How to calculate market equilibrium between multiple buyers and
sellers of the same product, with the only different factor being the
transport cost between individual buyers and sellers, the likely
difference in price for each origin seller to be shown as well

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Clarification of Question by philmyers-ga on 10 Jun 2004 07:49 PDT

An example of a scenario.

Ten sellers of Steel of the same grade. Ten buyers of Steel of the same grade.

The sellers only sell ex foundry, and the buyers only buy delivered to
their factory.

The sellers will only sell to middle-men, and the buyers only buy from middlemen.


The transport costs between each of the sellers to the buyers is
arranged by the middlemen who buy ex foundry from the sellers and sell
delivrered to the buyers factory.

All the transport costs are different.

If all the buyers buy on a delivered basis at the same price e.g. usd
xxx per ton, what is the calcualtion to achieve a clearing ex-foundry
price for each seller, relative to the buyers delivered price.

If there was only one seller the price ex foundry would be , buyers ex
- factory price (usdbxxx per ton) minus transport costs.

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Request for Question Clarification by hedgie-ga on 30 Jun 2004 01:08 PDT

In a realistic case, there would be issues of cost of setting up and operating
middleman's warehouses, capacity of producers etc.

If we  ignore those issues, the problem is solved by patitioning the map
into teritories surounding each producer, just based on the distance.

Each buyer gets all his supply from nearest suplier and  his cost is
production cost + transportation cost to the nearest producer.

There is an algorithm   which calculates such partitioning of a plane. 
Do you want description of that (and a computer program) as a solution?

Hi there Phil,

I understand you've waited a long time for an answer, and it is indeed
a very complicated question - both to understand the question itself,
and to solve it.  At a glance, most knowledgable economists will tell
you that it is highly unlikely that all buyers will purchase at the
same price.  However, since you included the presence of 'middlemen'
into the situation, I have solved the question.  Since this answer
section does not allow me to post formulas and calculations legibly, I
have posted the answer on the following page.

http://www.geocities.com/tox_ga/

I understand that the problem and answer is indeed very hard and
complicated and if you would like clarification on any part of the
answer, please feel free to request one and I will do my best to make
sure that you are completely satisfied.

Cheers,
tox-ga

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Request for Answer Clarification by philmyers-ga on 27 Sep 2006 09:59 PDT

Hi,

could you mail me the images or advise the current location.

Many thanks
Philip

It may be helpfull if you explain market equilibrium.   Neil

Market equilibrium would be a a clearing price and quantity for each
supplier - which will be based on the relative advantage aggregated
for all buyers ( who are assumed to all be buyers on a delivered basis
at the same time and price)

You mentioned that the buyers pay a fixed price delivered to their
door......is this true even though the transport costs from the
middlemen to the buyers would naturally be differnt (realistically,
not all buyers are located the same distance from the middlemen)?