Price is the cost of carrying around the empty space in our baskets. It accumulates according to the container algebra, and is specified by compression between the savings and loan trees.
The proof is by construction. Supply never equals demand in optimum congestion, inventories vary within their bounds. If supply equals demand, then there is never any need for pricing. So pricing is the cost of varying inventories, and taking the complement we get pricing is the cost of carrying around unused inventory space.
I say we leave it at that until something comes up.