[michael.f.burian]

Dear all,

I am having some difficulties understanding the table at page 123 in MAS (Johnsons value scale). I would like to understand how this table might be translated into a value scale with specific ends instead of horses and fish. This table can then be used to understand each trade that Johnson makes in the example. But unfortunately the aggregates (barrels of fish) are messing things up for me. I know it’s silly, but what can I do, I’m stuck. So I’ve simplified the example a bit, and I wonder if someone can tell me whether I have reasoned correctly or not. And if not, where I have gone wrong. I would be most grateful.

Here’s my simplified value scale:

a third horse
4 barrels of fish
3 barrels of fish
a second horse
2 barrels of fish
a first horse
1 barrel of fish

Lets assume that his value scale, containing ends not means, looks like the following:

Horses (or rather: ends that Johnson can satisfy with horses):

1. A
2. B
3. C

Fish (or rather: ends that Johnson can satisfy with barrels of fish):

1. D
2. E
3. F
4. G
5. H
6. I

Given these ends, is it correct to “translate” the simplified value scale to the following one (which would reflect his actual prioritization of ends)?

1. A
2. D, E, F, G, H, I
3. D, E, F, G, H
4. B
5. D, E
6. C
7. D

[jmherbener]

Jackson’s translated value scale would be:

1. A – 3rd horse
2. D,E,F,G – 4 barrels of fish
3. D,E,F – 3 barrels of fish
4. B – 2nd horse
5. D,E – 2 barrels of fish
6. C – 1st horse
7. D – 1 barrel of fish

This value scale assumes that his horses come in equally-serviceable units and that his barrels of fish come in equally-serviceable units. Equally-serviceable units of a good mean that any one unit can satisfy any one end. So 4 barrels of fish allow Jackson to satisfy his four highest-valued ends (D,E,F,G).

[michael.f.burian]

Thanks for your reply Professor Herbener. Unfortunately I am still as confused as before! 😀 Wouldn’t your value scale suggest that the price of a horse drops as the transactions progress? The first horse was traded away for 2 barrels of fish, leaving Johnson with two horses and two barrels of fish. Now, according to the scale you’ve described, Johnson would trade away a second horse, which is worth more than the first (because of increasing MU) for less barrels of fish (I’m focusing on the 3 barrels option, ignoring the 4 barrels option), namely one barrel, ending up with one horse and 3 barrels (serving ends D, E and F). Doesn’t this go against the law of MU?

I must have misunderstood something very fundamental. So here’s how I interpret Rothbards example at page 123, using my scale:

The transactions are conducted (or rather: will be conducted if they take place) in order starting from the bottom. Johnson has 3 horses and no fish. Line 6 and 7: Is one barrel of fish worth more than the least important end that I can satisfy with a horse? No, it’s not. Line 5 and 6: However, I would prefer a situation where I can satisfy the two most important ends that fish can be put to than the least important end a horse can satisfy. I do the exchange and end up with a situation of 2 horses and 2 barrels of fish. Line 2, 3, and 4: Now, Johnson would require 3 or 4 extra barrels in exchange of his second horse. I use the term extra because he is already in the possession of 2 barrels from the first transaction. Exchanging a more valuable horse for more fish than he demanded in the first transaction is consistent with the law of MU since the second horse is now worth more that the first one. The end it can serve is more important: so Johnson will require a higher price in fish.

Now, in your example (using my reasoning) Johnson would trade himself into an inconsistent position. The end that the second horse can serve is more important than the end that the first horse to be traded away can serve. And the first two ends that fish can serve (D, E) are also worth more than the end that the first horse can serve. But according to my reasoning applied to your scale Johnson would be willing to trade a second horse for obtaining an end that is less important than D and E, namely F (ending up in D, E, F). This is confusing since D and E together must be worth more than F, and they are also worth less than the second horse (second horse > D, E > F). But according to my logic Johnson is willing to trade away a second horse for F – a second horse is worth more than D and E, but is traded for something that is less valuable than D and E. He is willing to trade away something more valuable for something less valuable.

I understand that I’ve made a total mess of this, but I can’t see where. Where do you think I’ve made an error? All help is much appreciated.

[jmherbener]

The value scale Rothbard uses on p. 123 of MES refers to a seller of horses. In other words, Johnson has four horses and no barrels of fish. Rothbard indicates this by putting what a person does not have in parenthesis. The first horse, then, for Johnson is the least-valuable use he has for a horse. The first horse sold is at the bottom of his value scale. His supply of horses at a price of 81 barrels of fish (in Rothbard’s chart) would be 1 and at a price of 88 barrels of fish would be 2 and so on.

Rothbard goes on to develop the value scale for a buyer, Smith, on p. 125. On this scale horses are in parenthesis and barrels of fish are not. The first horse is the most valued use to which Smith would put a horse. The first horse bought is at the top of the value scale. He’s willing to buy the first horse at a price of 100 barrels of fish and at a price of 94 barrels of fish he willing to buy 2 horses and so on.

In Rothbard’s example, fish is the analog to money in developing the demand for and supply of a good from preference ranks. It isn’t necessary to determine the preference rank use for units of money (barrels of fish). To the contrary, the second law of utility, that a person prefers a large stock of a good to a smaller stock, suffices for constructing the demand for horses and the supply of horses in terms of fish (or money).

[Author]

Posts