Wednesday, May 27, 2009

Law of supply & ROI expectations

Today, my doubts regarding the collective wisdom of the economists concern the law of supply. In particular, I have my doubts about its monotonicity, as it has been presented to us. (Technically, I have my doubts that price P even can be a proper mathematical function of quantity Q at all, due to the vertical line test, though I think Q might always be a function of P.) This may well be just a case of simplification for a basic macroeconomics class, but it seems worth looking at anyway.

In particular today, I'm considering the possible effects of ROI expectations and attempts at achieving monopolistic dominance on the supply curve. Again, we return to Wikipedia for the basic definition (and assume you know basic law of supply and monopoly):

In finance, rate of return (ROR), also known as return on investment (ROI), rate of profit or sometimes just return, is the ratio of money gained or lost (realized or unrealized) on an investment relative to the amount of money invested. The amount of money gained or lost may be referred to as interest, profit/loss, gain/loss, or net income/loss. The money invested may be referred to as the asset, capital, principal, or the cost basis of the investment. ROI is usually expressed as a percentage rather than a fraction.

The initial value of an investment, Vi, does not always have a clearly defined monetary value, but for purposes of measuring ROI, the initial value must be clearly stated along with the rationale for this initial value. The final value of an investment, Vf, also does not always have a clearly defined monetary value, but for purposes of measuring ROI, the final value must be clearly stated along with the rationale for this final value.

This is a typical example of a supply curve. One of the key features, as presented to us, is that as quantity supplied increases, the price increases, and vice versa. Now, we were taught about certain ceteris paribus conditions (meaning, all else being equal) which must be kept constant for the law of supply to hold. But these ROI expectations and monopoly attempts don't seem to fall into any of these categories that we were taught. (Of course, the simplest approach to "fixing" the law might be to add these to the exceptions, rather than considering them separate.)

It seems to me that in modern markets, where a certain rate of return is often expected, this might provide an incentive to flip the supply curve, breaking the traditional law of supply. Follow along in this example graph which roughly represents what I have in mind:

As I see it, if for example a newspaper publisher is strongly expected to produce a 20% annual rate of return by and for the owners (a fairly ridiculous expectation on its face, but one that seems not uncommon of late, which may well be part of the problems resulting in major newspapers closing), but doesn't have much incentive to produce a better rate of return than that, he may be willing to increase the price of newspapers despite and because of dropping numbers of subscribers, so that the gross revenue (price per copy Pcover (the blue marks here) times number of copies Q), plus significant advertising revenue, which complicates things; let's ignore ad revenue for simplicity) minus costs (cost per copy Pproduction (the orange marks) times number of copies; I'm guessing that newspapers have significant fixed costs, in reporting, editing, and marketing, hence producing many copies costs significantly less per copy) in hopes that subscribers will stay subscribed out of inertia, who might not have subscribed initially at the new price. Note that the gross revenue minus costs can also be expressed as the number of copies times the difference between the cover price and the cost per copy (Q*(Pcover-Pproduction)). Geometrically, this is equal to the area of the rectangle bounded by the Y-axis on the left (keep in mind that this graph only goes as low as 25, and the Y-axis is at zero), the quantity produced on the right, the cover price on top, and the production cost on the bottom.

It's fairly simple, then, to create several different curves, such that this rectangle has a particular area, i.e. a certain return for the investors. And I could easily imagine a publisher trying to increase the price fully expecting a drop in subscribers, hoping to make it up in increased profit per copy, especially in the short term before subscriptions are canceled or not renewed.

That's quite a bit for now, so I'm going to go ahead and post the ROI discussion right now. I'll get to the monopolistic exception later tonight, or possibly tomorrow.

In other news, from discussion of price controls today, it seems that my teacher is fairly firmly in the free-markets-always-good, market-regulation-EVIL!!1! camp. *sigh* I'll try to muddle through regardless.

Production-possibility frontier & sustainability

As of today (well, it's after midnight here now, so to be precise, the 26th), I've started a short but intense macroeconomics class at school. Since it's sure to be fairly relevant, I'm going to blog about various subjects that come up, as we cover them (or sometimes, just because it's suggested by something covered), hopefully on a regular basis for as long as it lasts. For the first installment, I'll discuss the production possibility curve, as my teacher calls it. Wikipedia uses a slightly different term; I don't have a special preference myself, yet.

Let's start off with the basic Wikipedia definition of a production-possibility frontier:

In economics, a production-possibility frontier (PPF) or "transformation curve" is a graph that shows the different rates of production of two goods that an individual or group can efficiently produce with limited productive resources. The PPF shows the maximum obtainable amount of one commodity for any given amount of another commodity or composite of all other commodities, given the society's technology and the amount of factors of production available.

Here is a graph I made of the particular example that was used in class, where the X-axis represents butter, and the Y-axis guns. (A classic hypothetical example; no particular significance, other than one being a military want and the other a civilian want.) It represents this idea that as more of one good is produced, more of the other good must be sacrificed to produce the first, at an accelerating rate. When very little butter is being produced, sacrificing a small part of gun production can increase butter production significantly. When a great deal of butter is produced, a much greater part of guns must be sacrificed to achieve a similar gain in butter production.

The relevant facts of the curve for my purpose at the moment are that areas above or to the right of the curve represent productions that cannot be obtained with current technology, resources, and time (that is, the curve represents maximum production for a certain period, whether that's a year, or month, etc.). Points to the left of or under the curve represent production combinations that can be achieved, but the further they are from the curve (and the closer to the origin), the less the productive efficiency is. That is, at such points, the resources available are not being converted into guns and/or butter at the fastest rate possible. At points on the curve, this fastest rate is being achieved, and productive efficiency is maximized.

This is where I have to object to the way this is expressed and presented. It seems to be implied that any of these points under/left of the curve are inherently undesirable outcomes, and productive efficiency should be maximized. (We also covered positive and normative statements in economics today; this would be one of the latter.) This, in turn, means that we should seek to exploit natural (and other) resources as quickly as we can extract them. But, for resources that are nonrenewable and consumable (or those that are renewable, but at the PPF, are being used at a rate in excess of their renewal), such as oil and other fossil fuels, it can mean that in the end, they will be used less efficiently overall (there's probably a name for the particular kind of efficiency I mean here, but we haven't gotten to a term for it yet), and they will dry up sooner.

The End of Civilization As We Know It being accelerated is not what I, for one, would really consider an optimal solution. I hope that those who've taken more serious economics classes are getting a good clarification, that this production efficiency isn't always most overall efficient, and something to always strive for. But I'm afraid it might well be that it's promoted, with at best a few of those crazy tree-hugging liberals pointing out that this efficiency isn't necessarily ideal. And that would be, frankly, tragic.