximization of your self-interest given particular circumstances, but rather requires that the Constrained Maximizer choose a disposition towards not breaking their agreements. The reason that people must choose this disposition rather than deciding on a case by case basis is that people who decide on a case by case basis will be kicked out of society so they won't get the benefits that co-operation brings.

Finally, Gauthier points out that over time, a community where all are constrained maximizers will be expected to outperform a community where all our straightforward maximizers.

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To be honest, I didn't find this chapter, which is the heart of Gauthier's theory, very convincing. A few comments:

1) Back in chapter 3, Gauthier argued that prudence - taking into account my future interests - was no part of rationality. But now it seems that choosing the disposition towards constrained maximization rests on the sort of prudential concern that was dismissed as irrational in chapter 3 (unless I am confused). This is OK by me, I never really agreed with the notion in chapter 3 that it was rational to be imprudent, but it doesn't seem consistent.

2) It's not clear how the Straightforward Maximizers are going to be excluded. Who will exclude them and what incentive do they have to undertake the substantial costs of doing so?

3) Although the Constrained Maximizer is disposed to switch to Straightforward Maximization when confronted with another Straightforward Maximizer, it seems likely that the person who Straightforwardedly Maximizes full-time is likely to be better at it. For example, I buy a piece of artwork from a man who, after taking my cash, pulls a gun and demands that I give back the art that I bought. I might choose to repay this act of Straightforward Maximization by responding with violence myself, but if the man is a professional crook, it seems plausible that he is better with a gun than I am. And if I myself develop a great skill at Straightforward Maximization in order to successfully battle these lifelong criminals, then it seems possible that I might reach a point where it is in my benefit to become a crook myself.

4) Most fundamentally, this notion of people 'choosing a disposition' doesn't square with my intuition of how these sorts of decisions are made. I'm reminded of the joke about, I believe, Abraham Lincoln who was known for his honesty and incorruptibility.

As the joke goes, a businessman walks into his office, offers Lincoln $100 to change a piece of legislation and Lincoln smiles and says no.

The next day, the man comes back and offers $1000. Again Lincoln smiles and declines the offer.

On the third day, the businessman comes back and offers $10,000. This time Lincoln gets angry and throws the man out of his office. The man asks, 'why was your reaction so different this time' and Lincoln replies, 'you were getting close to my price.'

In real life, people don't simply adopt a disposition to keep agreements and then dispense with any thoughts of breaking them. People are constantly weighing whether or not it makes sense to keep an agreement.

You can see this clearly in the different levels of security that attend situations with different rewards to agreement breaking. A dollar store has little in the way of security other than keeping more expensive items behind the counter. A jewelry store however, where the small size and high value and resaleability of the merchandise provides greater incentives for agreement breaking (theft), tends to have much higher security.

It seems more probable to me that people incorporate morals into their decisions, not by adopting a disposition based on long run maximization of their interests, but rather by applying utilities to the morals themselves, where actions that involve violating one of our morals attract a negative utility that offsets the potential gain from the action. This would explain why we are so concerned with the words used to characterize a situation: "it wasn't really a lie" we say or "technically it wasn't stealing", statements which don't make a lot of sense under Gauthier's framework. But I'm getting beyond the scope of the current discussion.

It seems likely that straightforward maximizers are not excluded from constrained maximization society based on society's perception of their disposition but rather in response to specific acts which demonstrate that disposition at a level beyond what society is willing to tolerate. Therefore, to the extent that straightforward maximizers could carefully choose their transgressions so as not to get caught or to the extent that they could acquire enough power that society was unable to exclude them (think organized crime) they might be able to avoid being excluded from society regardless of their disposition.

22. Morals by Agreement: Cooperation and Bargaining

Note: This post is the twenty-second in a series. Click here for the full listing of the series.

This is the fourth of what should be a few posts on the book Morals by Agreement, by David Gauthier.

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The clip above is 'Opportunities' by the Pet Shop Boys. The chorus says, "I've got the brains, you've got the looks, let's make lots of money" and this is a pretty good summary of chapter 5 of Morals by Agreement.

Of course, in Gauthier's language this translates into, "we become aware of each other as potential co-operators in the production of an increased supply of goods, and this awareness enables us to realize new benefits"

Gauthier's argument is that, given the opportunity to work together to better (or not worsen) their position, people are rational to do so. I agree not to play my tuba late at night and you agree not to mow your lawn early in the morning. Or maybe we form a joint partnership (in order to make lots of money). Or maybe I agree to give you my wallet and you agree not to shoot me*, etc.

Now, I guess to most people it probably seems fairly obvious that people make agreements of this sort all the time and it makes sense to do so, but you have to remember that Gauthier is starting from his notion of the rational human as one that does nothing but maximize its own interest in the present, with no ability to work together with others in a cooperative fashion.

The problem is that, unlike in the perfectly competitive market where people could (per Gauthier's theory) reach optimal outcomes by strictly pursuing maximization of their self-interest, situations where cooperation would be beneficial are situations where the market has 'failed' meaning that simplistic pursuit of self-interest by all parties will lead to sub-optimal solutions because it fails to consider superior 'joint strategies' where the people in a situation choose their strategies together (by bargaining to reach agreement) rather than separately.

You can think of a basketball team that has a better chance of scoring if they follow the play their coach drew up for them than if they all just do their own thing and hope for the best.

Or if we think back to the original Prisoner's Dilemma, if the prisoners were able to make a binding agreement with each other not to confess, then this would open up a new, optimal (from the prisoners' standpoint) solution to their dilemma that was unavailable when they were only able to each maximize their own self-interest.

Gauthier argues that in this context, rational behaviour requires that people agree to constrain their self-interest maximization for a while in order to secure a share of the benefits of cooperation.

Gauthier explains that, in the bargaining phase where the spoils of (the future) cooperation are being divided up, people are still acting to maximize their self-interest as best they can under the circumstances. But the bargain that is reached is an agreement to not maximize self-interest while carrying out the terms of the bargain.

So, I maximize my self interest as I push for the smallest concession possible when agreeing not to play my tuba late at night ('ok, I won't play after midnight, but I won't agree not to play between 11 and midnight' etc.) but when midnight strikes, I go against my self-interest by keeping the terms of the agreement and not just going ahead and playing my tuba anyway.

This question of whether the rational Gauthier people will actually stick to their agreements is one of the stickiest that Gauthier faces and is the subject of chapter 6.

I should also mention that Gauthier spends much of the chapter explaining his bargaining theory that if people have an equal willingness and ability to drive a hard bargain, they will end up making an equal bargain (one where everybody gains a roughly equal share of the spoils of cooperation).


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* You might think that the bargain where I give up my wallet in return for my life is not a fair one and should count differently than the others somehow - Gauthier agrees but defers discussion of the bargaining position of the parties until chapter 7

21. Morals by Agreement, Perfect Competition, Perfect Monopoly and the Market as a Moral-Free Zone

Note: This post is the twenty-first in a series. Click here for the full listing of the series.

This is the third of what should be a few posts on the book Morals by Agreement, by David Gauthier.

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While thinking about Jane Jacobs' Guardian and Commercial syndromes, one of the notions that occurred to me was that the Commercial syndrome reminded me of the microeconomic notion of 'perfect competition', while the Guardian syndrome reminded me of the microeconomic notion of 'Perfect Monopoly*'

Given that the ethics in the two syndromes often seem to come in opposing pairs (shun force vs. exert prowess, industriousness vs. making rich use of leisure), it seemed plausible to think they might represent two opposite conceptions, such as competition and monopoly.

However, it was not until reading chapter 4 of David Gauthier's 'Morals by Agreement' that I came across any substantiation of my intuition about the two syndromes. So before I get into chapter 4 of Morals by Agreement, let's first clarify what is meant by perfect competition and perfect monopoly.

Wikipedia describes Perfect Competition as follows:

"In neoclassical economics and microeconomics, perfect competition describes the perfect being a market in which there are many small firms, all producing homogeneous goods.
...
A perfectly competitive market may have several distinguishing characteristics, including:

Many buyers/Many Sellers – Many consumers with the willingness and ability to buy the product at a certain price, Many producers with the willingness and ability to supply the product at a certain price.

Low-Entry/Exit Barriers – It is relatively easy to enter or exit as a business in a perfectly competitive market.

Perfect Information - Prices are assumed to be known to all consumers and producers.

Transactions are Costless - Buyers and sellers incur no costs in making an exchange.

Firms Aim to Maximize Profits - Firms aim to sell where marginal costs meet marginal revenue, where they generate the most profit.

Homogeneous Products – The characteristics of any given market good or service do not vary across suppliers."

I don’t have much to add to this description. Basically, the idea is that each seller in the market is powerless to change the terms of the market and the only way they can pursue their interest is to maximize the amount of goods that they produce and can sell into the marketplace.

Now, perfect monopoly:

"In economics, a monopoly (from Greek monos , alone or single + polein , to sell) exists when a specific individual or an enterprise has sufficient control over a particular product or service to determine significantly the terms on which other individuals shall have access to it. Monopolies are thus characterized by a lack of economic competition for the good or service that they provide and a lack of viable substitute goods.
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a pure monopoly can -unlike a competitive firm- alter the market price for her own convenience: a decrease in the level of production results in a higher price. … An important consequence of such behaviour is worth noticing: typically a monopoly selects a higher price and lower quantity of output than a price-taking firm; again, less is available at a higher price."

Again, I have little to add here. The idea is that in this case the seller has the power to decide how much they want to produce, since they don’t have to worry that if they cut back production, someone else will just take their place. Economics assumes that both the firm under perfect competition and the monopolist want to maximize their profits. However, under perfect competition, maximum profit is achieved via maximum production whereas under monopoly, maximum profit is achieved via optimal production, where the optimal production level does not equal the maximum production level.



So, back to Gauthier. Chapter 4 of Morals by Agreement is titled, "The Market: Freedom From Morality"

Gauthier comments that

"the idea of such a [perfectly competitive] market illuminates our understanding of rational interaction by revealing a structure in which the divergent and seemingly opposed interests of different individuals fully harmonize. Conceived as an ideal type, the perfect market, as we shall see, guarantees the coincidence of equilibrium and optimality, and so its structure is the very antithesis of the Prisoner's Dilemma"

Gauthier suggests that it might be an ideal world if every market could be perfectly competitive but, "because the world is not a market, morality is a necessary constraint on the interaction of rational persons."

He further notes that,

"the absence of force and fraud is essential to the workings of the market. Before [Adam] Smith's invisible hand can do its beneficent work, [Thomas] Hobbes war of every man against every man must first be exorcized. And this, as we shall see, means that the ideal of free interaction which Smith celebrates is not natural but artificial, arising, for rational persons, only within a framework of agreed constraints. In understanding the perfect market as a morally free zone we shall be led back to its underlying, antecedent morality."

To be honest, I'm not sure I follow the argument that the market is morally free but has an antecedent morality (where people give up using force or fraud to get what they want) which somehow precedes the market but is not a part of the market.

At any rate, Gauthier goes on to specify a few more conditions of the market as a morally free zone:

1) No externalities, either positive or negative.

2) Private ownership, composed of two parts:
- initial factor endowment
- free individual market activity

3) Private consumption, composed of two parts:
- private goods
- mutual unconcern (note that this is an extension of the initial conception of rational behavior from chapter 2 which permitted one person to have an interest in another's well-being (for its own sake) - now in the morally free zone, such concerns are no longer allowed)

4) Both production and exchange are carried out under certainty (perfect information)

Gauthier then makes reference to what is known as the 'The First Theorem of Welfare Economics' which states that a perfectly competitive market is 'pareto efficient' or pareto optimal meaning that given the results of the competitive market, nobody can be made better off without anyone else being made worse off. It might be interesting to see if their are any moral assumptions smuggled into the First Theorem, but that would be a project for another day.

Gauthier then notes that the market takes as given the initial distribution of factor endowments and comments that the results of the market are fair only if these inputs are fair. The question of what makes for fair inputs is left for another chapter.

Gauthier then moves on to argue that the market does not contain any form of partiality that would justify a moral constraint needed to overcome this partiality. I didn't follow exactly what Gauthier means here. He seems to be trying to establish that nobody is unfairly harmed or benefitted by the operation of the market, but I'm not 100% sure on that. At any rate, the only form of partiality he detects in the market is (economic) rent. Says Gauthier,

"to the extent to which certain factors are in fixed supply - to the extent to which certain abilities or materials are not freely substitutable in the market - there is the possibility that demand for the goods produced with the use of these abilities or materials will bring about a market price for their use that includes rent.

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We shall return to the subject of rent, in considering the establishment of the perfectly competitive market as one of the terms of agreement among rational persons. For the present, we should note that our argument in support of the claim that the perfect market would create a morally free zone has not been shown to apply to those parts of market transactions that involve rent."

The next section, which I literally read 10 times but still don't quite follow, explains why there is the assumption of mutual unconcern or 'non-tuism' or that people take no interest themselves in other peoples interests. In Gauthier's words,

"It is neither unrealistic nor pessimistic to suppose that beyond the ties of blood and friendship, which are necessarily limited in their scope, human beings exhibit little positive fellow-feeling

...

The fundamental distinction between 'us' and 'them', between blood-brothers and strangers, has limited the scope of co-operation ... among much of humankind. We invoke the assumption of mutual unconcern to determine if that limitation is an inescapable evil of the human condition."

But if Gauthier is assuming that mutual unconcern exists (it seems he has never gone to the movies, where large groups of people squirm and laugh and cry and get angry on behalf of characters they have never met before and that they know are fictional, but I digress), then why the need to further make it an assumption of the competitive market? Why not just remain silent on the topic unless mutual concern would somehow interfere with the operation of the market. And if mutual concern interferes with the operation of the market (as we noted that Joseph Heath argued back in post 9 of this series, as I'm sure you recall :), then wouldn't the need to refrain from exhibiting mutual concern itself be an impartial constraint on people's behaviour and thus qualify as a moral rule by Gauthier's standards?

Anyway, Gauthier then goes on to note that the scope of this mutual unconcern is properly limited to the market,

"In real quasi-market societies there is a temptation, manifest both in thought and practice, to see the social world as falling within the scope of the market, and thus free from all forms of constraint. On the one hand the ideal of a morally free zone is extended to embrace all social interaction, and on the other hand all human relationships are interpreted as self-interestedly contractual, lacking in interpersonal concern. Thus neither the need for moral and political constraints nor the possibility of genuinely affective human ties is sufficiently recognized.

As we have already insisted, one of our fundamental themes is that the morally free zone created by the market can arise only within a deeper moral framework. We shall show that moral constraint is not only compatible with mutual unconcern, but indeed rationally required given this unconcern and the typical structures of interaction."

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* economists typically just use the term 'monopoly' or 'pure monopoly' rather than 'perfect monopoly' but I felt the language used for the two concepts should be parallel in order to reflect the nature of monopoly and competition as opposite ends of a single scale.