One would be willing to offer a sum of money that is equal to the cost of gaining the benefits of the next best alternative. If the next best alternative is employing a taxi and the taxi trips totaled $10,000, then one would be willing to pay up to $10,000 in ransom.Likewise, if the taxi trips totaled $40,000 then one would still be willing to pay up to $40,000 in ransom. The retail value of the car is completely irrelevant. All that matters is the opportunity cost.

Note: one would also have to factor in non-monetary benefits and then attempt to attribute a dollar amount to those benefits. Since the question did not provide data for non-monetary benefits they were ignored in the answer. Non-monetary benefits might include: not having to wait for the taxi to arrive, enjoyment derived from driving ones self, status symbol of having a nice car, etc.

DL (in place reply) --

Megas,

Although most of what you say  is true, it is already accounted for in the personal value scale. The $35,000 in my illustration would be larger or smaller if the expected outlays for taxis were larger or smaller.

The retail prices matter because the market can cause you to rearrange your value scale. You wouldn't spend $35,000 for a car even if it could be justified if a car were available on the market for $20,000. Your actual actions must be consistent with your value scale, which must include non-monetary benefits when appropriate.

Thanks, Don

I would consider the alternatives of the auto-parts-napper. What is the fan-belt without car worth to him?

I'd bid $1 above that in order to create a win-win situation!

DL --

PC,  The problem will be that you don't know his value and have no way of guaranteeing that he will act accordingly. Even if you know that the fan belt has a value of  $x to him, he may still turn down x+1 or even 2x. Then you are much worse off with no fan belt.

Regards, Don

I'm not very academic, so I don't really want to make a fool out of myself, nor disrupt your discussion here.

But I'm wondering if there isn't a symmetry between his fan belt without car, and my car without fan belt? If it is argued that I should be prepared to pay $20,000 for the fan belt, then why wouldn't the other guy be prepared to pay me $20,000 for the rest of my car?

Is the question really:

"How do holders of complementary goods agree on a price?"

DL --

PC, 

With qualifications, I agree on the symmetry logic.

Regards, Don

Don,

I need some clarification. Is it understood that all parts of the car are unique to that car and all remaining parts hold no value to anyone other than the owner of that specific car? For example, my engine would be of no value to anyone else.

Thanks,

Geoff

DL --

Geoff, 

No, there is no implication of any such understanding.

Regards, Don

Assuming that paying the ransom for the part is the only way that I can can again engage in auto-mobility, then the maximum dollar amount that I'd be willing to pay in ransom for restoration of the fan belt and car function is the the opportunity cost I'd incur by having to forgo the use of the car, or 20,000, whichever is lower, and I won't know that until I start walking . . .   :)

Without my knowing his opportunity cost for not selling me back the part, I can assume that the minimum dollar amount he will accept will be at or about his opportunity cost for holding it.  I'll know what that is once I start bidding (starting at .01 cent and raising my bid till it's either accepted or we hit my threshold).

Where his opportunity cost for holding onto the part and my opportunity cost for choosing to walk interest is where the part will be handed over, if at all . . .

I typed that really fast, so it may not fully convey what I'm thinking . . .

but the crux of answering the problem lies in knowing what the opportunity cost for the thief (his next best use) is.

There's not much difference between a thief and an autoparts store, if the autoparts store has a monopoly on any one part.

DL --

DD,

Setting aside your first paragraph, I disagree with your concentration on the partsnapper.  That's a different problem where you are, in part, tryihng to get the better of the partsnapper. There could be such a problem, but my model would be that the partsnapper makes a one time ransom demand, and after solving this problem you know whether to accept or reject., depending on whether you are better or worse off.

Regards, Don

To come up with the maximum dollar amount for the fan belt, I'd try and determine how much the rest of my car either stripped to it's parts or minus the fan belt and sold would be worth. Then I would subtract that amount from the replacement cost for an equivalent car and whatever cost I attributed to finding that new car (maybe I like car shopping, maybe I hate it, maybe an equivalent car will be easy/quick to find and maybe it will be difficult).  I'd also consider my opportunity cost for going around selling all of these car parts or hiring a tow truck to take my car to a dealer and all of that jazz. Whichever number was lower (maybe the opportunity cost of going out and picking a new car makes that whole parts operation cost more expensive than it's worth) would be my price.

If they're both over $20k, as long as the opportunity cost - sale value of stripping the car apart or selling it isn't negative, I do that an start walking. If it is negative, I just start walking (maybe I buy a non-automotive form of transporation).

I feel like my answer is probably wrong because the 2 subsequent problems are then really easy (it just changes the amount of money I get selling the car). The hard part about this was holding to the constraint that there was no way to replace my fan belt or EFI otherwise.

DL --

Wes, Try simplifying your answer and give what would seem to be reasonable sounding dollar amounts for the three problems.

Regards, Don

He's just going to steal the fan belt again if you pay the ransom.  So better to just shoot him.

DL --

Brian,

Only if you leave your car in the airport lot again and tell him about it.

Regards, Don

There are so very many things fundamentally logically WRONG with this "question" that I'd rather would want to call it:

THE WORLDS *EASIEST* AUSTRIAN ECONOMICS PROBLEM!

To begin with, the THEFT of the fan belt violates the axioms of Austrian Economics.Anyone investing in his car would have assumed that his property rights in the same would be respected. So much so that he didn't even get an insurance against theft although he knew that his fan belt is irreplacably unique for his usage of his expensive car.

I'd think that anyone who assumes *all that* is simply a little bit, well, not so very fast in his head. But that's just what I'd think...

So the whole "problem" here is kind of logically identical to the "problem" of what Marxism would have been if Marx would have been Mises... Was either of them a good car mechanics?

PROBLEM: From mises.org/.../the-world-s-hardest-austrian

I suspect this is wrong, becuase it seems too obveous, but would it not be

Max price <  [marginal utility of transport] + [market price of car-fan belt]

assuming transaction costs are negligible. If you don't like this assumption, they nmake little difference.