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.