I found a mistake in The Theory of Money and Credit. I couldn’t find any explanation of where it came from by searching here. The mistake occurs in the H.E. Batson 1934 translation. Specifically at the bottom of page 256 of the Liberty Fund 1981 edition. It also occurs in the middle of page 225 of this online version http://mises.org/books/tmc.pdf
I’ve vigorously made sure there were no logical or mathematical errors in the book as I’ve been reading it and this seems like quite an elementary mistake.
Mises supposes that every year the value of money decreases by 10% of what it was at the start. He correctly identifies that the value of money over time forms a geometric series with a ratio of .99. He then goes on to state that the value in year n is 100*.99^(n-1). That is actually the value of the money at the beginning of year n. The value of the money at the end of year end is 100*.99^n
Is this mises mistake, or is this a mistake in the translation or editing? His method of logical deduction is brilliant, and he seems to have a solid grasp on mathematics so its hard to beleive he could make such a simple mistake.
His theory of money in that book was circular, not to the point of devastating inaccuracy, but still more coherent than any theory up to that point. The erros in that book were held against him, and he has since never been fully exonerated. Fortunately in Human Action he provided a revised and flawless theory of money.
His monopoly theory was incomplete, and expanded upon by Rothbard. In addition, Hulsmann provided a more formal backing for the ABCT, which Mises did not.
Actually this is not a mistake. As you said Mises is defining that the value of money decreases by 10% from what it was at the BEGINNING of the year. And that is exactly what the formula finds. The value of the money at the beginning of the year or more specifically the value at the end of the year before.
For example:
Lets find the value of money at the end of 1899 using your equation 100*.99^n
so 100*.99^1899 = 5.14e^-7
Now let’s use Mises equation for the value of money at the beginning of 1900 (100*.99^(n-1):
I doubt the “considerable expenditure” of Mises’ optimal state, or even his time period, comes close to what contemporaries’ would think of as a “considerable expenditure”, so its not that shocking.
Well kefka888, he never mentioned starting with the year 0 A.D. as his first year. When doing time value calculatins, you begin at time t=0 representing present time. Time t=1 would then be the end of year one/ beginning of year two. I can’ see how time value calculations would have changed since Mises’ time.
He either mean to say the formula for the value at the beginning of year n was 100*.99^(n-1),used some kind of wacky old school time-value calculations that considered year 0 the first year rather than year one the first year, or he made a mistake.
Now I’m dissapointed that I’m going to begin finding a bunch of mistakes as I read.