This will probably be the most technical post I've ever written. I will need a lot of graphs and diagrams to explain things.
Unfortunately,
most of these will be graphs of supply and demand. I don't really like
using supply and demand arguments, especially in graphical form,
because I think that this form of argument is often used in place of
actually understanding the situation. It is easy to fool yourself both
of your understanding and of the certainty of a conclusion by drawing it
up in a technical-looking graph. I suppose this is because graphs can
convey the illusion of mathematical certainty and precision of thought,
even when it isn't necessarily present. In the case I will be
discussing -- the incidence of sales tax and the possibility of
attainment of a monopoly price -- I think that there has been some
confusion about what a graph actually shows, which I think has led a lot
of people into a conceptual error.
I will begin with a
basic layout of supply and demand schedules to show how subjective
valuation information can be used to construct graphs of supply and
demand. Then I will do something a bit unusual with them to make a
point about what I think are errors of analysis applied to the types of
graphs Rothbard uses in discussing monopoly and the incidence of
taxation.
***
In
the earlier chapters of Man, Economy and State, Rothbard describes how
supply and demand schedules can be used to create graphs of supply and
demand and determine market pricing behavior, which, for my purposes,
can be condensed into something like this--
Suppose
that 7 buyers and 7 sellers of a certain good meet at a marketplace, and
their individual subjective valuations for the item are as follows --
Each seller has one item for sale, and each buyer is interested in purchasing one item.
From
this information, it is easy to arrive at the available supply and
demand of the item. Supply can be determined by counting how many
sellers would be willing to sell their item at a given price or below.
Demand can be determined by counting how many buyers would be willing to
purchase the item at a given price or above. This gives the following
supply and demand schedules --
Here
one can see that under these conditions, 4 items will be sold -- at the
price-point where quantity supplied and demanded are equal -- and the
market price will be $3. Sellers 4,5,6 and 7 will sell to buyers 1,2,3
and 4. Graphing the two curves gives the following supply and demand
graph --
This
is, of course, rather crude. For most markets, there will be many more
than 7 buyers and sellers, and multiple items will be bought and sold,
etc. I will also neglect Rothbard's discussion about the discontinuity
of the graphs (basically, supply and demand cannot be continuous
mathematical functions because each valuation is discrete and
corresponds to an individual) because it isn't really relevant here.
This is just an illustration.
There are two far more
important reasons why this analysis does not directly apply to normal
markets. The first is that in this case, many of the sellers have some
considerable valuation of the item in question. Such a situation might
apply at a flea-market or garage sale, but most of the time, sellers
simply want to sell whatever they have produced because they have no use
for their inventory themselves and usually do not wish to store it. At
any given time, the supply curve will tend to be vertical or near
vertical at whatever quantity is presently being held, and the seller
will simply take what money he can get on the market for it. If he has
made a mistake and oversupplied his market, he will cut back production
going forward, but he can hardly withold existing product for long
because he has bills to pay and must put his capital back to work.
The
second big reason is that this analysis is kind of like playing poker
with the cards up. The whole game of poker consists in not knowing what
cards the other players have. Likewise, in a market, nobody is going to
reveal his own subjective valuation for others to see, so buyers and
sellers are operating in the dark. Each one is really operating on only
two data points -- his own valuation, and the price the item has
exchanged for in the past. Everyone knows the 'going price' for the
item in question, and what he himself is willing to pay (or be paid) for
it. Once the 'going price' on the market is established, buyers are
not going to offer much more, and sellers are not going to accept much
less, until such time as it is clear that conditions have changed.
In the extreme, a market as experienced by its participants might really 'look like' the following --
The market price is X, there is Y quantity available at this price, and that's that.
So,
in practice, supply and demand curves will be 'experienced' by buyers
and sellers in a very different fashion than he first graph would
suggest. This is important to understanding Rothbard's arguments. All
the graphs he uses to argue about monopoly and the effects of taxation
come with the important modifier of expressing the demand curve 'as it
is experienced by an individual producer.' In other words, he is not
drawing graphs of subjective valuation schedules, he is drawing graphs
of demand as experienced by firms competing for consumer spending.
Drawing
a horizontal line through the market price of the first graph reveals
an important concept that this way of viewing things will tend to
overlook --
The
effect of markets is to cause transactions to occur at a uniform price
regardless of the valuations of the individuals making the transaction.
All one can know is that the exchange took place because the two
parties valued the object differently, and therefore, the uniform rate
of exchange established by the market will in large part not reflect the
valuations of most of the buyers and sellers who engage in trading.
Only for marginal participants -- those with valuations very close to
the market price -- will the price reflect their actual valuations.
For
the others, there is a substantial 'consumer surplus' of value which
the trader enjoys because he has not had to pay anything close to his
own valuation of the good in order to acquire it. If the reader has
ever thought to himself, 'Wow! What a great deal!' he is giving
expression to this phenomenon. In fact, if one thinks about it, most
purchases really are of this type. It is what free-exchange is all
about, mutually beneficial transactions, and is one of the very great
things about markets. But as far as this discussion is concerned, the
existence -- indeed, the ubiquity -- of consumer surplus means that for
the vast majority of buyers,
a higher price of the good would not have dissuaded the buyer from making the purchase in and of itself.
What
keeps prices down -- and up, for that matter -- is the existence of
choice. It is because there were multiple sellers that the
high-valuation buyers did not have to pay their full subjective
valuations to receive the good. Likewise, it is because there were
multiple buyers that the sellers did not have to settle for a price
exactly equal to their own valuations. If there had been no choices of
whom to do business with, buyers and sellers would have been forced to
deal with only one other party, who could have named his price right up
to the highest or lowest valuation as it served his interests.
In
terms of demand curves, the existence of choice -- which is to say,
competition -- tends to flatten the curve as it moves beyond the market
price. Other sellers will accept the market price, so why should the
buyer offer more? Thus,
the demand curve as experienced by an individual producer will not reflect the actual valuations by consumers.
Each individual producer will experience a high elasticity of demand
above the market price. A higher price will meet with a drastic
reduction in quantity demanded, such that total revenue falls if there
is any attempt to raise prices. Each producer will also likely
experience a high elasticity of demand below the market price as well,
as buyers of his competitors goods switch to his good, though for the
purposes of this discussion this is mostly irrelevant since it will not
profit the producer to do so.
What will the demand
curve look like under these circumstances, and from this point of view?
It will probably be a little different for each product, but in
general, I should think there would be some sort of 'bend' near the
equilibrium price point. Above this point, buyers of the good will
change their preference to another competing good, and below this price
buyers of competing goods will migrate to this product. I would think
that these two processes would occur at different rates, since there
will generally exist at least some 'product loyalty' which will probably
differ in some degree from one product to the next. So, it is
impossible to say just exactly what the 'bend' will look like, and it
may not be noticeable at all in extreme cases of practically no loyalty
or an indistinguishable difference of loyalty. But in any event, in a
competitive market the curve will be relatively flat above the market
price, and at some quantity the market will reach 'saturation' -- i.e.
it won't go to infinite demand at zero price, simply because some price
exists for storage, transport, etc.
The point of all of this, though, is that the upper end of the curve is flat not because of demand schedules,
but because of competition. The market price is determined by the marginal buyers, and
in a sufficiently competitive market, almost all buyers become marginal from the point of view of individual producers.
Rothbard's
arguments about monopoly and the incidence of taxation turn on
elasticity of demand. He claims that prices cannot be raised so long as
the demand curve is inelastic above the market price, which is why 1) a
sales tax can never be 'passed forward' on to consumers, but only
backwards to the factors of production, and 2) a monopoly can never
succeed in raising prices without state intervention. The argument that
is often made is that if prices could be raised, the sellers would have
already raised them. Prices are already as high as they can possibly
be, so that a tax or a monopoly premium cannot be profitably added on.
Demand would fall too dramatically to make this strategy profitable. He
makes this argument in several other creative forms, but they amount to
the same thing.
Hopefully, it is immediately clear
from my discussion why these arguments do not hold, but just in case it
isn't, I will walk through some different scenarios for the resolution
of a new sales tax imposed on a product. Rothbard is correct that if
the demand curve is inelastic above the market price, then prices cannot
be raised. Where he is wrong is in assuming that the shape of the
demand curve will not change in response to the change of situation. By
making the arguments that he does, he assumes that the demand curve
takes the shape that it does purely as a result of demand schedules, and
ignores the effect of choice and competition -- which is to say, the
actions of producers -- in producing its 'apparent' shape. The concept
of consumer surplus is ignored.
Or maybe he just forgot about it since he had discussed it about a thousand pages earlier.
***
First,
I'll look at a free-market example of the market 'as experienced by an
individual producer.' I've drawn in a demand curve, the market price,
and cost curves. Rothbard uses a number of these graphs in his
discussion, however, I think they were a bit unrealistic. I made a
curved, highly elastic demand curve -- implying a highly competitive
market, being as generous to Rothbard as possible -- but a very
different set of cost curves. Rothbard's curves look like the nose of a
torpedo, which is silly.
Most
businesses have a number of fixed costs associated with overhead and
fixed capital and the like, and variable costs associated with the
production of each unit of a good. But on the whole, unit costs will
not usually increase much per unit at higher quantities. Most cost
increases at high quantities will be associated with 'saturation' of
fixed capital as production levels move beyond optimal capacity, which
will occur rather slowly. So, cost curves will tend to be broad (which I
think Rothbard noted at one point), except that they will rise faster
at lower quantities as costs of fixed capital are spread over fewer
units. The upper cost curve 'crosses' the demand curve somewhere near
optimal production levels, at least if the market is competitive and the
capitalists have done their homework. This is the equilibrium point.
There
is a second, dashed cost curve which represents the 'cost' due to
interest. This is important for understanding how the market will
'digest' the imposition of a new tax. Capitalists expect a return on
their capital. In a competitive market at equilibrium, this will be the
natural rate of interest, and will be the same for all forms of
capital. Any change in the rate of return -- for example, the emergence
of an enrepreneur's profit above the natural rate of interest, or a
market change which makes collecting even the natural rate impossible --
will cause behaviors to change such that this disparity is eliminated.
At equilibrium, there is no entrpreneurial profit, and every factor and
all capital receive the same rate of return (I am ignoring differences
in wages since human beings have no capitalization value and are not
'for sale').
The cost curve therefore incorporates
the interest due to capital, plus factor costs, and no entrepreneurial
profit. In this example, I will assume an interest rate of 5% and a
newly imposed tax of 7%, which I have added to the cost curve such that
it absorbs all of the interest due to capital and imposes a 2% loss on
top of the loss of interest --
This
assumes that factors have already been paid, and the capitalists are
stuck selling a perishable good at a loss due to the imposition of the
tax. Rothbard would argue that this is the case because, once the
product had been produced, the costs are out of the picture in the past
and the product must simply be sold for whatever it can fetch on the
market. Supply is what it is, demand is what it is, and the price will
therefore be what it will be under these circumstances and the
capitalists just have to live with it.
This assumes
that there is no possibility for the capitalists to 'hold out' for a
higher price, which may or may not be a valid assumption. As far as
this essay is concerned, it depends on how the rest of the argument
turns out. Since I have not finished the argument, I will pass over the
point for now, but only use it to set up the situation and examine the
elements which must be resolved.
In order to come back
to equilibrium, the natural rate of interest must either be restored or
this particular market niche must go into obsolescence. Supposing that
the market does not shut down, there are two possibilities -- either
factor prices must fall, or consumer prices must rise. These two
possibilities are pictured below --
The
capitalists may be forced to accept the loss upon the initial
imposition of the tax, but they absolutely will not bear it going
forward, at least not insofar as they are not owners of the factors and
are operating purely as capitalists. In practice, this is almost never
the case, as business owners usually do have a stake in the factors they
are using. This may take the form of extensive land holdings and the
like, or limited to nothing more than in managing the operation, which
is a form of labor.
But in general, in a free market
businesses purely as such do not bear the burden of such a tax over the
long run because they do not have to. If nothing else, they can always
redeploy their capital into another line of production.
So,
in which direction will the market resolve itself? According to
Rothbard, it is exclusively in such a direction that factors absorb the
tax. I think he is wrong, that the burden may be passed in either
direction depending on circumstances but is usually shared. I'll analyze
four scenarios to see how it plays out, which shall hopefully make my
point for me. In each case, I will broaden the base of the tax, and the
question that will have to be answered is 'can the price be raised?'
How this question is answered will determine who pays the tax. I will
use a very mundane good for my example -- dishsoap.
***
The
first scenario is easy. In this case, consider four or five major
producers of dishsoap, making practically indistinguishable products.
The tax is imposed on only one of the companies, say Company A. What
will happen?
Will Company A be able to raise its price
to cover the tax? That depends on whether or not consumers will switch
to an alternative producer. Rothbard asserts that only a consumer can
serve as judge to determine whether or not two products are 'different.'
To be sure, this is correct, and is one of the points of this
exercise. If there 'is' a difference, and consumers are 'willing' to
pay for it, such that the demand curve is inelastic, then the producer
may safely raise the price and the consumer will pay the tax.
But
by Rothbard's own argument (again, correct in this case), if this had
been the case, the producer would already have raised the price to
collect an above-market profit. But an above-market profit is excluded
by this scenario in that the market is at equilibrium and competitive
(do you see where I'm going with this?)! Thus, the argument cannot
apply. The price is what it is
precisely because of competition,
and if other producers do not have to pay the tax and are willing to
accept the natural rate of interest, which is the definition of
equilibrium, then the taxed firm cannot pass the tax on to the consumer.
From
the other side, however, the firm cannot pass the tax on to factors of
production, either. Total demand for dishsoap has not fallen (because
the price has not been raised) so demand for factors of production for
this good will not fall and the going rate for these factors will remain
the same. If Company A cannot afford to pay the going rate for factors
and still make a profit, other producers will simply bid away these
factors and increase their own production to collect the natural rate of
interest.
So, in this scenario, the taxed firm cannot
make a profit and is destroyed. Perhaps that is what is meant by 'the
power to tax is the power to destroy.' In any event, it illustrates why
a tax must of necessity be fairly broadly based, and why it is
impossible to single out and force 'corporations' to pay for things.
Either the corporations will pass the burden on to someone else as the
natural rate of interest reasserts itself, or they will cease to exist
altogether.
***
Now consider the case that the tax is imposed on
all of
the dishsoap companies. Now, none of them can make a profit at current
prices and still pay the going rate for factors. Where will the burden
fall?
Will the consumer pay a higher price if it is
raised? The consumer is no longer protected by the fact that there are
other firms willing to produce 'the same' good at existing prices. But
there are 'substitute' goods -- barsoap, handsoap, etc. Again, one is
confronted with the issue of whether or not the consumer considers these
goods to be 'different.'
The argument that the market
is 'still competitive' begins to look squishy -- which is the point I'm
trying to illustrate by broadening the application of the tax. Rothbard
chooses to take this very philosophical, detached point of view that
asks the reader to check his common sense at the door. Bar soap and
dishsoap are different. They may substitute for one another, or they
may not from any individual's point of view, but it is hard to argue
that there will continue to be the same competitive dynamic no matter
what is happening. What I am describing here is considered a different
form of competition by most people -- a substitute good vs. an identical
good -- but Rothbard wants to continue on as if there is no difference.
To his mind, there is always competition. He has a point, as I'll
show later, but I don't think it is the point he thinks it is. The
consequence is different from what he predicts.
These
kinds of taxes interfere with competition. Rothbard cannot continue to
argue that competition will continue to keep the demand curve inelastic
as competition is being whittled away. Since it is competition which
shaped the upper end of the demand curve, he cannot continue to assert
that inelasticity prevents price increases as the demand curve itself
changes.
But back to the concrete example. To the
degree that consumers prefer using dishsoap to making do with other
goods, the demand curve may shift upwards. Since there can be no other
firms producing dishsoap who can make the natural rate of interest at
existing prices, there is nothing to prevent the firms from raising the
price to some new equilibrium point, at which a non-marginal number of
consumers switch to using a non-taxed good. This will of course depend
on the degree to which consumers consider other goods interchangeable
with dishsoap.
In addition, factor prices may fall this
time. There are no untaxed dishsoap producers who can bid factors
away. There are, however, barsoap and other such manufacturers who
might do so, depending on whether or not these materials were
nonspecific to dishsoap and might be used for barsoap. To the degree
that consumers accept such products as substitutes, the dishsoap
manufacturers may be totally wiped out as in the last example.
But
to the degree that consumers do not accept substitute goods, and to the
degree that factors are specific to dishsoap, factor prices can be
pushed down. I think this is most likely in such a case. It is
probable that the tax will be borne by a combination of lower factor
prices and higher consumer prices, depending on just how everything
falls. But obviously, if this proves correct, it will not fall
completely on either, for the reasons I have given.
The demand schedule is not the same thing as the demand curve that individual businesses experience, so it cannot be argued that the demand curve is fixed.
Hopefully,
Rothbard's case is looking weak at this point, but I'll keep going just
to see how things play out. There are still good arguments in his
favor which will need better examples to come out.
***
In this example, I want to consider a tax that falls on all soaps and detergents. Now, are there any substitute goods?
Rothbard
would argue that there still are -- and to a degree, he is right! But
I'll save that for later. However, it should be clear that these
'substitutes' are going to be considerably less 'substitutey' and more
like completely different goods. Maybe one could get a dog to lick off
the dishes before rinsing. I don't want to think about washing...other
things...that way, but the message is clear -- it is very hard to argue
that in this circumstance the market is still so 'competitive' that the
demand curve doesn't change.
It is hard for me to
imagine that factor prices would absorb the entirety of the loss,
either. There is no longer any reasonable producer of 'soapy stuff' who
does not pay the tax and may still make the natural rate of interest at
present prices. The consumer surplus may take a beating, but I'm
willing to bet that most people would fork over 7% more for soap rather
than live without soap. They might cut back and conserve, but only
'marginal' buyers would balk altogether. And who 'wastes' much soap,
anyway?
Finally, consider a tax on all
goods, period. Now obviously, assuming the tax is effective and
avoidance is impossible, this precludes any sort of goods substitution
to avoid the tax. I'm not interested in that anymore; I want to look a
this case to discuss something for which I do not know the name, but
which I might call 'orthogonal competition.' Basically, all goods are
in competition for the consumer's dollar all of the time, regardless of
their function. Even if they're not in competition in the sense most
people think of, nevertheless, they do compete in the broadest sense of
bringing satisfaction to the consumer. Everything the consumer buys is
an attempt to acquire utility, so to the degree that all goods are
capable of supplying utility, they compete for the consumer's dollar.
This
brings out the last good defense of Rothbard, and is one of the key
insights, I think, of the Austrian school. I have used a form of this
argument before myself in wage markets. It does not make sense to me
that wages should show the large spread that they do if labor markets
are truly competitive. It doesn't matter that there are so many
positions for firemen and so many for teachers and so many for CEO's,
etc., and only so many people qualified for such positions.
Nevertheless, almost all people are either qualified or qualifiable for
at least a few different positions, such that every position has
multiple possible takers and every person has multiple possible
opportunities. Further, every large wage differential presents an
opportunity for entrepreneurs to devise a system of training and
application of capital to qualify a lower wage person to perform the
higher wage task. The labor market does not have to be perfectly
competitive to be effectively competitive.
This is
exactly the sort of argument Rothbard is using to defend the effective
elasticity of demand, basically no matter what. And to be sure, his
argument is partially correct, as I have shown. There is always a
degree of substitutability, and so there is always a degree of
elasticity above and beyond that provided by raw demand schedules. The
question is what does it get him in the real world, which is how I've
been arguing these examples.
I'm willing to accept that
there will always only be effective competition rather than perfect
competition in labor markets, so that a certain spread of wages on a
free market will always exist, but should probably not be enormous --
say, within an order of magnitude, or two, or so. That just makes sense
to me.
So, to return to the tax example. Suppose the tax is imposed
across the board. What happens to the price of dishsoap and, say gold,
at least according to me? Yes, I did choose these two deliberately.
To
understand this, one must look at the whole picture. Each good will
have an associated demand and cost curve. Again, the return to all
capital must come to the natural rate, so factor costs must either fall,
or prices rise, or a combination of the two, in each and every case.
What one must do is determine the changes in patterns of demand to
determine which way the axe will fall.
Clearly, the
gloves of competition are off, as there are no producers at all who may
make a profit at the natural rate and current prices, so demand curves
are free to change. Factor owners are going to resist falling prices
wherever they can, it is simply a question of where they may resist.
Unfortunately, the problem is complicated by the fact that the factor
owners are also consumers. So the changes in consumption will cause
changes in factor income...which will cause changes in consumption,
which will cause...
To a degree, this is a problem of
all economics, and all sorts of sciences -- fleas on fleas on fleas.
But if I may be allowed an approximation for the purposes of
illustration, I think the general idea will shake out.
Suppose
that, whether because of lower income, or higher prices, or merely
because government is now claiming a portion of the economic product,
that every consumer must give up a portion of consumption. What will
happen?
Consider the following list of consumers, and assume that they are representative of the population --
The
list of goods represents each person's ordinal preferences, from
highest to lowest priority. If every consumer gives up one good, which
goods will be given up, and what effect will this have? Yes, I chose a
skewed example; in the real world there would likely be a great deal
more variety and broader representations. But the point is to
illustrate that it is possible for exceptions to Rothbard's rules to
occur. Further, I doubt that many people would argue that basic
necessities like food are not going to systematically get higher
priority on most lists, and relatively non-essential items are likely to
systematically appear lower.
Obviously, every
consumer will give up consumption of his least preferred goods. In
order for 'orthogonal competition' to force the tax onto the factors of
production to the complete exclusion of consumer prices, it is necessary
that all goods experience a roughly similar drop in demand -- that all
varieties of goods be represented roughly proportionately at the bottom
of lists. If there are any goods which are roughly so represented or
overrepresented in the lower portion of these lists, then clearly prices
cannot be raised much on these goods and factor prices will be forced
downwards. But if there are goods which are generally high-priority
goods, so that proportionally fewer consumers will give these up, then
prices may rise on these goods, and factor prices will be relatively
more firm. The forces of production will shift resources away from the
marginal goods and towards the non-marginal goods.
To
be more concrete, in these lists, dishsoap is lowest priority on only
one list. So, total demand for dishsoap -- at whatever the fianl price
-- will only fall about 20%. To the extent that the factors of
production used for making dishsoap are non-specific, the fall in total
demand for these factors will be somewhat less than this -- perhaps a
great deal less, depending on their use in other markets. So, the fall
in demand for these factors will be marginal, and therefore the change
in price negligible. Therefore, the price of dishsoap must go up to
restore the natural rate of interest for dishsoap production, and it can
thanks to consumer surplus.
As for gold, it appears at
the bottom of several lists. Demand for gold will be hit very hard.
Prices cannot possibly rise in this market, and the factors of
production can expect to bear the brunt of the loss.
***
In
general, even though one can't predict exactly how things will fall
out, there will be some marginal goods for which factor prices will be
forced down, and others for which consumers will pay the tax. For most,
it will likely be a combination of the two.
So,
dishsoap really did compete with gold -- the problem for Rothbard is
that dishsoap won too handily! Its demand curve shifted upwards in
response to the imposed tax, while the curve for gold fell. Factors of
production will tend to move from mining into soap production going
forward. Rothbard's argument did work, partially, but it turned out
that orthogonal competition was not enough to ensure sufficient
elasicity in all cases. Rothbard's error was to assume that all goods
were equally marginal -- that their prices 'couldn't' be raised.
Elasticity can only be ensured when a large enough fraction of buyers
are effectively marginal, and this is only the case when markets are
sufficiently competitive. It is not a property intrinsic to demand
schedules, and such a claim flies in the face of the ubiquity of
consumer surplus.
Thank goodness it is wrong. I
would hate to think about life in a world where such an argument was
correct, and the benefit of every transaction hung on a knife's edge.
It
doesn't take a lot to see how this argument about taxation applies to
monopoly as well. The argument that a monopoly 'can't' raise prices
because they are already as high as they can be does not hold water.
This ignores the effects of competition in markets in shaping demand
curves and denies the existence of consumer surplus. Rothbard's
arguments about the difficulty of establishing and enforcing a monopoly
are still valid, though difficult is not the same as impossible.
But
when specifically asked about a lack of competition, 'elasticity of
demand' is the one answer he can't use. And I, for one, do not find it
persuasive in the slightest that since his oponents cannot sufficiently
define 'monopoly' to his satisfaction that monopolies can therefore not
be said to exist in a 'free market.'
I think they can, and do.
