## Thursday, May 29, 2008

### The plow

Part I: The definition of the village
Part II: Value and cost
Part III: The plow

In our village, some genius invents the plow. The plow has the following characteristics:
• It takes 90 hours to make a plow
• If a family uses a plow, they can produce 1.1 pounds of food in 1 hour
• A plow will last for 9,000 hours of use (900-1,000 days or about 3 years)
It's fairly easy to calculate that the value of a plow is equivalent to the equilibrium value of 900 pounds of food (9,000 * (1.1 - 1.0)); the excess value of a plow is 810 pounds of food (900 - 90). A plow is thus a commodity, an object that has a cost, a value and, because it must be traded, a price.

Assuming that it's less efficient for each family to make its own plow (for reasons I'll describe later), both the Nash equilibrium and the Pareto optimum is for one family, Alice's family, to make plows and sell them to families for 99 pounds of food each. It's irrational for Alice to sell plows for less than 99 pounds; she could just make her own plow and then produce 99* pounds in the same time as it takes to make a second plow. If she tries to sell plows for more than 99 pounds, then Bob or Carol will realize its more rewarding to make plows than to grow food, and they'll undercut her price.

*The cost of making the first plow, amortized over its lifetime, is negligible.

In a free market — i.e. a market lacking both physical "gun-to-the-head" coercion as well as economic "work-for-me-or-starve" coercion — the price falls to the opportunity-adjusted cost, and the excess value is spread out pretty much equally across the community. In this case, the opportunity-adjusted cost (the value of that which Alice herself does not make) is a little different than I described earlier (the value of the thing that nobody makes) because in our village labor itself is not (yet) a commodity.

In the next post, I'll describe how bottlenecks affect the price of plows.

1. And is the first bottleneck a patent for the plow so no one else is allowed to make one? ;)

2. I will indeed examine that bottleneck, but much later. I want to first establish the character and effect of physical bottlenecks, so I have a context to examine socially constructed bottlenecks.

3. What about a skill bottleneck? Would that be physical?

I'm not talking about trained versus untrained, though that is certainly one aspect of it - and could be an explanation for it:

I'm talking about where Bob is so skilled (or so fast) that he can make a plow in only 50 hours time that is just as good as the 90 hour plow everyone else makes. Thus, his plow is worth 850, not 810, but then only when he makes them. Yet to everyone else, the value of the plow is the same as the plow that takes longer to make.

But then Bob could sell the plow for 55 pounds of food and since no one else has the skill to make a plow that fast, every other plow maker would go out of business because no one would buy one for 99 pounds of food and so no one would make one...

Or alternately, Bob could sell the plow for 98 pounds of food, and get the same result. So for Bob, he's coverted 50 hours of labor into 98 pounds of food.

Now, how did Bob get to be such a prodigy? Was he a plow-maker for 20 years in some other village? Was he just born with a talent for plow making? Did he just come up with some trick of the manufacturing process that makes it go faster that he then decided not to share with anyone?

I guess this gets into specialization and such and probably way more complicated than you want it to be right now, but it is fun to think about anyway.

Another possibility is if Bob takes 90 hours to make a plow, but if his plows are of such fine craftsmanship (a Plow+1?) that they can make 1.2 units of food in 1 hour. In that case, you can see where the value goes to the buyers as they then pay 99 for a regular plow or 108 for one of Bob's. So that really isn't all that interesting, that's the same example with a different number. But you could see how price for one affects the other.

4. DBB: Assume a plow takes ~180 hours to make (therefore one family cannot make all the plows for the village). Assume that Alice and Bob are the two most efficient plow makers in the village. Alice take 170 hours to make a plow, and Bob takes 180 hours. Charlie tries his hand at making plows, but it takes him 190 hours. However Charlie is also an inefficient farmer, so even with a plow, he can make only 1.05 pounds of food in an hour.

What is the price of the plow? The answer is left as an exercise to the readers.

5. The plow costs 199.5. That's the cheapest Charlie could make it to make it worth his while to make one. Bob could not make one for cheaper than 198 and Alice could not make one cheaper than 187, but if none of them can supply all the plows anyway, say each does 1/3 of the plows needed, then there's no reason for anyone to sell cheaper than Charlie's price. Sure, maybe they could get a plow for only 198 if they are as good as Bob, but we already know Alice and Bob are the two most efficient in the village, so likely no one will match that, and after seeing Charlie's attempts, perhaps they'll decide that it is better to quit while ahead...

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