“If A is in such a way more efficient than B that he needs for the production of 1 unit of the commodity p 3 hours compared with B’s 5, and for the production of 1 unit of q 2 hours compared with B’s 4, then both will gain if A confines himself to producing q and leaves B to produce p. If each of them gives 60 hours to producing p and 60 hours to producing q, the result of A’s labor is 20 p + 30 q; of B’s, 12 p +15 q; and for both together , 32 p + 45 q. If, however, A confines himself to producing q alone, he produces 60 q in 120 hours, while B, if he confines himself to producing p, produces in the same time 24 p. The result of their activities is then 24 p + 60 q, which, as p has for A a substitution ratio of 3/2 q and for B one of 5/4 q, signifies a larger output than 32 p + 45 q. Therefore it is manifest that the division of labor brings advantages to all who take part in it. Collaboration of the more talented, more able, and more industrious with the less talented, less able, and less industrious results in benefit for both. The gains derived from the division of labor are always mutual.”
I do not understand what the “substitution ratio[s]” refer to. Can some one explain that to me? Thanks.
A is slightly better than B at producing p. A is MUCH better than B at producing q.
Therefore, it’s better if A produces q and B produces p, and they trade, rather than A making all the p and q he needs himself, and B making all the p and q he needs himself.
Mises could have picked an example with round numbers.
The “substitution ratio” is the efficiency gain to A and B by trading. A benefits more than B from the trade, because he’s more skilled, but B also benefits.
In the present, the State imposes taxation costs on all economic activity, via the income tax. If income taxes were zero, then A and B would trade. With a 50% income taxation rate, A and B are better off not trading, because they pay income taxes whenever they trade.
In this specific instance, the quote is saying that A is 3/2 (or 1.5) times more efficient at producing q than at producing p, and B is 5/4 (or 1.25)times more efficient at producing p than at producing q. If this quote is from an economics one would hope that (it’s not Austrian) the author has already specified that all other prices are identical. For example: intermediate cost of materials are identical, p and q’s sellling prices are identical, demand for p and q are identical, etc. In the real world such an example never occurs. The author has created a make-believe world for the purpose of ‘proving’ that his belief that people should work in fields at which they are most effficient is true.
I have learned never to study maths written by economists. Economists never learn maths. Further, economists use math as examples of their theories. They clearly state this. They do not use maths to further develop their theories, and if they try they come up wrong. This exercies is undertaken for the purpose of making their study look ‘scientific’. All these economic maths examples presuppose many excluded variables stipulations.
No, most economists would say that you need math to enter the classroom, but once you’re there, it’s economics you need to know. IOW, maths is the language of economics. Now, you might have a point if you were saying that economics often too caught up on the style at the expense of the substance, but the notion that economists one day got together and said “hey, you know what? If we use more math we’ll be taken seriously” is absurd. Math is used in economics because of the unfortunate fact that two of founders of modern economics had their background in the natural sciences (Jevons and Walras).
As for your “economists never learn math”, I’m not really sure what you mean. Of course they do, go to any undergraduate economics classroom and you’ll see that they might do as many subjects in math as they will in economics. This is, of course, forgetting grad school. Now, what you might say is that economists should use more advanced math, which is a point Hayek made.
One final point, mainstream economists don’t all use math. No matter what you learn from Rothbard, plenty of them eschew the use of math for whatever purposes.