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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

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

"Where there are problems there is life."

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Verified by abskebabs

£1?

"The limits of my language mean the limits of my world." ~ Ludwig Wittgenstein
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£1?

Not quite. More like 1 - epsilon :)

The Voluntaryist Reader - read, comment, post your own.
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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.

Hmmm, well the costs for A and C are necessarily sunk at the time of the decision and wouldn't factor into the decision unless they could produce other goods or can be sold to another producer for a higher price than the expected product price, neither of which were explicitly accounted for in this example (if they were, then yes the profit/loss decision to make the products producible with would have to balance the revenue from their sale against the highest of these opportunity costs).

 

The main point however is that the marginal revenue actually gained from buying B is £1 and hence it definitely would not be worth paying more than a £1 and likely would be less by an epsilon (£1-e) naturally affected by the interest rate(s) and rates of return from other possible avenues of investment. This would determine the profit margin required to make this better than other modes of investment for the capitalist. Whether a seller would actually be willing to sell B for less than a £1 is of course a fair question, and would depend on their production and trading possibillities, i.e. whether they have access to the requisite factory equipment or a trading partner who might conceivably bid say up to £6 for the factor B.

"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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