My question is in regards Chapter 4, Section 7 of Rothbard's Man, Economy, and State, particularly in regards to the table below.
Simply put, how did Rothbard arrive at these values? If future income in one year is discounted by the market at 10% then why wouldn't future income two years from now be discounted at a rate of 20%? I feel really sheepish for having to come on here and ask this question, but for some reason I just can't wrap my head around this otherwise benign concept.
Also, in either the first or second chapter I remember Rothbard describing a rightward/leftward shift in the demand curve as being a uniform increase or decrease in quantity demanded at every hypothetical price. But couldn't the demand curve be shifted by a change in the preferences of the marginal buyer alone, thus leaving the quantity demanded at each price by the submarginal and supramarginal traders intact but transforming the equilibrium price?
I'll give it a stab.
I'm not sure what is obscure to you, so I'm going to elaborate on points that might be simple.
To make sure we are on the same page, I'll define the terms here. Say apples are a dollar a pound right now in the store. A marginal buyer is someone who will buy the apples for a dollar a pound, but not for $1.01 a pound. A submarginal buyer won't even pay 99 cents a pound. A supramarginal one will pay $1.01 or more if he had to.
Next we have to make sure we understand that there is nowhere in the real world that has the data needed to draw a demand curve, or a supply curve for that matter. If we want to draw a demand curve for yesterday, for instance, we can know that 100 people bought apples yesterday when the price was a dollar a pound. Do we know how many would have bought apples if it they were 90 cents a pound, or $1.10 a pound, or any other number besides a dollar a pound, which was the market price? No we can't, for we are not mind readers. We cannot travel into alternate universes where the price of apples was different and see how many people bought apples in those alternate universes.
Thus, the whole supply and demand curve thing is a very abstarct theoretical construct, a visual way that helps some people communicate and/or understand certain concepts of economics.
The only things we can say with certainty are that if apples were cheaper, there would not be less people who bought them, all other things being equal, etc. [Rothbard describes this by saying the curves have to be rightward sloping].
So when we say a supply curve moves to the right, we are saying that we are going to analyze two hypothetical situations at two different times. One the first day, we know by Divine revelation not only the price of apples and how many people bought them, but also how many people would have bought apples at every price possible. On the second day we not only how many people bought apples and at what price, but again we know by Divine revelation all the might have beens.
As we examine the data, we notice that for any given price, more people would have bought apples on the second day than on the first day, no matter what price we choose to examine. This is captured on the curves [Chapter 2, Section 9, on page 144] by the fact that at any given height on the charts, the second day curve is to the right of the first day's curve.
Obviously, to be able to say that the whole demand curve moved to the right, we have to be able to see the whole demand curve. Meaning that if Divine revelation had merely shown us a part of the curve, for example just the dot where the actual price was, we would have no idea what the rest of the curve looked like. For example, the second curve may look what you would get by moving the first curve two units to the right, and then rotating it forty five or more degrees counterclockwise, which would cause part of the second curve to be to the right of the first one and part of it to be to the left.
The situation you are describing in your original post would [I think] move a part of the curve to the right [or left], and leave the rest of the curve intact, as if someone had poked the curve right at the actual price, causing it to bulge a bit locally. That is an interesting situation, but Rothbard decided to discuss a different one, where the whole demand curve moved.
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Geez, sorry about that; the table shows up when I click on my post to edit it but it's not showing up in the thread for some reason. Anyways, the table I'm referring to describes how one would arrive at the capital value of a house via time preference.
I'm not entirely sure I got your question right, as the graph isn't showing up, but I think this is your answer, and it's very simple. "Two years from now" is simply not "two" of the same unit of time as "one year from now", at least when it comes to time preference. There's no reason to expect that interest increases/decreases on a linear or geometrical line.
Could it be possible that Rothbard has his table wrong? For example, he starts his analysis by saying that the individual actor discounts 10 ounces of gold one year from now by ten percent. Thus, the present value of future goods, or the price of future goods in terms of present goods, is 9 ounces of present money traded for 10 ounces one year from now (or 1 ounce for 1.1 ounces). I don't have a problem grasping this concept. Rothbard then demonstrates in the table that ten ounces two years from now will be traded at 8.1 ounces of present gold, which is the previous value of 9 ounces discounted by ten percent. Rothbard continues this for the remainder of the graph, with ten ounces three years from now being the previous value of 8.1 discounted at ten percent, and so on.
It's entirely possible that I'm reading the table wrong, but this analysis doesn't seem to harmonize with you said or what Rothbard says a few chapters later in the book, namely, that a future good further away from the present will command a different time preference by the actor in question. It seems to me, then, that the 10 ounces two years from now would be discounted by a unique rate of time preference and would not simply be calculated by discounting the value that came before it.
It's discounted at 10 percent per year, if we're looking at the same table. It's discounted at 10 percent the first year, and then ten percent of that is discounted and so on infinitely, leading to the ultimate price of about 59 ounces. I think I understand where you're coming from but that you misinterpret it in that this is value, not loan size (hope that makes sense). Does this answer your quesiton?
It's discounted at 10 percent per year, if we're looking at the same table. It's discounted at 10 percent the first year, and then ten percent of that is discounted and so on infinitely, leading to the ultimate price of about 59 ounces.
That's certainly the same table, but what I don't understand is why the value that was arrived at by discounting the ten ounces of the first year is then discounted continually by ten percent; it's the ten ounces two years from now that the actor should be considering, not the present value of ten ounces one year from now bizarrely discounted by ten percent. I mean, the decreasing values make sense (an actor could be willing to trade eight ounces now for ten ounces one year from now but only five ounces for ten ounces two years from now), but the methodology seems off.
This whole section of the book just seems bizarre to me. In later chapters he refers to the rate of time preference as the percent change between a good traded in the present for a good in the future, e.g. if 100 ounces now traded for 110 ounces one year from now the rate of time preference for that exchange would be 10%. But in the chapter I'm asking my question about Rothbard seems to be working in reverse; he discounts the future goods by some percent and then says that this is the rate of time preference. The method used most often in his treatise is a "marking up" of the present good to the future good, while the method used in this section is a "marking down" of the future good to the present good. Very, very weird.
Again, I could be totally misreading the section in question. Also, do you happen to have an answer for my second question pertaining to demand curves?
About the chart. In real life, people don't make charts like that for themselves. They have some vague notion that they use to come up with a price they will pay for the house. But although we do not know exactly how they are thinking, [because they don't either], we can say the following things with certainty:
1. If he will pay ten to have it right now, and only nine to have it next year, that cannot mean that for each year he will pay 10% less, 9, 8, 7 ,6 etc. Because that means he is unwilling to pay anything now for the eleventh year, which is certainly false. That eleventh year is worth something, however little.
2. If he will pay 9 to get after one year, he certainly will not pay 9 to get it after two years, but less than 9. Imagine two guys trying to sell you something. One promises delivery in a year, the other in two years. Will you offer them both the same amount of money? Of course not.
Thus we know that each year is worth less than the year before, but no year is worth zero. Rothbard decided to use a simple model that captures these two criteria, mainly that each year is worth 10% less than the year before, as in the chart.
I think I get what you're saying. So basically Rothbard wasn't postulating that there's a linear relationship involved in time preference; he just used a ten percent discount on each preceding value to make the concept more readily understandable, but by no means would that rigid ten percent discounting exist in real life. Huh, I guess I did read the passage wrong, but that's still a rather confusing way to present the subject. His dissertation on time preference in the latter chapters more than makes up for it, though.
Smiling Dave, would you mind answering my second question too?
Smiling Dave,
Thanks for the thorough response! Would you say that my understanding of Rothbard's model in my previous quote is correct, i.e. that Rothbard chose to continually discount values by ten percent for the sake of simplicitly but that nine ounces traded for ten ounces a year from now moving to six ounces traded for ten ounces two years from now would still be correct? Sorry if I'm sounding vague or muddled; some of this is relatively new to me and I don't yet have the vocabulary to communicate these concepts effectively.
I would like a second opinion on this, but I think you are right.
After all, the big lesson AE has to offer to the world is that people are not machines or physical particles that are bound by rigid mathematical laws. Even in a theoretical situation one makes up, where one is like a god creating theoretical people with predefined properties and "creates" them in such a way that they obey some mathematical law, your audience will assume that your creatures are exactly like humans except for those features you spell out to be different.
And humans are quirky. They might very well demand a ten percent discount for one year, but a much higher one than ten percent of ten percent for two years. Why not?