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Marginal utillity puzzle

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abskebabs posted on Sat, Nov 17 2012 1:33 PM

Here's a fun little puzzle to try if you believe you've properly understood marginal utillity.

 

Let's say there are 3 means/production goods A,B and C that could be used by the operator of a business. There are 3 ends a, b and c that are consumer goods that can be produced using these goods as specified below.

 

A is a non-specific means that can be used to make either good a or b.

B is a specific means that can be used to make a good b.

C is a non-specific good that can be used to make good a or c.

 

We can assume the that the required complementary factors required to make goods a-c are plentiful, specific and do not differ depending on which of means A-C they are combined with ( a generous assumption I know, but it helps one realise more easily the analytical answer that helps expose the true nature of marginal utillity).

 

The firm expects to be able to sell one of good a for £3, one of good b for £6 and one of good c for £1.

 

In the beginning the firm has one of means A and one of means C. A producer of B approaches the firm and offers to sell one of means B. If the firm owner is looking to maximise his profit, what would be the maximum reservation price he would be willing to offer for the factor B?

 

Enjoy! ;)

"When the King is far the people are happy."  Chinese proverb

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"Where there are problems there is life."

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£1?

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£1?

Not quite. More like 1 - epsilon :)

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Zlatko replied on Sat, Nov 17 2012 1:59 PM

abskebabs:

The firm expects to be able to sell one of good a for £3, one of good b for £6 and one of good c for £1.

Can they sell only one of each?

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Zlatko:

Can they sell only one of each?

Yes, in fact it is only possible for the firm to be able to sell one of each since they can onl possibly get their hands on one of each factor in this puzzle by construction, since they have one of A and one C and can get one of B from the seller. I made the puzzle this way for simplicity, once you allow for diminshing marginal revenue productivity other complications extraneous to what I wanted to expose with the above example result. We must learn to walk before we run I guess. :P

"When the King is far the people are happy."  Chinese proverb

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Can they sell only one of each?

Probably yes, otherwise the solution is trivial (and not related to marginal anything).

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Zlatko replied on Sat, Nov 17 2012 2:08 PM

Ooooh, alright, I seem to have jumped over this sentence:

abskebabs:
In the beginning the firm has one of means A and one of means C. 

and only read this one:

abskebabs:
Let's say there are 3 means/production goods A,B and C owned by the operator of a business. 

The way I read it initially it wasn't much of a puzzle at all :P In light of the new (to me) information I'll need more time to think about it.
 
 
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and only read this one:

abskebabs:
Let's say there are 3 means/production goods A,B and C owned by the operator of a business. 

The way I read it initially it wasn't much of a puzzle at all :P In light of the new (to me) information I'll need more time to think about it.
 
Ah, that's embarassing, sorry about that. No wonder there was confusion. I've modified that sentence now to remove the confusion.

"When the King is far the people are happy."  Chinese proverb

For Alexander Zinoviev and the free market there is a shared delight:

"Where there are problems there is life."

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£1?

Not quite. More like 1 - epsilon :)

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Interesting, you guys have exceeded my expectations. Or perhaps this puzzle really was pretty trivial. :P

 

Like with the Law of Costs, I think the above example shows how you can find distinctive results with the Austrian approach to this subject that can't be found using a Neoclassical approach.

 

Feel free to explain your answers. (Interestingly the same reservation value would have been realised for product b if it was being sold instead of factor B. This makes a nice connection between the value/price relations between substitue means and ends. Maybe I should have asked the question that way to make the puzzle slightly more challenging. :P

"When the King is far the people are happy."  Chinese proverb

For Alexander Zinoviev and the free market there is a shared delight:

"Where there are problems there is life."

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The problem with real life is - it is never certain.

And if there is even the slightest chance of, say, A breaking down before producing b, then the valuation of B will change. Dare to upgrade the puzzle? ;)

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The problem with real life is - it is never certain.

And if there is even the slightest chance of, say, A breaking down before producing b, then the valuation of B will change. Dare to upgrade the puzzle? ;)

Of course, the permutations are endless! It's funny, I'm beginning to think it might be a good idea to make a book of praxeological puzzles, that I think would be also a good way to teach the subject too. It might emulate what this author, an old professor of mine, achieved for mathematics

"When the King is far the people are happy."  Chinese proverb

For Alexander Zinoviev and the free market there is a shared delight:

"Where there are problems there is life."

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You should do that. A book of Austrian puzzles
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Of course, the permutations are endless!

It's not a permutation, it's a fundamentally different dimension. Jokes aside, I am not aware of any Austrian treatment of problems with even limited uncertainty (when the kinds of possible events and their probabilities are known). Maybe I should read something by the brother of LvM...

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I am not aware of any Austrian treatment of problems with even limited uncertainty (when the kinds of possible events and their probabilities are known). Maybe I should read something by the brother of LvM... Quote

 

Yes I'm not aware of any explicit treatments either. What I do find interesting with the above type of problem however, is that I was able to generalise a prior version I asked on this forum using a simple decision theoretic approach and this provides an intriguing connection since such approaches are also used to deal with stochastic or nonstochastic uncertainty in a non-probabillistic manner.

 

I guess very primitively, you could say if the probabillity of A breaking down in producing B is 0.5, and thus assign expected value to work out B's valuation, but doing so of course makes brave assumptions regarding the actor's risk preferences as is also well known in Neoclassical economics.

 

"When the King is far the people are happy."  Chinese proverb

For Alexander Zinoviev and the free market there is a shared delight:

"Where there are problems there is life."

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Can someone explain the answer to me?

The way I can explain it is that as is (without B), the producer could make product b with A and product a with C (these yield the highest revenue). Hence, the benefit of attaining B is to be able to produce b with it and free up A to make a and C to make c. Hence, the only benefit of an added B is one more c (due to the reallocation of production goods).

Is this correct?

If so, I don't think this is necessarily complete. We know how much revenue the firm receives, but not how much profit. If it receives negligible profit from both a and b, then the assignment of factors of production as described by me above would not happen. Instead, c would be getting produced by C and either a or b by A. Gaining B, at that point, would depend on the profit the firm makes off of a or b, of which we know nothing.

Furthermore, capital goods are a fixed cost, not a per-product cost. At least according to basic neoclassical theory, fixed costs do not matter in the long run - only marginal costs determine the quantity produced.

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