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Old 10-07-2013, 10:30 PM   #1
hal
 
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Default [SPACE] World Trade

Hello Folks,
I'm guessing that there are others who have utilized the world building rules from GURPS SPACE for 4e and that they've worked out some potential issues already...

Question: can a world with say, 18 trade partners within relatively easy reach of space travel, each taking up say, 9% of the world's Economic volume by trade, have a trade level that is 18 x 9% or 162% of the world's economic volume? Is Trade limited to having to be UNDER 100% of its Economic volume and that it can't have trade with more than a handful simply because the trade would reach levels that the world just can't sustain?
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Old 10-07-2013, 10:53 PM   #2
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Default Re: [SPACE] World Trade

Well in real life there are certainly places that exist primarily as convenient places for people from all over to come and trade with each other, so it's possible. But I generally assume that trade only happens between close-by partners to avoid the trade volume tending to infinity.
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Old 10-08-2013, 08:01 AM   #3
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Default Re: [SPACE] World Trade

make sure you are dividing the value by distance for each world, and then consider lowering the value of K.

And how big is this world compared to the others?
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Old 10-08-2013, 02:09 PM   #4
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Default Re: [SPACE] World Trade

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Originally Posted by ericthered View Post
make sure you are dividing the value by distance for each world
Divide by at least the cube of the distance to each world.

To get things really right, use a multinomial logit model with income and generalised transport cost as the explanators to divide each world's output between the possible consumers.
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Old 10-08-2013, 02:16 PM   #5
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Originally Posted by Agemegos View Post
Divide by at least the cube of the distance to each world.
Eh, I'm not sure that follows, though any power greater than 3 at least results in finite total trade. Dividing by the square is probably from Far Trader, which was generalizing models used for terrestrial trade and doesn't entirely work even there.
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Old 10-08-2013, 02:32 PM   #6
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Default Re: [SPACE] World Trade

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Originally Posted by Agemegos View Post
To get things really right, use a multinomial logit model with income and generalised transport cost as the explanators to divide each world's output between the possible consumers.
Wow. If ever there was a sentence to make me feel dumb...Could you elaborate on this a little bit, speaking in small words? Maybe supplying a formula with variable definitions in GURPS terms?
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Old 10-08-2013, 02:56 PM   #7
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Originally Posted by Anthony View Post
Eh, I'm not sure that follows, though any power greater than 3 at least results in finite total trade. Dividing by the square is probably from Far Trader, which was generalizing models used for terrestrial trade and doesn't entirely work even there.
That's right. The theoretically correct approach is to use a discrete-choice model. Probit is theoretically soundest, but it converges to the much more tractable logit as you add bins. I'd use a spreadsheet to set up a logit trade model for eighteen worlds because there are hundreds of calculations to do, but it isn't actually difficult mathematics.

The tails of the logistic function are asymptotic to exponential decays, so in a universe where transport costs are significant compared to the prices of goods, and trade volumes are correspondingly small it would probably be okay to use an exponential of the generalised cost of transport if a logistic function were too tough for you, but this will not allow you to treat the split between domestic consumption and export endogenously.


Yes, correct, you are right. Trade economists use gravity models in which the trade volume on a country pair is the product of their GDPs divided by the square of the transport costs between them, not logit models. And yes, I am a transport economist, not a trade economist. My explanation is as follows. (1) Discrete choice theory is not adequately covered in training economists. When I was doing this sort of stuff I had to go to marketing theory to get the mathematics I wanted, and I found that none of my colleagues were aware of the hedonic discrete choice or the theoretical connections between discrete choice and probit and logit models. The trade economists are probably mostly not aware of the possibility of using logit models (2) Gravity models of trade have no theoretical foundation, they are an empirical fit and not an especially good one; the data is thin, its range is narrow, and its disturbances (owing to cultural factors, historical trade relations, etc.) large enough that the statistics can pick the curvature as more than 1/x but can't distinguish the higher polynomial terms.

Take that with all the salt you like.
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Old 10-08-2013, 03:11 PM   #8
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Originally Posted by Agemegos View Post
That's right. The theoretically correct approach is to use a discrete-choice model.
Even there, I think you need a model for how price varies with place -- in extreme cases, if everything you want can be made locally for the same price it would be available in trade, there's no reason to ever trade, and if something is necessary, has only a single source, and has no adequate substitutes, you'll trade however far is necessary. A gravity trade model should come naturally out of certain models for the price and variance in price of goods.
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Old 10-08-2013, 03:51 PM   #9
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Default Re: [SPACE] World Trade

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Originally Posted by Jerander View Post
Wow. If ever there was a sentence to make me feel dumb
I'm sorry. You shouldn't feel dumb. It's not especially clever, just highly specialised knowledge. Unless you work in marketing research there's no particular reason that you ought to know about hedonic pricing, discrete choice, or logit models.

Quote:
Could you elaborate on this a little bit, speaking in small words?
If I had to use small words I would need to use a lot of them.

Quote:
Maybe supplying a formula with variable definitions in GURPS terms?
Well, the generalised cost of transport is the freight rate including launch to orbit, landing, and handling; plus the travel time times the interest rate times the value of the cargo; plus insurance and taxes. Trade volumes should depend on that rather than distance itself; distance is used in trade economics as a proxy for transport costs.

Following a whole bunch of assumptions about the values that different consumers place on different goods, it looks as though unless there are special demands for goods from particular places at particular places, the probability that a particular item produced at world 1 will end up being consumed on world 2 ought to be proportional to

P(1, 2) = V2 / (1 - exp (k.G(1, 2) + l)) space for format*

and therefore that the volume of exports from 1 to 2 ought to be proportional to

T(1, 2) = V1.V2/(1 - exp (k.G(1, 2) + l)

Where V1 is the economic volume of world 1, V2 is the economic volume of world 2, k and l are unknown constants, and G(a, b) is the generalised cost of transporting goods from producers on world a to consumers on world b.

This does apply to P(1, 1). So having settled on values of k and l you can sum all the T(1, b) and divide that into V1 and get the constant of proportionality for the equations above. That means that the model itself will tell you what proportion of world X's output is consumed locally and what proportion exported (which gravity models will not do).


Note:

* Since in equilibrium everything produced is consumed or invested somewhere, the sum of all the probabilities P(1, x) including x = 1 must be one.

Last edited by Agemegos; 10-08-2013 at 04:05 PM.
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Old 10-08-2013, 04:00 PM   #10
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Originally Posted by Anthony View Post
Even there, I think you need a model for how price varies with place
Price is an endogenous equilibrium variable, not an exogenous system determinant. What you need is a model of how willingness-to-pay varies from place to place. The simple logit model assumes that mean willingness-to-pay varies from place to place as a linear function of explanatory variables, and that either (1) individual willingness to pay is a distributed as an extreme value type two or (2) the number of consumers in each location is large (more than about thirty, practically); with a uniform standard deviation either way. If you want to assume that the disturbances are different in different locations, as would be expected where there is a wide range of income, for example, then you would get an hierarchial multinomial logit model.

It is possible that idiosyncratic demands (treated as part of the disturbance in this model) might by chance mimic the results of a gravity model. But the hierarchial multinomial logit does not converge to gravity.
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