This is a chapter where Rothbard begins his development of money prices.
This is a critical aspect of Man Economy and State.
And he starts off in exactly the spot that Peter Klein had mentioned in the last lecture,
the relationship between money prices and the general equilibrium array of barter prices
that would be the object of a mainstream approach.
And the particular topic that he takes up in this respect is to point out
that money prices are, in fact, not barter exchange ratios.
In other words, this whole approach of saying,
let's do price theory by system of equations,
and we solve for the barter exchange ratios,
and then we pick one of the goods as a numeraire and then we do a we just do a numeric calculation
and we put all the barter exchange ratios in terms of this numeraire is not the same thing as money
prices and let's just take this simple illustration let's say let's say that we want to convert all
prices in the barter exchange system into Apple prices and so let's say we have an actual exchange
The exchange of two bags of apples for four gallons of gas,
so that's a barter exchange ratio that we come up with in the system.
But bags of apples do not exchange directly for plates of spaghetti.
So there, all we have is a barter price in terms of gallons of gas.
So to get the barter price in terms of apples,
we just do the appropriate calculation, right?
So we can trade two bags of apples for four gallons of gas,
And then two gallons of gas would trade for one bag of apples.
And so the spaghetti price would be two, two gallons of gas would be one bag of apples
for the plate of spaghetti.
So the first point again that Rothbard wishes to make here is that this won't do at all.
This is not, this is not giving us money prices, right?
This is not the same thing as giving us money prices.
And he gives three reasons for this.
The first is that when we have money prices for all things, the ratios are all in terms
of the general medium of exchange, right?
With barter exchange ratios, we do not have a general medium of exchange.
This means that we cannot have actual exchanges between bags of apples and plates of spaghetti.
We might have in the numeraire that we pick, let's say, to take a general case of this,
You might have, let's say, 10 goods out of 100 that are directly traded for the numeraire.
But the other 90 are not, right? These we just calculate.
So when we get to, when we talk about money prices, since money prices are the general
medium of exchange, they trade against all other goods.
Now the importance of this is not just a technical fact, right?
The importance of this is that because of the existence of money prices, we can now
now engage in economic calculation, whereas with barter exchange ratios, we cannot.
This is because we cannot actually exchange apples for a plate of spaghetti, right?
So we can't actually do accounting in bags of apples.
This doesn't aid us as a tool of decision-making in the monetary economy.
There, we have to have the common medium of exchange where we can actually exchange money for all these other goods
so that we can make comparisons of the money sums that we spend to get this set of goods
and the money sums that we receive when we sell these sets of goods.
Now secondly, he points out that while the prices of all goods are the same for all traders
in the market at any point of trade, so the trading two bags of apples for four gallons
This isn't true for money. This would be true, of course, in the barter exchange world, right?
All the prices that are actually being exchanged are exactly the same for all the traders at that moment.
But with money, this is true for all goods, but it's not true for money, right?
There, we have a separate purchasing power of money or a separate exchange ratio of goods against money.
Purchasing power of money or a separate exchange ratio of goods against money for each person.
This is because each person buys only a particular set of goods, not all goods in the economy.
So this is another difference that's important theoretically between money prices and barter prices.
And then the third thing he points out is that the actual price structure that would exist,
The actual exchange ratios that would exist in a monetary economy are entirely different
from what prices would emerge in a barter economy.
This is because the preference ranks upon which these exchange ratios are based in a
monetary economy is a comparison between the marginal utility of the goods and the marginal
utility of the medium of exchange.
And that set of preference ranks will be entirely different than barter exchange ratios that
emerge from preference ranks that have, you know, apples against gallons of gas or gallons
of gas against plates of spaghetti and so on.
So we get an entirely different array of prices in a monetary economy.
We can't think that.
It's simply the same as explaining that there's an array of barter prices and then we can
simply choose a numeraire and calculate arbitrarily what these prices are.
Now this leads into the next step which is if it's true as he claims that in order to have a real theory,
a realistic causal theory of money prices, we have to be able to place or perceive the buyers as placing goods
is against money on their preference ranks,
then we have to have a marginal utility theory of money.
Because we have to have a unitary or integrated preference rank.
We have to be able to say, in other words, that this bag of apples
is worth more or less to me than $5.
But if $5 is a general medium of exchange,
we have to value it then according to its marginal utility.
We have to place it on the preference rank in this fashion.
And so this is what leads him then to the development
This is why, by the way, he, contrary to previous authors in this tradition, by Rothbard, puts the regression theorem, the money regression theorem in this chapter.
It's not in the macro chapter, it's not in the chapter on money, right? It's in the chapter on money prices. Why?
Because you can't have a theory of money prices, a marginal utility theory of money prices, until you've talked about the marginal utility of money.
Interestingly, by the way, also in the money chapter, Rothbard gives us his full, complete
theory of the prices of goods.
It isn't until the money chapter, chapter 11, that we get the full definitive answer
to what are the causal factors behind the prices for all goods.
This, again, is very unusual, right, it's not the mainstream approach at all.
Now let me just point out again how this distinction exists between the mainstream approach.
And so here is just the standard indifference curve, right?
Difference curve approach to this question of how do we treat the utility?
How do we deal with the question of marginal utility or the utility of goods?
And it's precisely because there's no marginal utility theory of money that the mainstream
approach and consumer choice theory bifurcates these elements of the decision, right?
So the goods are treated in a utility fashion.
Now we have utility function, right?
We generate the indifference curves, so we get U1 is the level of utility that we would
enjoy from the different combinations on that indifference curve.
But money is not valued.
Money never enters into the utility function, right?
Money is just an element of the budget constraint.
So we have a given amount of income, that's the I-1, the straight line, the budget constraint.
I did different prices for X and Y to give us the slope of that line.
And this point A is selected by the rational consumer, not because it gives greater utility
than B or greater utility than C, right?
The utility of all those points is exactly the same.
And A is selected because for a given utility that we get at A, the same utility we could
get at B or C, we spend less money.
It almost seems as if the idea of money is just that it has some sort of objective value.
I have $100, that must be worth more than if I have $50.
If I spend $100 to get combination A, that's better than spending $120 if I get combination
B.
Right? But money never falls under the utility calculus of the system.
In fact, if you established a preference rank for the different combinations,
it's, you know, behind the utility function,
but it looks something like what I wrote on the side there.
So the combination of X and Y, 2, 3, that's the combination at A,
would have the exact same preference rank as the combination 4, 2, right?
They would be at the same rank level.
And then combinations like 2-2 or 1-2 would have less utility because they have fewer units of x and y.
And so again, as we'll see in a minute, the Rothbardian approach to this, of course,
is just to simply put units of the good against units of money on the same preference rank.
It's an integrated approach that requires us to apply directly marginal utility theory to money.
Okay, so let's go on to that.
Let me just put this out directly from the book.
So this is Rothbard's example where he has the buyer,
where he has grains of gold against pounds of butter.
The convention for Rothbard is things that the person doesn't possess are in parenthesis.
So this person has a certain stock of money, but doesn't possess any butter.
We get the principle of diminishing marginal utility for the butter, right?
So the first pound of butter is ranked above the second pound, above the third, and so
on and so forth.
And then we'll explain, Rothbard explains why there's marginal utility theory of money
later in the chapter, so we'll follow his lead here.
But here, let's just suppose that there is, in fact, a marginal utility that we can apply
to money.
Then the argument would be, well, okay, so there's then a value that we place upon the
seven grains of gold, right?
There's a marginal utility that the person places upon this for the usefulness of that
sum of money.
And then it must follow also, then, that diminishing marginal utility would exist for money.
So that as a person moves down this preference rank, since he's expending money, the marginal
utility of the rest of his money, the money he retains is rising, while the marginal utility
of the good is going down, right?
So he's acquiring more of the good, marginal utility is falling.
He's using more money to do this, so his money stock is declining and the marginal utility
of money is rising.
And so from this then we get the law of demand.
So he goes on to the next section, right, where he constructs the demand, the demand
curve from the, or demand schedule, from that preference rank, right?
So here's, you know, his, this is how his argument runs, and it's completely integrated
with the money and the good together, and then he gives us more, he goes to the market
by simply adding up the quantity demanded at each price from all the different buyers.
Somebody asked a question about this, pointing out that it wasn't Rothbard saying that,
or isn't he contradicting his idea of subjective value by saying that he's adding up these demands.
But what he's adding up are just the quantity demanded at each price.
So it's a hypothetical price.
adding up the amounts of the good that each person would buy given their preference rank.
He's not trying to add up utilities or preference ranks themselves.
Okay, then he gets to the aggregation of this, right, to supply and demand,
and Professor Salerno has gone over this, so we won't go back again and talk about demand and supply.
But we want to pause for this section where he makes the application to the seller.
So he says the same considerations exist.
On the left-hand side with seller X, we have a person who has a use value for butter.
So this person owns butter, and then it's money that's in parenthesis, the person doesn't
have money.
And we see the laws of diminishing marginal utility, again, applied or integrated for
the good and money, lead to the law of supply, right?
So it's exactly the same argument.
Simply the seller has the units of the good, desires money, so as he sells, his stock of
the good goes down, so the marginal utility rises, and his stock of money is rising, so
the marginal utility of money goes down.
These are reinforcing aspects that bring about the upward sloping supply curve.
And then he gives us this case on seller Y over here where he says it would also be possible
that we could have a case where a seller had no use value for the good.
What would happen then?
There was no marginal utility, no particular marginal utility in personal use for the good.
And he says there the person would simply set a reservation price, as he says, some minimal price that they would accept and it could be that they would offer their entire supply then at any price above that, right, whatever the price, so in this case it would be two grains of gold, right, two grains of gold were offered for a pound of butter, this person would offer, would sell all six pounds of butter, he would also sell all six at six grains and so on, so this is the vertical supply relationship that Rothbard
Rothbard points out is not uncommon again in the division of labor we have people who have previously produced goods that they have no use value for and then these are not durable goods but perishable and so they would be willing to offer the entire supply at above any minimal price okay and again we can just then aggregate these and we would get the overall the market demand
and the Market Supply.
Okay, now, the next thing he points out, again, this is going back to what Professor Salerno talked about,
is what condition then comes about and exists in the market
once the buyers and the sellers come together and begin to engage in exchange.
And so this is the equilibrium price, the market clearing price, the plain state of rest or the state of rest, as Rothbard puts it.
This is the point where the quantity demand and quantity supply are the same.
The argument he makes about why price hits this point is that, of course, this is the point where the greatest mutual satisfaction of people's preferences is achieved.
So, since that's the point of exchange, or the point of any action, naturally this is the point that is achieved in the market.
And he also makes this additional technical argument that this, at the point where demand and supply are the same,
the quantity of demand and quantity of supply are the same, this is also the point where total demand is equal to the total stock.
He uses that pedagogy later in the book, especially when he's working through the purchasing power of money.
But he introduces it here just to show that these are equivalent statements, right?
And the argument then is just contained here by definition.
So if we have the supply of the good as the total stock minus the reservation demand,
and total demand is just defined as exchange demand or regular demand plus reservation demand,
Then, where demand is equal to the stock, we just substitute S in for D, obtaining this equation, right?
The total demand is total stock minus the reservation demand plus reservation demand, so it's equal to the total stock.
And he provides a diagram of this, but the point is that he wants to be able to use these statements interchangeably,
so that we understand that they are just algebraically equivalent.
Okay, so as he points out, these markets clear.
The other major point that he makes here that we might elaborate on in the market clearing
is that he goes on to discuss in more detail what it means when he says that this is a state of rest.
So he gives this distinction, or illustrates this with a distinction saying that what happens in the market is that buyers and sellers come together with these reverse preferences as we discussed before, right, and they then exchange, and they exchange out to the point where no more exchanges are mutually beneficial, no more units can be exchanged that are mutually beneficial, they then at that point are at a state of rest. The market ceases in other words, or as he puts it, the opportunity for exchange is then exhausted at this point.
And he means this literally, right?
He means, in other words, that the exchanging stops between these two parties.
So you go into the grocery store and you want to buy bread.
So you see the price of bread is $2 a loaf and you buy two loaves of bread.
You walk out of the store, that's a state of rest.
There is no more mutually advantageous trade between the two of you.
And as Rothbard points out, what this means in practice, what this means in markets,
is that markets are, if they're ongoing, are constantly being regenerated
by the renewal of preferences or the changing of stocks of goods
that generate additional possibilities for mutual benefit.
But there are obviously some markets where this wouldn't happen.
The example he gives is Chippendale Chairs, right?
So Chippendale Chairs, right?
This market only occurs periodically.
So here we see the state of rest can extend for years,
and a Chippendale Chair may not come onto the market.
It would only come onto the market when the conditions that underlie,
these preference conditions that underlie exchange change
in such a way as to create reverse preferences between the buyer and the seller.
So what he's saying again is that all markets are like that, even the markets that are regenerating
all the time, that seem to us to be continuous, or seem to observers to be continuous, are
actually just regenerating states of rest, right?
Other buyers coming into the store and buying things and then leaving and others coming
in after them and leaving and so on.
Okay, so this is also again an important distinction between the Rothbardian approach and the mainstream.
In other words, Rothbard is saying that this theory is designed to explain these prices,
these prices that actually exist for goods that are actually realized in exchanges, not
hypothetical prices, not barter prices, not long run prices and so on.
Okay, now let's get to the marginal utility of money and the regression theorem.
So Rothbard says, okay, we want to apply the marginal utility theory to money.
This is quite straightforward.
Money is a good.
It's divisible into equally serviceable units, so it satisfies this condition, right, our
condition of applying the theory of diminishing marginal utility.
And he says these different units of the good will be, just like for any good, will be self-selected
by the actor.
So the person, in other words, chooses, say, the amount of the good that's suitable as a means to the end,
a bag of apples for a week's worth of consumption, or a loaf of bread for two weeks worth of consumption, whatever it might be.
The same with money. So this is a unit selected by the actor, $10 or $100, whatever the unit of money is.
Then it's possible obviously for the actor to allocate this unit of money or sequential units of money to different ends.
So equally serviceable units, remember, are units of a good that interchangeably satisfy a single end.
So $100 could be used to buy a new jacket or something or maybe a new pair of shoes.
So the person acting with the money is able then to rank order these different uses for the units of money.
And he outlines in general what these uses are.
One general use would be to purchase consumer goods, right?
So we could rank order the units of money in terms of the value of the consumer goods that we purchase with these units.
Or to buy producer goods, and again the same sort of thing, right?
There would be more important producer goods that we would purchase first with the first
unit of money and then lesser important ones that we would purchase next with the second
unit of money and so on.
Or we could hold these units of money in our cash balances.
So again, he's integrating this with the macro analysis to come later.
And then he gets to the critical point, right?
The critical point being that there seems to be then a problem of logical circularity
in this argument.
And the problem is that with goods, when we talk about the marginal utility, we're able
to do so without reference to the price.
So it's possible that, conceivable, right, that a person can assess the marginal utility
of a bag of apples just by its usefulness.
He doesn't need to know the price in order to assess the usefulness or the utility or
The use value of the bag of apples, same with producer goods.
So an hour of labor, a hammer and so on can all be valued for their usefulness.
We do not need to know the price in order to assess the value of the thing.
But with money, this will not do, right?
With money, in order to assess its marginal utility, we in fact have to know its price.
We have to know what set of goods can a given amount of money purchase.
Otherwise, we can't rank order it against goods.
We would be at a loss to know how much money to hold or to value with respect to different goods.
This is precisely because money is the medium of exchange.
So, of course, the regression theorem is the solution to this problem.
This is, again, a purely logical problem that Rothbard is trying to solve.
Again, he's just following Mises in this demonstration.
There were a few comments about this, a few questions about the regression theorem in this respect.
One was, well, wouldn't the regression theorem require a certain restrictive assumption about expectations that people form?
Doesn't it require, say, rational expectations for the regression theorem to work?
And so then another comment was sort of the opposite of this.
It was like, wouldn't general expectations about the usefulness of the medium of exchange affect the regression theorem argument?
Let's say, for example, what if people came to expect that money would collapse?
There was impending hyperinflation.
Wouldn't that then lead them to give up the use of money?
and they wouldn't any longer than, you know, proceed along this logical path of saying,
I think I need to know the value of a money in the past at a certain point in order to
say what I would pay, what marginal utility I'd place on money and what I would pay for
goods in the future.
But I think this, I think especially this latter point, it is true that people could
to formulate different expectations about future events with respect to money and that
they might have biases in this respect.
They might under-appreciate the possibility of a collapse of the money because they haven't
lived through a hyperinflation or they think it's just a remote possibility based on their
own experience or something.
But I don't think that really has anything to do with the logic of the regression theorem.
All the regression theorem wishes to establish is the necessity of some historical set of
prices for money, some historical purchasing power of money, in order to logically demonstrate
that there's a causal theory with respect to the marginal utility of money.
We can say, in other words, that the same considerations for goods, the use value of
the good and the idea of an equally serviceable unit are sufficient for explaining the price
of money or the utility that we place upon money.
So here all we need is just this argument that Mises gives us, which is it isn't this
alleged circularity can be broken out of by introducing time and simply pointing out that
It isn't that we need to know today's prices in order to set today's marginal utility
of money that we then use on our preference ranks, it's that we use the purchasing power
of money, the prices of goods in the recent past in order to formulate our marginal utility
of money today.
And so this then gets into the possibility of an infinite regress and as Rothbard points
The Regress actually ends on the last day of barter, the last day that the particular commodity that is money was used solely for its use value.
Remember again, the regression theorem then is just a, as is being used here, is just a theory of a logic itself, right?
It's just trying to explain how it's possible to have a causal argument with respect to the marginal utility of money.
Okay, now let's go on then to the summary that Rothbard gives at this.
He says that money prices of consumer goods, then we can summarize the argument up to this point,
are these actual prices of existing stocks of goods
that these prices exist in markets moment to moment
as they clear in these plain states of rest.
And let me again try to illustrate the distinctiveness of this argument.
We can do this by, you know, a couple diagrams.
So one on the left is a standard Marshallian kind of analysis, right, where we say that demand and supply,
we can integrate into the same time framework somehow by saying that demand is,
the consumer demand is somehow synchronous with production.
And so supply would be based upon production costs here and demand upon preferences.
And so here we don't have a completely subjective value theory.
We have this, you know, dual scissor, you know, the blades of the scissors theory.
But again, the problem with this is it completely ignores the actual way in which human action is existing in time, right?
It just assumes, in other words, there's some manner in which we can synchronously think of demand
and Production.
But as Rothbard points out throughout the book, the actual realistic view of time doesn't
permit this.
The production costs that exist for these units that are being produced exist in the
past when they're being demanded by the consumer.
And so there isn't any way to synchronize this, right?
Even if newly produced, even if you have something like ongoing demand and ongoing production,
We're not synchronizing these things in the same time, right?
Every good that's being produced today is being sold next week.
And it's that that needs to be kept in mind.
The goods that are being sold today that determine the price with demand were produced last week.
And as far as actors are concerned, those costs are sunk or not relevant for deciding
whether or not to sell.
Or to put it more simply, Rothbard separates correctly, places in time, the separate decisions
of production and sale.
These are not synchronous, they're separate in time.
And so we get the middle graph, right?
That would be one way to depict this from the Austrian viewpoint.
The demand by the consumers, the actual demand that they have, and then the opportunity cost
by the – as we pointed out, we didn't use that phrase, but as we argued before.
Another way to do this would be if we wanted to have a production diagram for supply, then
what we would have to do is place it on a diagram with anticipated demand, and it's
the demand that's anticipated by the entrepreneur that is, so to speak, synchronous with production
cost.
When the entrepreneur is incurring or deciding to incur the production cost, he can only
anticipate what that demand will be.
And so these two things could be synchronized, or again, in the middle graph, we could have price theory,
where we're determining actual prices, where those things are synchronized, but not the Marshallian analysis.
Okay, and then the last thing on price theory in the chapter that I wanted to mention is Rothbard deals with the two different cases of goods, of consumer goods.
Right up to this point, we've just been talking about the non-durable goods.
Perishable goods are technically, we might say, goods that have only one unit of service.
Or, alternatively, we're looking at just pricing of the unit of service of a good.
But Rothbard points out, they're also durable goods.
And durable goods are goods that contain within them multiple units of service.
And, in fact, we might even have two cases here.
There could be goods, although this would be maybe rare instances,
but there could be goods where the multiple units of service could, in fact, be consumed simultaneously.
Maybe not by one person, but by many people.
Okay, then the units of service would simply be priced according to demand and supply value scales, as we said before.
And then the entire good would be valued according to the summing up of those individual prices.
That's what would be paid in order to purchase this bundle.
But the more normal case is that the multiple units have a time structure to them.
They cannot, in fact, be consumed simultaneously, even if you have enough consumers to do this.
So, for example, an automobile can only be driven by one group of people at one time,
right?
And then next week, another group could drive it around and so on.
So all of the driving services that are provided for it, can't be consumed by a single group of people, no matter how large, all at once.
Refrigerators are like, most durable goods are like this.
So here Rothbard points out the one addition that we would have to make to our theory is to realize the effect of time preference.
So it is true that arbitrage would tend to equate the price of the bundle of service
with the sum of the prices of the individual services that make up the bundle, except for
time preferences.
Time preference then would require a discounting, right?
So the sum of the prices that go into the price of the durable good would be discounted
by time preference, and he gives some illustration of how this would be done.
Okay, then the last major topic that I'll just briefly mention is welfare economics.
At the end of the chapter, Rothbard points out that there are really two different senses
in which we can define a consumer good.
Consumer good could be defined praxeologically, like it is in the early chapters, as a good
A consumer good that provides its usefulness directly, it's directly serviceable.
He says, or it can be defined catallactically, which is what we're doing in this chapter.
A consumer good defined catallactically is the good that's sold to its final user, right?
So that we can call a consumer good for the purposes of price theory.
So here in the last section, he wants then to move from the catallactic definition to
the praxeological.
So he just, he says, well, what about the utility, the actual utility of consumption
of these goods that are being sold as consumer goods, whose prices we've determined in this
following way.
And let me just mention the following points that he makes.
First, and he's trying to distinguish again his view here from the sort of mainstream
view.
So he says, first of all, action, it is true that action brings about a higher ranked alternative
that in every action, in other words, we're proceeding to obtain something we value more
and setting aside something we value less.
And it is true that doing this eliminates the difference in value between the options
because of diminishing marginal utility, the options come closer together, right?
But they do not come into equality.
So we don't have something like equal value of bags of apples and money at the equilibrium.
It's also the case, it follows from that or it follows from what underlies that, that
also while we can get the greatest level of utility, so to speak, from exhausting exchange,
we don't do something like maximize utility in a functional sense.
So because we don't have a utility function that's operative here.
And then he points out that also in a functional sense, there would be a relationship between
Between total utility and marginal utility, marginal being the first derivative of the total is summing up the marginal, we get the total.
But as Rothbard points out, that isn't the case in his analysis with an ordinal approach to a utility.
Total utility is just the utility that the person places upon the set of units of the good.
And that utility is not related necessarily, at least, to the utility of each unit of the good in its own use value.
So it might be that, you know, six pounds of butter could be used for an entirely different use.
Let's say, greasing slides at the park for kids.
You know, that one pound, that each unit of the one pound of butter would not be put to.
and therefore might have a value entirely different, right, from the value of the sum, so to speak,
of the uses of the individual pounds of butter used one at a time.
Then he makes a remark about indifference and using questionnaires and so on
and how this differs from his own view, where he points out that indifference
Preference and answers people give to questionnaires are really psychological questions.
They address psychological matters.
Whereas the question of preference and indifference is really a praxeological, or at least Rothbard
defines these terms in a praxeological way.
And so they're not related to each other, right?
They're categorically different things.
So, Rothbard is simply saying that when we act, we have a preference,
because we have to choose, and choosing, if it's purposeful, is based upon a greater value, as opposed to a lesser.
And therefore, if we don't have a preference, let's call that indifferent, then there isn't any action that would proceed, right?
We wouldn't act with respect to this particular aspect of acting.
Okay, so this is what he means by it, right?
And what neoclassical economists mean by it is something else.
They're just using the same word to refer to a different thing.
Oh, and then the very last point he makes
is one that was made before
about money not permitting comparisons of utility.
This was mentioned in the consumer surplus discussion,
so I won't reiterate that.