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What's the deal with Reswitching?

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TenTonHorse posted on Sat, Jan 8 2011 3:11 PM

The theory of "reswitching" is the economic equivalent of a French Art Film -  it's worshipped by a select few, but you don't understand it's appeal. Since the premise of this thread is me asking those with knowledge about reswitching, it's a pretty good assumption that these knowledgeable folk will already know about Sraffa, the Cambridge Captial Controversy, and all the rest, so I won't go into it's origins.

From Robert Murphy's daily article, "The Reswitching Question":

...reswitching refers to a situation in which one mode of production is profitable at a high rate of interest, then unprofitable at an intermediate rate, but then profitable again at a very low rate of interest.

He then gives an example from Paul Samuelson and lays out the implications:

Suppose there are only two techniques for producing one unit of a certain good. Technique A requires 0 units of labor input the first period, 7 units of input in the second period, and 0 units in the third period. After this time, one unit of output is produced. (We can interpret the last period, which requires no additional input, as waiting for the unfinished capital good to "ripen" into the output good.)

Technique B, on the other hand, requires 2 units of labor input in the first period, 0 units in the second period, and 6 units in the third period. After these are applied, one unit of output is produced.

Now the question is...which of these two techniques should be used? It depends on the interest rate. For a rate higher than 100 percent, technique A is more profitable. For interest rates between 50 and 100 percent, technique B is superior. But once the interest rate slips below 50 percent, once again technique A becomes more profitable.

...[The is because] the interest rolling over on the initial outlay for 2 units in technique B dwarfs other considerations. On the other hand, at very low rates of interest, the fact that B requires a total of 8 units of labor, versus the 7 required by the other process, makes it unprofitable again. Only for intermediate rates of interest is technique B more profitable.


Firstly, and at risk of sounding dumb, can someone explain why technique B is more advantageous at intermediate rates than the others? Unfortunately, this flies right over my layman head.

Now, in regards to "roundaboutness", I thought this referred to switching to more productive and/or advanced means of production. Even if technique A is superior at both high and low rates in comparison to technique B, isn't the point of the Austrians that more of the technique can be done at the lower rate than a higher rate, due to the increase ease at which capital can be acquired at lower interest rates (i.e. being able to build more factories that do technique A since large loans are cheaper), thereby causing more total output of the particular product in the economy than there would have been if credit was less easier to attain? I know it's largely due to my unadvanced knowledge, but I fail to see why reswitching impacts so heavily upon Austrian capital theory? Thanks.

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TenTonHorse:
He then gives an example from Paul Samuelson and lays out the implications:

Suppose there are only two techniques for producing one unit of a certain good. Technique A requires 0 units of labor input the first period, 7 units of input in the second period, and 0 units in the third period. After this time, one unit of output is produced. (We can interpret the last period, which requires no additional input, as waiting for the unfinished capital good to "ripen" into the output good.)

Technique B, on the other hand, requires 2 units of labor input in the first period, 0 units in the second period, and 6 units in the third period. After these are applied, one unit of output is produced.

Now the question is...which of these two techniques should be used? It depends on the interest rate. For a rate higher than 100 percent, technique A is more profitable. For interest rates between 50 and 100 percent, technique B is superior. But once the interest rate slips below 50 percent, once again technique A becomes more profitable.

...[The is because] the interest rolling over on the initial outlay for 2 units in technique B dwarfs other considerations. On the other hand, at very low rates of interest, the fact that B requires a total of 8 units of labor, versus the 7 required by the other process, makes it unprofitable again. Only for intermediate rates of interest is technique B more profitable.


Firstly, and at risk of sounding dumb, can someone explain why technique B is more advantageous at intermediate rates than the others? Unfortunately, this flies right over my layman head.

I illustrated this in an MS Excel spreadsheet for you. look in http://mises.org/Community/members/nirgrahamUK/files/Attached+Files/default.aspx

for illustration of...reswitching scenario.xls

Where there is no property there is no justice; a proposition as certain as any demonstration in Euclid

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That's the best explanation I could have hoped for. Thank you very much!
 

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