Gravity model of trade volumes - Page 3

Agemegos · 08-01-2006, 05:20 AM

In the otherwise good planetary design sequence in GURPS Space, there is a formula suggested for estimating the volume of trade (T) between any pair of planets with given economic outputs (V1 and V2), separated by a distance D. The formula is

T = k.V1.V2/D

where k is a constant set by the GM to reflect the specifics of his setting.

Anyone who attempts to map any reasonably large number of worlds and apply this formula pairwise is in for a nasty surprise. The amount that a given world trades with another world at distance D drops off with D^-1, but the number of worlds existing at about D rises with D^2. The result is that the total amount of trade that a given planet does at range D (so long as D is not larger than the radius of the settled part of space) is proportional to D. Ie. there will be more total trade at long ranges than at short. In any reasonably large setting k will have to be tiny to prevent all planets from having trade volumes far larger than their economies. And that will mean negligible trade volumes with neighbours.

The economists who use these models usually fix this problem by raising D to an exponent that is larger than the dimensionality of the space they are working in. When discussing transport economics on a world surface, for instance, they square D, producing a formula that shows you exactly why the term 'gravity' model is appropriate:

T = k.V1.V2/D-squared

To achieve the same fix in three-diensional space you would need to use a higher exponent, such as

T = k.V1.V2/D-cubed.

If you wanted to prevent the integral from diverging as the trade space expands indefinitely, it would be necessary to use an even higher exponent.

I would like to add that this formula would work better if you were to replace D (in parsecs or whatever) with C (cost in $/ton). Because the cost of getting goods into orbit in the first place, or up into orbit and out into the jump zone, can produce significant effects. Taking this into account will save the system from producing absurdly high figures for interplanetary (as contrasted with interstellar) trade volumes.

I don't suggest going this far in designing a game setting, but I will just add that any transport economist worth his or her salt would use not C (the freight and loading cost) but G, the 'generalised cost', which would include import and export duties, the interest cost on the capital value of the cargo for the transit and loading time, and possibly wastage and depreciation costs on perishable cargoes.

As for economists who are worth more than their salt, I didn't use gravity models myself, as being too crude. You wouldn't want to use a full network flow analysis, but I would suggest that a logit model would produce better results than a gravity model in this case.

08-01-2006, 05:20 AM	#1
Agemegos Join Date: May 2005 Location: Oz	Gravity model of trade volumes In the otherwise good planetary design sequence in GURPS Space, there is a formula suggested for estimating the volume of trade (T) between any pair of planets with given economic outputs (V1 and V2), separated by a distance D. The formula is T = k.V1.V2/D where k is a constant set by the GM to reflect the specifics of his setting. Anyone who attempts to map any reasonably large number of worlds and apply this formula pairwise is in for a nasty surprise. The amount that a given world trades with another world at distance D drops off with D^-1, but the number of worlds existing at about D rises with D^2. The result is that the total amount of trade that a given planet does at range D (so long as D is not larger than the radius of the settled part of space) is proportional to D. Ie. there will be more total trade at long ranges than at short. In any reasonably large setting k will have to be tiny to prevent all planets from having trade volumes far larger than their economies. And that will mean negligible trade volumes with neighbours. The economists who use these models usually fix this problem by raising D to an exponent that is larger than the dimensionality of the space they are working in. When discussing transport economics on a world surface, for instance, they square D, producing a formula that shows you exactly why the term 'gravity' model is appropriate: T = k.V1.V2/D-squared To achieve the same fix in three-diensional space you would need to use a higher exponent, such as T = k.V1.V2/D-cubed. If you wanted to prevent the integral from diverging as the trade space expands indefinitely, it would be necessary to use an even higher exponent. I would like to add that this formula would work better if you were to replace D (in parsecs or whatever) with C (cost in $/ton). Because the cost of getting goods into orbit in the first place, or up into orbit and out into the jump zone, can produce significant effects. Taking this into account will save the system from producing absurdly high figures for interplanetary (as contrasted with interstellar) trade volumes. I don't suggest going this far in designing a game setting, but I will just add that any transport economist worth his or her salt would use not C (the freight and loading cost) but G, the 'generalised cost', which would include import and export duties, the interest cost on the capital value of the cargo for the transit and loading time, and possibly wastage and depreciation costs on perishable cargoes. As for economists who are worth more than their salt, I didn't use gravity models myself, as being too crude. You wouldn't want to use a full network flow analysis, but I would suggest that a logit model would produce better results than a gravity model in this case. Last edited by Agemegos; 11-14-2007 at 01:35 AM.