(1) Price does not scale with distance. It scales with supply and demand. If you bring coal from 100 miles away, and someone else brings coal from 25 miles away, i'm going to pay both of you the exact same amount for the coal/lb. The buyer doesn't care how far away it came from.
The price scale with distance. In this examples it scales backward to the source. If the price to haul coal is 10 every 25 miles and coal cost 50 at your city then the price at the city 25 miles away IS 40 and at the city 100 miles away IS 10.
Proof at the city 100 miles away: if the cost is 11 then the merchant will not even try to haul coal to your city so your example don't hold. if the price is 9 then there is some merchant that will start hauling coal until the price rise to 10,then it stop.
This prove that price scale with distance.
Um, what. No seriously, that made no sense.
Ok, lets imagine 3 cities in a line.
City A, imports coal
City B, 25 miles away from A and 75 miles from C, produces coal
City C, 100 miles away from A and 75 miles away from B, produces coal.
Let Cb be coal produced in B.
Let Cc be coal produced in C.
Let Px be the price of coal in city X.
B ships Cb to A. They receive price Pa for it.
C chips Cc to A. They receive price Pa for it.
C ships Cc to B. They receive Pb for it.
B sells Cb locally. They receive Pb for it.
What effects Px?
Demand for coal. If we assume A,B,C use coal for the same purpose, say, electrical power, then the demand for coal scales with population.
Supply of coal.
In B and C this is directly related to the rate at which coal is mined in each of them. It is also related to the coal produced at the other in some lesser way.
In A this is related to the coal produced at B and C, modified for how far away they are.
So the effect of distance is on perceived supply, not directly on price.
I'll permit Wikipedia to instruct you on how the Law of Supply and Demand works. Of course, as any student of economics knows, by supply we actually mean perceived supply, and by demand we actually mean perceived demand. Agents are not omniscient, after all.
Anyway, most relevantly, there is exactly one Pa. There is not a separate Pa for Cb and Cc. A treats Cc the same as Cb because its exactly the same to A. Now, this makes it vastly more profitable for B to ship coal to A than for C to do so, but it may still be profitable for C to ship coal to A.
Since P(Cb) = P(Cc), this disproves that distance has any direct effect on price.
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Neonivek:
What does the law of supply have to do with this?
That's a rather surprising claim you're making. I'd love documented proof that the cost of shipping exactly explains the difference between prices in Nunavut and the rest of Canada, especially since somehow the rest of Canada has a uniform price of $1 (according to you) despite variable shipping distances required.
I won't believe this claim until you prove it, it makes no sense.
(Internet seems to suggest trucking cost is ~$1.5/mile, a 48' truck can carry 20 pallets of soda, and there are 108 cases x 24 cans = 2592 cans/pallet. Or 51840 cans total)
Nunavut is 1104 miles from MN, where i know there is a soda cannery. There's probably a closer one. That's a low cost of $0.03/can to ship from MN to Nunavut.
I categorically reject your claim.
(Edit: of course the law of supply is involved. But the Law of Supply and Demand is the relevant one, and of course, supply that is farther away is not supply here and now, and so should be weighted less than supply here and now, hence, perceived as lower).