[dorianb0620]

Hello,
I am reading Bohm Bawerk’s Capital and Interest: A Critical History of Economic Theory. I am on Book 6: The Exploitation Theory, and he is critically reviewing Rodbertus’s theory of value. So, Rodbertus believe that labor should get the full value of the product. Bohm Bawerk, for the sake of argument, allows this point. He states that he will assume that all goods are only produced by the cooperation of labor and free natural powers, and by capital goods that have themselves originated by the cooperation of labor and free natural powers.
He then tells us to imagine a steam engine that will have a value of 550 at the end of 5 years. The worker can only receive the total future value of the steam engine in the future, at the end of five years.
If the worker wants to be paid at the end of the first year, he will get paid the whole value, present value, of what he has created at the end of the first year. One might imagine that it will be a fifth of the product which is 110. This is incorrect though, because the value of 110 is a fifth part of the value of a completed steam engine. “But what the labourer has produced up till now is not the fifth part of an engine that is already completed, but only a fifth part of an engine that will not be completed till four years more have elapsed.”
He then goes on to state, “If this is so, that which has been made by our labourer in the first year, i.e. the fifth part of a steam engine which is to be completed four years later, has not the entire value of a fifth part of an already completed engine, but has a smaller value.”
I understand all of this. My issue arises when he introduces number figures to try to explain how much smaller. He mentions that if the usual rate of interest is 5 percent, then the product of the first year’s labor will, at the close of a year, be worth 100.
I don’t quite understand how he got the value of 100. Is it possible that you could explain to me exactly how he arrived at a value of 100 for the first year? He doesn’t explain, mathematically, how he arrives at 100, which is a smaller value than one fifth of the completed steam engine… Thank you.

[jmherbener]

He explains the division of payments a few pages after the quote you give. On page 268, he shows that if there are five workers each to be paid at the end of five years when the steam engine is sold for $5,500 and the rate of interest if 0.05, then the payments would be.

1st worker who waits four years to be paid: $1,200
2nd worker who waits three years to be paid: $1,150
3rd worker who waits two years to be paid: $1,100
4th worker who waits one year to be paid: $1,050
5th worker who gets paid immediately: $1,000

This division is necessary to make the total $5,500 with the rate of interest 0.05.

The present value of the 1st worker’s effort four years before completion of the steam engine is $1,000. That is $1,000(1.05)(1.05)(1.05)(1.05) = $1,215

The PV of the 2nd worker’s effort is $1,000(1.05)(1.05)1.05) = $1,157

For the 3rd worker $1,000(1.05)(1.05) = $1,102

The 4th $1,000(1.05) = $1050

The 5th $1,000

As B-B says, his figures do not compound the interest.

[dorianb0620]

Once again, I am grateful for your help. I love reading Bohm Bawerk! I see also that BB had to round the numbers in order to have a total of 5’500 and a rate of 5 percent interest at all stages due to competition… Thank you so much Professor Herbener!

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