Economics: The Logic of the Financial Markets

This is part of a series of posts on economics.  Unlike my typical posts, these posts are dynamic—I'm going to come back and edit them as my thoughts develop.  I am basically "thinking out loud."  I am trying to fit things together in a modular way, so that each piece stands on its own analytically.  But no promises.

Now I want to take a closer look at the logic behind the financial markets.  Remember that we have individuals who want to maximize their utility, which they achieve by consuming goods and services.  And recall that many (maybe all) people experience diminishing marginal utility from consumption, meaning that the first dollar the person spends in any time period is more valuable than the second dollar, and so on.  This has two implications:  first, it means that people can sometimes increase their utility by shifting their consumption over time, and second, it means that people have different levels of tolerance for risk.  People with sharply diminishing marginal utility are more risk-averse than others.

Moreover, people discount future consumption using their consumption discount rate, which varies from person to person.  Finally, let's assume that people's wages are not constant over time.  People are sometimes unemployed, and almost everyone wants to retire at some point.

Putting these things together, it's easy to see that there will be demand for at least three things that can be provided by the financial markets.  First, sometimes people will benefit by borrowing money at one point in time and repaying it at a later point in time with interest.  This could be done for many reasons.  Someone who anticipates higher wealth in the future might want to "shift consumption back in time" in order to take advantage of the higher marginal utility of consumption in the present.  Someone with a high consumption discount rate might want to do the same thing, but this time in order to take advantage of the lower discount applied to present consumption than the one applied to future consumption.  Finally, someone might have an investment opportunity—a good or service in the non-financial markets that will yield a rate of return more than sufficient to repay the interest on the loan.  (An example would be borrowing to buy equipment for your business, which will hopefully generate enough income in the future to repay the loan with money to spare.  Another example—hopefully!—would be a student loan.)

The second demand that can be satisfied by the financial markets is the desire to shift money in the other direction—to save money today in order to consume it (plus interest) tomorrow.  This is just the reverse of the situation in the previous paragraph.  Of course, when you shift consumption into the future, you are always pushing against the consumption discount rate (no one discounts present consumption more than future consumption).  But if the interest rate is higher than your discount rate, then you could shift consumption to the future to take advantage of the disparity.

It could also be advantageous to shift spending power to the future if the individual has enough to consume today and wants to make sure she will have enough to consume in the future.  This is especially true if she anticipates the possibility of unemployment or retirement.  Just note that this would not be true if the individual did not experience diminishing marginal utility of consumption—in that case, the inability to consume in the future would not matter, because the individual could obtain the same (or higher) aggregate utility by consuming today.

The third and final demand that can be satisfied by the financial markets is the demand to shift risk among individuals.  A risk-averse individual can improve her utility by entering into insurance-like contracts that are "statistically unfair."  To see how this works, imagine an individual who owns an asset that will, at time t = 1, be worth either $1,000 or $0, with equal probability.  Imagine that this individual has a marginal utility of consumption of 1/2, meaning that this person's utility from consumption follows this function:

U = C^1/2

For the sake of simplicity, assume that this individual does not discount future income at all (this is just so that we can leave out some math).  And finally, assume that the individual's only source of wealth at time t = 1 will be the asset.  She will sell the asset (if it is worth anything) and consume the proceeds.

What is her expected utility?  It is:

U = (0.5)($0)^1/2 + (0.5)($1,000)^1/2

That is, there is a 1/2 probability that she will have a utility of 0 and a 1/2 probability that she will have a utility of (1,000)^1/2 or ~31.62, for an expected utility of ~15.81.

Now what if someone offers to pay her $400 at time t = 1 in exchange for the proceeds of the asset (regardless of its value)?  (We will assume this is a credible promise—she can rely on receiving $400 if she takes the deal.  We might address counterparty risk later.)  This is a statistically unfair exchange because the expected monetary value of the asset is $500.  But should she take the offer?  Well, here is her expected utility:

U = ($400)^1/2 = 20

So if she keeps the asset, her expected utility is about 15.81, but if she takes the $400 instead, her expected utility is 20.  Of course in reality she should try to get a higher price, but any price above $250 will increase her utility relative to no deal at all.

All right, so, if the financial markets are working properly, what should we observe?  We should see people with higher consumption discount rates borrowing from people with lower consumption discount rates.  We should see people with high current incomes saving money in anticipation of unemployment or retirement.  We should see anyone with a real-world (non-financial) investment opportunity borrowing money to finance it, as long as the interest rate is below the rate of return on the project.  On the other hand, we should not observe anyone investing in a project if a higher rate of return is available in the financial markets (taking risk into account).  We should see risk-averse people buying insurance (whether or not it is formally labeled "insurance") from people or institutions that are less risk-averse.

Economics: Modeling Individuals

This is part of a series of posts on economics.  Unlike my typical posts, these posts are dynamic—I'm going to come back and edit them as my thoughts develop.  I am basically "thinking out loud."  I am trying to fit things together in a modular way, so that each piece stands on its own analytically.  But no promises.

We will model people as economic agents who engage in the following market activities:  working (selling labor in the labor market), consuming (buying goods and services), borrowing or saving (either buying or selling financial products), and investing (that is, spending money in anticipation of generating future wealth, but doing so outside the financial markets).  The difference between saving and investing can be illustrated with this example:  a saver might take $1,000 and put it in a bank account for future consumption, while an investor might take $1,000 and buy a solar panel so that he can enjoy cheaper electricity in the future.  Both are spending money to increase future consumption, but only one is doing so through the financial markets.  This is a non-standard use of the term "investing," and so I will try to be careful to make myself clear when using the term.

We are going to model people as though they are motivated to maximize their consumption over time.  However, we will be open to the possibility that people care more about present consumption than about future consumption, and more about near-future consumption than distant-future consumption.  We'll call this the consumption discount rate:  the rate at which future consumption is discounted in the individual's utility function.  We'll allow people to have different consumption discount rates.  We will also distinguish between the consumption discount rate and the effective discount rate, which may take into account other factors such as the market interest rate and the rate of inflation or deflation.  That will be a topic for another segment.  The consumption discount rate will vary between 0 and 1, with 0 indicating no preference for present spending, and 1 indicating no expected utility from future consumption.  You can determine the utility from a unit of consumption in the future by multiplying it by:

(1-d)ⁿ

where d is the consumption discount rate and n is the number of time periods between now and when the consumption occurs.  (For current consumption, n = 0 and so consumption is not discounted at all.)

We will also allow for the possibility that people experience diminishing marginal utility from consumption at any given time.  This is reflected in a variable that on the high end approaches 1 and on the low end asymptotically approaches 0, as in the following equation:

U = C^m

where U represents utility, C represents consumption, and m represents the marginal utility variable.

So for instance, imagine that a person has $1,000 at time 0 and no expectation of working in the future.  This person might seek to transmit some of her spending power to the future (by saving or investing), even though future consumption is (other things being equal) less valuable than present consumption.  This is because (for instance) two instances of $500 consumption are collectively worth more utility than one instance of $1,000 consumption (although you would have to discount the second $500 round of consumption if she has a nonzero consumption discount rate).

In the example I've just given, the diminishing marginal utility of consumption is pushing in one direction (saving rather than consuming, so as to shift consumption to a time when its level is lower and its marginal value is therefore higher), while the consumption discount rate is pushing in the other (consuming rather than saving because present consumption is more valuable than future consumption).  It is also possible that both factors will push in the same direction:  for instance, an individual might borrow money and spend it today in the anticipation that she will be wealthier in the future.  In that case the person is increasing utility by shifting consumption toward the present and by shifting consumption toward a time when its level is low and therefore its marginal utility is high.

We will assume that work is unpleasant and people experience disutility from working (or utility from leisure time), so that people have to be paid wages to induce them to work.

Finally we will assume (or really just note) that people will seek the most advantageous means of shifting consumption/spending power from time period to time period.  So when they shift spending power to the future, they will look for financial products or investment opportunities that offer a high expected rate of return, and when they borrow they will look for a low rate of interest.  People who have diminishing marginal utility from consumption are risk-averse and they will also seek a certain degree of safety when saving or investing.  (In other words, someone who gets diminishing marginal utility from consumption is not indifferent between a certain $500 and a 1/2 probability of $1,000, because the first $500 of consumption is more valuable than the second $500.  Someone with no diminishing marginal utility from consumption is risk-neutral and would not generally have a preference between a certain $500 and a 1/2 probability of $1,000.)  So in other words people maximize their utility from borrowing, saving, or investing taking into account both the rate of return (or rate of interest) and the level of riskiness.

Ein Klein Whining

Yesterday Elisa Gabbert tweeted:

I don't like the word "creepy" because it seems like behavior is deemed creepy or not creepy based on how attractive the man is.
— Elisa Gabbert (@egabbert) February 5, 2015

I basically agree with this sentiment, but I also agree with the sentiment expressed by Catherine Nichols (e.g. here) that creepiness is a word used to describe unwanted male attention, and it's just a fact of life that male attention is more likely to be unwanted when it's coming from an unattractive man.

I want to take a step back and consider the way the sexual match-making process works.  In the U.S., at present, the general expectation is that men will be the agenda-setters.  In other words, men initiate things by indicating interest in some way.  This is obviously not an absolute rule, but in general a man must take affirmative steps to get the ball rolling, and by the same token can dial things down simply by not doing anything.  A woman generally must wait for expressions of interest, and then must take affirmative steps to shut things down.  Again, I do not mean to say that this is how things should be, or how they are in every case, but I think this is the norm.

The dynamic I've described above is not great for women, obviously, but it's also a very unfortunate dynamic for socially awkward men.  I think here is (very roughly) how things play out.  Men express their interest in women with varying degrees of adroitness.  When this attention is welcome, women are happy.  (They may not express their pleasure directly—they may play hard-to-get or feign disinterest or whatever—but they certainly don't often label men "creepy" when the attention is welcome.)

When the attention is unwelcome, it puts women in an awkward position (even if it is otherwise appropriate).  Sometimes, of course, the woman can simply communicate her disinterest, and that's that.  But the less perceptive the man, the more he is apt to ignore the "easy outs" that women may be trying to provide him.  "What is needed," he may be thinking, "is more persistence!  I just haven't gotten my message through with enough vigor."  When in fact the target of his affections is trying very hard to get him to stop.

Now the unfortunate thing here is that you can see how unpleasant this is for the woman (and therefore how she might be tempted to label the man "creepy"), and yet how unfair it is to pathologize the man's behavior (assuming, again, that the behavior is appropriate but for the fact that it is unwelcome).  Both the man and the woman in this scenario are behaving in a way that is rational given the context.  (The man is being oblivious, but he is behaving reasonably given his limitations.)  The culture expects him to be aggressive; he doesn't have the option of passivity.  Or at least, not if he wants to have a decent chance of finding a sexual partner through the normal channels.

The woman, meanwhile, really wants to dissuade this kind of behavior, because it puts her in a very uncomfortable position.  It would be different if there were clear, unmistakable ways to signal lack of interest.  But there aren't.  (Remember, it's not good enough to be reasonably clear to the average person.  It needs to be a signal that is clear to a less-perceptive-than-average person who is highly motivated to err on the side of aggressiveness.)  A woman can't extricate herself from the situation simply by dropping the matter.  That is (in general) the man's prerogative.  The woman may also want to signal to other people just how little interest she has in the man (to emphasize, in other words, that she has not encouraged the attention of this loser she has on her hands).  And so she labels him "creepy."

Where I think this leaves us is in an unfortunate equilibrium, one that is very disadvantageous to awkward/unperceptive men (something I'm keenly aware of).  The word "creepy" is used to encompass both truly problematic behavior and behavior that is merely awkward or tone-deaf.  Socially awkward men, who are understandably horrified at being lumped together with predators, respond by withdrawing from the market.  Or they adopt a much more tentative approach, which often amounts to the same thing, since women respond poorly to ambiguity or signals indicating lack of confidence.  (Some of this may be biological rather than social.  In Sheila Heti's How Should a Person Be?, the narrator is greatly aroused by what is essentially asshole behavior—what is, in fact, quite creepy behavior, except for the fact that it is welcome.  Hence my dismay, expressed in the comments section of Elisa's blog post on the book.  The narrator's reaction definitely seems to validate the idea that creepiness is almost entirely a function of attractiveness—when an attractive man says even the creepiest things, it's not creepy.)

And so a certain proportion of men are intimidated into passivity, while single women wonder where all the men are (or so I assume, what do I know?).  It's a frustrating situation all around, worsened I think by the weakening of old institutional forms of match-making.  And worsened also, I think, by the unfortunate (though understandable) tendency to use the same word to describe very different behavior.

As a kind of coda, here is another tweet from Elisa:

Thank heaven for non-awkward men
— Elisa Gabbert (@egabbert) February 6, 2015

Indeed.  In the world we live in, the non-awkward man is king.