[SPACE] World Trade

[Anthony]

Originally Posted by Agemegos

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.

No, you're talking about modeling demand. You also have to model supply.

[Agemegos]

Originally Posted by Anthony

No, you're talking about modeling demand. You also have to model supply.

I'm not sure what you are driving at here. If you are talking about aggregate supply then yes, but that means unpicking "economic volume". "Economic volume" tells is that supply is such and such, and the generalised cost of transport tells us about price differences. If you are talking about examining the idiosyncratic trade, for example the "outlier" trade volumes between Brazil and China, then yes, but that means a separate logit model for each tradeable commodity. In either case the results that GURPS Space produces will not support that level of analysis. What I'm suggesting is an improvement over gravity modelling, and I think it is an unambiguous improvement of gravity modelling even though it doesn't go all the way to general equilibrium.

[hal]

What I'm wondering is this:

If you have Population X, that has a production capacity of Y, what percentage of Y is used for domestic consumption, and should the Max production capacity Y be usable for Exports?

For example - let's use just 6 trade partners.

If World A is a relatively low pop world (pop 5) with a given Economic output of Y, if 10% of world A's production is the MAXIMUM it can afford to export without consequences to its own productivity and infrastructure - then no matter whether it works out to A trading 2% with each of five worlds, 1% with one world, 3% with another world, 1% with another world, .5% with a fourth world, and 2.5% with the last world - we're looking at combined totals of the five world trades with the one world - 10% of the one world's total economic output.

So, what goes into the trades that are going on? Well, suppose that you're manufacturing widgets that require you utilize 15% of your population. They in turn, COULD have been engaging in food production, but - because they are producing widgets that are being traded for foodstuffs, they're effectively STILL in food production. They're just not directly producing it.

If one man could produce 1.5 food units worth of product, and he needs 1 unit to stay alive, he's producing a surplus of .5 units of food to be used elsewhere. If on the other hand, one man can produce a widget, and he can get 3 units of food for his widget, after having to buy materials worth 1 food unit, then the breakdown looks like this:

3 food units less 1 food unit (man) less 1 food unit (cost of materials for widget) equals 1 food unit's worth of excess production. Now he's doubled his food production as it were, perhaps freeing up someone else's labor for something useful.

The problem is - infrastructure costs have to be paid regardless, or the infrastructure decays. You can't throw money at it. You have to throw money AND manpower at it.

In the end, no matter how we care to look at it, abstractions are necessary for use when describing things in the Traveller Universe or any 3D space universe or what have you. Both game universes are an attempt to describe what it is that player characters have to interact with. I just find it hard to believe that any given world can have more than a given percentage of its output, be exported to nearby trade partners before a hard limit is reached.

Long story short - when I saw the TRICO factory move out of Buffalo and into Mexico, my thought at that time was "If this continues with other jobs, Buffalo won't have enough people making sufficient money, to buy the things being produced in other countries (aka Mexico, China, etc). Sadly, this has turned out to be more prophetic than I knew. Buffalo, NY, once home to a swarming multitude of major businesses, is starting to look really scary. The rapid transit line built to make it easier to go down town, ended up killing Main Street Buffalo where seeing boarded up buildings is relatively common :(

So, yes, perhaps a world can have a HUGE economic output for export, and still end up having a poor population - simply because robots and robotic factories are producing things for consumption elsewhere. <shrug>

[Agemegos]

Originally Posted by hal

If you have Population X, that has a production capacity of Y, what percentage of Y is used for domestic consumption, and should the Max production capacity Y be usable for Exports?

A trade model based on discrete choice theory can give an answer for this question, as I pointed out in post #9.

[hal]

Originally Posted by Agemegos

A trade model based on discrete choice theory can give an answer for this question, as I pointed out in post #9.

But I need to have guidelines on how that works, how to model it, etc. As might be guessed, I'm not too happy with GURPS TRAVELLER FAR TRADER, and I started to look at the rules contained in both INTERSTELLAR WARS and in GURPS SPACE trying to find something that I think would work. Problem is - GURPS SPACE requires that the GM play with two variables until the GM gets a number he likes. INTERSTELLAR WARS on the other hand, is, while slightly different, very much similar to GURPS TRAVELLER FAR TRADER in various aspects.

So, I thought I'd put out the question to see what others think, what others have tried, etc. Anthony has pointed out that he's used his own house rules, but hasn't indicated what those house rules are. You've mentioned alternatives, but haven't mentioned what they are ;)

With luck, maybe someone will bring something up and I can go with it. At present, I'm starting to consider looking at WORLD TAMER'S HANDBOOK as well as POCKET EMPIRES to see if perhaps something can be found in there. At least with POCKET EMPIRES, there is a section on resources and whether or not any given world is a net importer or not. It also nicely explains why some cultures spend a lot of money on certain things while other cultures spend very little.

So, I'm searching for ideas that I can use to incorporate within my "Hal's Traveller Universe - making it unlike most GDW knockoffs. I'm tired of things not making sense, and will be detailing the fact that certain Ministries within the Imperium really do have TEETH. In the Third Imperium for Hal's universe, there are worlds that fall under one of three classifications:

Outposts: Worlds with populations that do not intend to stay for the duration. These are generally resource extraction communities (mining, lumber, etc) whose corporations or businesses pay a fee to the Third Imperium equal to about 1% of the material extracted. Other outposts for scientific reasons, are suggested that they register with the Ministry of Colonization, so that they can be added to the list for Scout ship visits from time to time to check in with the outpost inhabitants in the event that the outpost has any needs (aka, shipping of goods to or from the world). Colonies on the other hand, fall under certain rules and regulations that difference them from Member worlds. Member worlds in turn, are totally free from the ministry of Colonization's influence.

But, in the meantime, I'm struggling the "trade" rules to utilize for my campaign - and more and more, it seems as though I'm going to go with the Merchant Prince version of the rules unless I can somehow tweak the FAR TRADER rules sufficiently to make them usable. Even now, speculative trade rules are being tweaked in the hopes I can make it work - but more and more, I'm thinking "why reinvent the wheel?". I may even use the rules from GURPS STARSHIPS, because they seem a bit nicer overall, but for the fact, that I'm right back to square one where it comes to determining trade between worlds - hence this thread ;)

[ericthered]

Agemegos, couple of questions on the numbers:

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.

When you have a period you want us to multiply, right?

Are you sure you have the denominator right? as written when the denominator is positive increasing the cost of transport causes MORE trade to happen. And if its supposed to be negative... please explain.

[Agemegos]

Originally Posted by ericthered

When you have a period you want us to multiply, right?

Yes.

Are you sure you have the denominator right? as written when the denominator is positive increasing the cost of transport causes MORE trade to happen. And if its supposed to be negative... please explain.

Oops! Bad mistake. I have a minus sign completely out of place.

The basic form of a logistic function is

F = 1 / (1 + exp (-t))

Where t is a linear combination of explanatory variables giving the expected value of the option. Generalised cost ought to appear in t with an exponent of -1. And that gives

P(1, 2) = 1 / (1 + exp (k.G(1, 2) - l))

This probability applies to each item produced on world 1, so that the total amount produced on 1 and consumed at 2 is

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

Casting my mind back (it has been eighteen years since I used this stuff), it seems that the correct way to include the economic volume of the destination is not to multiply through by it, but to take into account its effect on the expected maximum value of an item at 2 (more people, richer people means more chance that the highest value anyone there places on an item exceeds a given value), so the population and mean income of 2 ought to appear in l. I'm going to have to look some stuff up, because I don't remember how to do this. I'll get back to you.

[ericthered]

linear combination of the explanators of the mean willingness-to-pay of tradeable goods on the destination world

I get most of these words: explanator is a new one, and pretty central to the sentence. Could you explain what it means? I understand that technical jargon is powerful, but could you dumb it down for those of us who only get mathematics?

I think you mean that you want a number to represent how "complementary" two worlds are: two industrial worlds could have a very low number (trading hammers for hammers is rather pointless), while an industrial world and an agricultural world could have a pretty good number. Unique luxury goods are another matter (I don't think its a constant). I don't know where this number goes though: my gut says it goes on the front of the whole thing, but If you could tell me where it goes I would be most pleased.

Answering the OP: build a spread sheet and play with the numbers until they look nice. With the right sheet, this is a matter of just typing away at two fields. If you're getting answers that say a world has 168% trade and you want the rest of the numbers, you likely have a cluster of very close worlds where your transportation model breaks down: you're calculating the trade between Manhaten, Long Island, Queens, Brooklyn, and you're getting weird numbers because transportation isn't the ruling factor at that scale.


Edit: Thanks for continuing to answer!

[Agemegos]

Okay, we treat each possible destination world as a nest of independent consumers, and making heroic assumptions about independence and unimodal distribution it has inclusive value equal to ln (population) * EV, where EV is the expected value of the item for a randomly-selected member of its population. That's a linear combination of explanatory variables including G with a negative coefficient, but it's no immediately obvious to me how GDP per head enters.

I think we might do best by assuming a zero balance of trade for each world, and that requires that each world's consumption of each world's production has to average over all worlds equal to the consuming world's share of total production, which brings us back to

T (1, 2) = V(1).V(2) / (1 + exp(k.G(1, 2) - l)) / sigma (T(1, i) over all i)

[Agemegos]

Originally Posted by ericthered

I get most of these words: explanator is a new one, and pretty central to the sentence. Could you explain what it means? I understand that technical jargon is powerful, but could you dumb it down for those of us who only get mathematics?

Sorry, it's just short for "explanatory variable".

What we are doing here is basically modelling the logarithm of the odds ratio for a choice, that is ln(p(choice)/p(not choice)) — which is ln (p(choice)/(1-p(choice)) — as a linear combination of continuous or binary variables that contribute to that choice. That turns out to be equivalent to assuming that the value of an option has an expected value V equal to the linear combination substituting the values of the explanatory variables plus a random component with a mean of zero and a bell-shaped distribution called "Extreme Value Type II". That distribution is not too different from normal, and has the attractive property that the maximum of a set of variables that has that distribution is itself a random variable with the same distribution and a mean that is easy to calculate from the means of the options.

I'm sorry: now that I think on it it was 1995 when I last used these techniques, and I just don't remember them as well as I thought I did. If you want to crack this I think you have to research either "nested multinomial logit" or "hierachical multinomial logit" together with "discrete choice" and maybe "destination". "Random utility model", maybe — that's a term that wells up from the depths of my memory.

I think you mean that you want a number to represent how "complementary" two worlds are: two industrial worlds could have a very low number (trading hammers for hammers is rather pointless), while an industrial world and an agricultural world could have a pretty good number.

Well, if I were estimating such a model from real-world data I would use variables or dummy variables to represent specialisation or degrees of specialisation in such things, then do a multinomial logit regression to estimate the appropriate co-efficients for them.

But working the other way, that is, building the trade model up from a random-utility discrete choice model I don't have an obvious way to find suitable variables. I could do it with input-output tables, but (a) we don't have input-output tables for ultra-tech industry, and (b) that would be superheroic over-kill.

All I meant in that case was using the data that we do have for various worlds: population, economic volume, average income, maybe tech level, as explanatory variables in the model. That is, finding an expression for the expected value that a person on planet i puts on a unit of output that is a function (ideally, a linear combination) of these variables. The more I think about it the more I convince myself that it comes down to an exchange-rate effect that we ought to ignore by dealing with nominal value throughout.

Unique luxury goods are another matter (I don't think its a constant). I don't know where this number goes though: my gut says it goes on the front of the whole thing, but If you could tell me where it goes I would be most pleased.

Well, I really wasn't planning to decompose the model by different types of goods. If you do that you start having to deal with economies adapting their mix of outputs, and that sucks you into general equilibrium modelling. What I'm doing is saying "Consider an item produced on world 1. What is the probability that it will be consumed on world 2? Now obviously the conditional value of that probability would vary from product type to product type. But if you grab an item at random you can use Bayes' Theorem to get an unconditional probability, and that's the one I'm talking about.

Obviously that probability is proportional to total consumption on world 2, and assuming neutral balance-of-trade that means it's proportional to production on world 2, GURPS not distinguishing between those. (They are both just Economic Volume.)

It's less obvious, but discrete choice theory and a bunch of simplifying assumptions suggest that it is a logistic function of generalised transport cost.

And then total exports from world 1 to world 2 is equal to the output of world 1 times the unconditional probability that an item produced on 1 will be consumed on 2. And there we have

T (1, 2) is proportional to V(1)*V(2) / (1 + exp(k*G(1, 2) - l)). Where the overall constant of proportionality is such that the numbers add up to 1 (everything produced is consumed (or invested) somewhere, in equilibrium. So you calculate V(i) / (1 + exp(k*G(1, i) - l)) for all i, add them up, and divide each result by the sum of the results to get the final probability. i = 1 is included with G(1, 1) = 0, and the proportion of output consumed at home drops without needing a special case.


I'm sorry not to be more helpful about deriving k and l, but I have simply forgotten, and just now my mind isn't working very well. I'd suggest building a little spreadsheet with cell references for k and l, and with G proportional to distance plus a load and launch cost, and then fiddling with k and l until the numbers look like fun.