Supply and Demand Offers No Useful Analytical Information On The Pricing of Financial Assets

And the mathematics we can use instead of scarcity

Apr 20, 2025

This is going to be a rapid fire edition today, because there are simply so many closely related concepts and principles, any one of these I think could suck me into hundreds of hours studying and researching.

So as to not bury the lead, I will first explain why supply and demand is not useful for financial assets. In my post “Cargo Cult Science is Prevalent in Economics”, I described supply and demand as a “spontaneous” model of production and consumption, and in particular argued that the supply curve is contradicted by economies of scale, where a greater volume of production lowers costs. I should for purposes of reference, acknowledge Piero Sraffa as an early critic of the supply and demand model. In his book, The laws of productivity under competitive conditions, he put forward detailed arguments critiquing the model. Sraffa, as a contemporary and collaborator with Keynes, is still influential among Post-Keynesians today.

The reason why supply and demand is not helpful for financial assets, is much simpler. Buyers and sellers do not have distinct criteria for assessing the prices of financial assets. When you go to buy a home, you ask, “is this a good location, is it quality built, does it meet my needs”. When a builder plans out a home, they ask: “What will the materials and labor cost, is this a growing market, does my profitable price point align with what other houses are worth in the area?”

But for a financial asset, both buyers and sellers want to know one thing: will this go up or down in value? So both buyers and sellers are looking at the exact same information, so you can’t break price dynamics into two independent price curves. Buyers prefer low prices, and sellers prefer high prices, but they are using the exact same criteria.

Depth Charts And Order Books

Depth charts are a visualization of an order book, using a cumulative distribution. You can see the number of outstanding orders to buy or sell an asset at a given price.

Importantly, unlike supply and demand, a depth chart does not convey information on potential sellers below the current market price or potential buyers above the market price. This is because those orders would already have been fulfilled. A depth chart only has current outstanding offers to buy or sell an asset in an active exchange.

If you want to get even more pedantic, we could also clarify that an order book doesn’t show what would happen if prices actually changed. People seeing news of price changes could respond to that information, and thus make new orders that are not currently in the order books. On the other hand, supply and demand claims to show exactly that. The demand curve is how many buy orders would show up at every possible price level, and analogously the supply curve shows all

This “multiverse problem” is inherent in the construction of the supply and demand model, and is why you will almost never see an actual empirical price curve, it is all based on hypotheticals that are impossible to measure and would just be a guess anyway.

The Strange Elusiveness of Empirical Price Curves

While you may frequently see supply and demand charts, they are almost always just simple cartoons, and not a chart of any real data. If we were to explain that the path of a projectile follows a parabola, we might cartoonishly draw an arch to represent that path, but it would be simple enough to get measured data from a real world projectile, or mathematically plot the formula:

$y = y_{max} - \frac{g}{2} \cdot (t - \frac{dt}{2})^2$

$dt = 2 \cdot \sqrt{\frac{2}{g} \cdot y_{max} }$

This formula is the vertical position of a projectile thrown upward from zero height on level ground which attains a maximum height ymax, and is airborne for a period dt starting at t=0. Note that in this idealized scenario without air resistance, and a uniform gravitational field, the horizontal displacement is completely independent and so does not affect the calculation for vertical position. Idealized projectile motion is the one time physicist will use a flat earth model, but you could argue projectiles always follow elliptical orbits even if those orbits would be arrested by intersecting with the earth’s surface.

If you see a supply and demand drawing, you are going to be very lucky to have any kind of label with real units, much less anything with empirical data points. This is because the economic data we gather takes the form of time series, while supply and demand is a set of conjectures about a counterfactual: what would sellers or buyers do if the clearing price were different?

Most of the graphics I could find in a quick google image search show two demand curves and a fixed supply curve or vice versa. In other words, the claim is that in a given scenario, when prices change, one of the curves stays fixed, and then the other curve shifts. These shifty curves of counterfactuals should lead you to question if the model is even helpful at all for empirical purposes.

Overall, I would prefer to have a balanced approach. The supply and demand model can be a useful teaching tool for understanding markets with many different buyers and sellers where they use different criteria for how they choose their bids to buy or sell. The entire benefit of the model is to analyze buy orders and sell orders independently. For financial assets, it is typically much less important to do independent analysis of the buy orders or sell orders, and you can just do general price analysis based on information discovery. Unless there is active insider trading happening, where one group is able to consistently benefit from private information, there is not a benefit from separating the two halves of the order book into independent price curves.

Linear Programming

Fortunately, there is a much more direct mathematical model we can use to introduce the principles of prices, such as resource tradeoffs, finite limitations, and the effects of allocation choices. This is the mathematical subject of linear programming. Linear programming is a very basic but powerful generalized mathematical optimization model.

As an example, a simple linear program can be derived from the following scenario:

You have 3 recipes: cakes, brownies and cookies.
Each recipe uses some combination of 3 limited ingredients: flour, sugar, and eggs.
You can make partial batches of any recipe. You need to make some combination of these recipes for your school bake sale. You have a certain amount of ingredients available, but don’t have time to go purchase more.
A batch of brownies sells for a profit of $1, a batch of cookies has a profit margin of $2, and batch of cake generates a $3 profit(The school agrees to reimburse you for the raw ingredient costs)
Assume all baked goods will get sold, how many batches of each recipe should you make?

The other information you would need to solve this problem, is how much of each ingredient is needed for each recipe, and how much of each ingredient you have available.

This crude example is really to just introduce unfamiliar readers to the topic, the study of linear programming and more general mathematical optimization techniques is basically its entire own mathematical discipline.

Linear programs are applicable to wide variety of decision making problems, not just economics or business. But the critical insight that should be communicated to beginning economics students, is that for this particular class of problem, the optimal solution, or at least one of the optimal solutions, is always at a boundary of your constraints. In everyday language we might say that getting the best possible outcome often involves pushing yourself to your limits. Linear programming is an entire class of useful mathematical problems, where an optimal solution, if one exists, can always be found at the boundary of constraints.

Meanwhile, in a supply curve, costs would be expected to scale smoothly as you approach full resource utilization. While there is always necessarily a hard limit on production in a finite world, as the cost of one more marginal product goes to infinite, there is no particular reason why the ultimate or the penultimate product would have higher costs. If there are 100 apples in an orchard, it could be that all the apples are easy to pick, or it might be that there are a few apples that are very difficult to pick.

The lesson is two fold. Yes, there will always be limitations and tradeoffs in any finite system, but we should not assume any uniform behavior near the limitation. Many things in the modern world operate on small margins of safety. Opposing traffic on a high speed highway often will pass less than one carwidth apart. If you made such a road wider, how many fewer crashes would you get? You cannot assume any particular scaling response to strict limitations that applies across very different problems.

Scarcity As a “Smoothly Scaling” Constraint

This problem of understanding how costs change near a binding constaint or limitation, is essential to the study of economics, and yet, supply and demand, can lead to very reductive thinking on this question.

The issue of scarcity is often presented as the central principle of economics. We live in a world of limited finite resources, so there are tradeoffs involved in allocating resources. This is the standard story, and then soon after, students are introduced to the spontaneous model of production and consumption: supply and demand.

But what do we actually mean by scarcity? There is a connotation associated with it as desirable or enviable, or valuable, when we say something is scarce. So does scarcity merely mean “finite”, does it mean “limited”, or does it mean something else?

I would argue, that going back to our apple orchard example, if some apples are attainable but difficult to obtain, then that fits the connotation we make around the word scarcity. After all, if something is difficult to attain but still possible, then it must be value.

And so we see here, how the word “scarcity” is often used to talk indirectly about value. Things are valuable because they are difficult, but we do them anyway. Things are valuable because offer significant challenges, but they are still possible.

If a resource like our apple orchard example, has a fixed number of apples, but they are all fairly easily recovered, then I would argue that “limited” would be a more apt description than “scarce”. And this idea that things can be scarce, difficult but not impossible, challenging but attainable, leads to the desire to see the price of financial assets rise. It creates an inherent bias toward seeing the economy as an engine of creativity, as a catalyst for discovery.

But in practice, what we do to make the price of financial assets keep rising, is so far from this ideal of humanistic self perfection, that the disconnect is jarring. Would it be so bad, after all, if all prices fell except the price of labor?

All Financial Assets Are a Monopoly

If MMT, modern monetary theory, could adopt a single backronym, it would be “Monopoly Monetary Theory”. MMT is unique in thinking of money as a scarce resource issued by just one entity. Instead of breaking down the monetary system by various substitutes: M1, M2, M3, it considers who is the ultimate issuer of a particular currency to be the paramount question.

Every monopolist is a price setter. So the argument goes. If the government pays $10 for a bushel of wheat, then the price of a dollar is one tenth of bushel.

But where my framework diverges from standard MMT, is in asserting the importance of all financial assets as a monopoly, not just currencies issued by sovereign governments. However, governments, as public entities, do have one unique thing about them: they don’t have a bias toward scarcity.

Private Finance Mandates Scarcity, Public Finance Does Not

When a private entity issues a financial asset such as equity shares, their goal in this is to leverage economies of scale in order to gain a competitive market advantage. In other words, they want a monopoly. They want the ability to charge entry to the apple orchard at higher and higher prices, even if the price of individual apples is stable or falling.

Any capital raise is going invite more people to add their money to a pile of funds, and help a company grow faster and better. But this is not done altruistically. It is only done to the extent that people with money already in the pot will benefit.

Thus, scarcity is the operating principle of private entities issuing financial assets. If a company could raise more capital and grow more quickly and make all the investors better off, they are not going to do it unless the incumbent shareholders are better off than the alternative. So it always creates this private exclusive club environment, and that is why they want and need scarcity.

A private company doesn’t want to maximize the total wealth in the world, they want to maximize their individual wealth. Exclusiveness is the easiest way to achieve that. If global wealth grows at an anemic 1% or 2%, and yet certain portfolios grow at 5% to 10%, then you have a case where a small pool is benefiting from exclusivity. This is particular rate disparity that Gary Stevenson of the YouTube channel “Gary’s Economics” has discussed this phenomenon on more than one occasion: “Why aren’t we all getting rich from compound interest?”.

It is much easier to make a club and keep people out, than to grow the entire economy at a faster rate of growth.

However, for a public entity, that issues a financial asset, they don’t serve just shareholders, they potentially can and should exist to serve everyone, whether they already hold the currency or not. Thus public entities do not mind inflation, so long as total wealth keeps growing. There is no inherent bias toward exclusivity or artificial scarcity.

This is not to say that public entities can’t be diverted to benefit private interests, or become explicitly corrupt, all it means is that as a general operating principle, they have no inherent bias toward scarcity, whereas private entities do have this bias.

Important to this, is the realization that capital gains are not necessary to increase total wealth in system. If you earn money at a higher wage, then you can save more finanical assets, even if those assets do not appreciate passively.

Will The Real Supply Curve Please Stand UP! Flipping The Axis and Hitting The Wall.

The irony, is that modern firms do not care about the scarcity of the product they make, only the scarcity of the financial asset they issue. That is why there is this obsession with growth at all costs, because you can get very rich raising more capital, at higher and higher buy-in levels.

The first thing we must know about price curves, is that quantity belongs on the horizontal axis, because scale is the determining factor in production and consumption. Price belongs on the vertical axis, because costs respond to scale.

When I first learned the supply and demand model, I thought they had the axis wrong, because the individual price curves present the quantity as the response variable, and the price as the input variable. But having learned the model itself is janky an wrong, it turns out I flipped the axes back in my head, to match my understanding of scale as the first principle of economics. For a supply curve at least, it is imperative to put quantity on the horizontal axis, as the function input. As the quantity of production scales, costs change dramatically. The supply curve is in fact, not one to one, as production scales costs fall, until it gets too big, then costs rise again.

And here we see that supply, like demand, slopes downward. Quantity and price are inversely correlated, no matter how you draw the axis.

This works until you get to the very end, or limit of your system. Then the price rises sharply to infinity, where it would be impossible to produce more. This is hitting the wall.

Depreciation is Generational

The idea of capital continuing to grow over time forever and ever, is really disfunctional and bad. Like most parts of life, one generation has to pass the torch on to the next, and then assets fall off and new ones grow to replace them. There is a giant retroactive observation bias in our assumption that capital should just grow and grow and grow. It’s not how the world really works.

What Rate Disparity Actually Means

Rate disparity is just the idea that different assets, and especially different asset classes, can be stable at different rates of growth or return. Just like wage levels are not completely uniform, returns to capital, despite being competitive, do not all lie in a stable equilibrium.

Why not? the problem of ownership creates distance. What you can own requires a certain sphere of influence, and as that sphere grows, so do your costs to exert ownership. It’s a really simple principle, but it gets hidden by the mythology of uniform capital grown.

While it is possible for asset performance to destablize and accelerate through a sell off— as described by models of accelerating inflation— the problem of ownership always matters, so rates will never be perfectly uniform. Capitalism should be about seeing ownership as an opportunity to better the world, not an entitlement or guarantee of employment for money to generate returns.

Rate Disparity