PROBLEM:
From http://mises.org/Community/blogs/donlloyd/archive/2009/02/20/the-world-s-hardest-austrian-economics-problem.aspx
THE WORLD'S HARDEST AUSTRIAN ECONOMICS PROBLEM
by Don Lloyd
For background :
http://mises.org/journals/aen/aen21_3_1.pdf
REISMAN: If you open up the hood of an automobile, you see a number of individual parts that disable the entire car if they are broken. There’s a fan belt, a carburetor, a starter, among many other items.There’s no way that you can derive the value of those items from the value of the car, because you would have to attribute the entire value of the car over and over again. When you go to the car-parts store to buy another fan belt, you only pay a tiny fraction of the utility that you derive from it. You pay $20, but it restores the entire value of a $20,000 car. In this case, the value of the car is not imputed back to a part that makes it run. You are only paying a price based on the cost of production of the belt. What determines the cost of production is the value of alternative marginal products elsewhere in the economy.
While the above is primarily concerned with factor pricing, the following problem concentrates on the value of a component to the buyer, which cannot exist without a valued assembly and a valued end for which the assembly serves as a means.
On a business trip, you have left your two year old car in the airport lot. When you return you find a note on the car that indicates that the fan belt has been auto-parts-napped and is being held for ransom.
On your personal subjective value scale, the end that the car serves, auto-mobility, is presently ranked just above the sum of $20,000. For simplicity, assume that this remains true throughout this problem. (To illustrate one possibility, before you consulted the market two years ago, you ranked auto-mobility just above $30,000. However, the market caused you to rearrange your value scale, dropping the ranking nearly down to the $25,000 price of a suitable new car, one of which you purchased. Of course, this $25,000 is now a sunk cost and has no involvement with this problem. Today, used car equivalents to yours sell for as little as $20,000, fixing auto-mobility on your value scale. See note below.)
The initial problem is to describe in words how you would come up with a maximum dollar amount that you would be willing to pay in ransom for restoration of the fan belt and car function. Again for simplicity, assume that no fan belts are available, nor can any be fabricated, and thus the market cannot directly rearrange the ranking of a fan belt on your value scale.
The second problem is to repeat the first with an EFI (Electronic Fuel Injection) module substituted for the fan belt.
The third problem is to repeat the first with an EFI module being held for ransom along with the fan belt.
Note:
That is to say, opportunities for exchanging induce the individual to rearrange his scales of values. A person in whose scale of values the commodity 'a cask of wine' comes after the commodity 'a sack of oats' will reverse their order if he can exchange a cask of wine in the market for a commodity that he values more highly than a sack of oats. The position of commodities in the value-scales of individuals is no longer determined solely by their own subjective use-value, but also by the subjective use-value of the commodities that can be obtained in exchange for them, whenever the latter stand higher than the former in the estimation of the individual. Therefore, if he is to obtain the maximum utility from his resources, the individual must familiarize himself with all the prices in the market. -- Mises, The Theory of Money and Credit, page 48.
SOLUTION:
When the problem statement says :
On your personal subjective value scale, the end that the car serves, auto-mobility, is presently ranked just above the sum of $20,000.
What does it mean?
It means that you are willing to sacrifice as much as $20,000 in exchange for the services of the car. This could be because you simply prefer the services of the car to $20,000, or it could mean that you would prefer the services of the car to an even greater sum, but that the market has caused you to rearrange your value scale by making a car available for $20,000, leaving you no reason to pay more. The $20,000 sacrifice need not be limited to money, but can include assets that can be converted to money as well.
The key to solving this problem is realizing that the ransom to be paid is not the sole sacrifice to be made in restoring car service. In addition to paying a ransom for the fan belt, you need to throw the disabled vehicle into the pot as well. This implies an opportunity cost in that the disabled vehicle cannot be employed in a next best service, probably a sale to an auto salvage business. This implies that if you expect that you can get a total of $19,000 from a salvage sale, then your $20,000 sacrifice limit has only $1,000 remaining to pay in ransom for the fan belt.
Similarly, you may expect that a disabled vehicle without an EFI module may only yield $17,000 in a salvage sale, leaving $3,000 for a ransom payment for an EFI module. And finally, a disabled vehicle with neither fan belt nor EFI module may be expected to only yield $16,500 in salvage and a ransom payment of $3,500 at most for both the fan belt and the EFI module. Whether the estimates are accurate or not, they serve their purpose and will never be disproved if the ransom is paid and the car function is restored.
More generally, any bundle of parts, at least one of which is essential to function, can be analyzed the same way. You estimate the salvage yield of the disabled vehicle without the missing bundle of parts, and pay a ransom for the bundle, not to exceed the $20,000 total value minus the opportunity cost of not salvaging the disabled vehicle.
In an extreme case, you might retain the fan belt and have the rest of the vehicle to ransom. Wirhout the opportunity cost analysis, you might be left with paying the same $20,000 ransom for either the fan belt or everything else, depending on which you retain and what you need to ransom. Using the opportunity cost analysis, the fan belt will be associated with the much smaller number, whether it is the ransom or the opportunity cost., as would be expected.
end
Posted
Wed, Feb 25 2009 2:34 PM
by
Don Lloyd