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.

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