One Piece

The law of one price (LOOP) states that in the absence of trade frictions (such as transport costs and tariffs), and under conditions of free competition and price flexibility (where no individual sellers or buyers have power to manipulate prices and prices can freely adjust), identical goods sold in different locations must sell for the same price when prices are expressed in a common currency. This law is derived from the assumption of the inevitable elimination of all arbitrage.additional citation(s) needed

The law of one price constitutes the basis of the theory of purchasing power parity, an assumption that in some circumstances (for example, as a long-run tendency) it would cost exactly the same number of, for example, US dollars to buy euros and then to use the proceeds to buy a market basket of goods as it would cost to use those dollars directly in purchasing the market basket of goods.additional citation(s) needed

The intuition behind the law of one price is based on the assumption that differences between prices are eliminated by market participants taking advantage of arbitrage opportunities.

Example in regular trade
Assume different prices for a single identical good in two locations, no transport costs, and no economic barriers between the two locations. Arbitrage by both buyers and sellers can then operate: buyers from the expensive area can buy in the cheap area, and sellers in the cheap area can sell in the expensive area.

Both these actions will drive up supply relative to demand in the expensive area and drive down supply relative to demand in the cheap area. This will force prices to decrease in the expensive area and increase in the cheap one.-priced location, while the lowered supply in the alternative location will drive up prices there.

Both scenarios result in a single, equal price per homogeneous good in all locations.additional citation(s) needed

For further discussion, see Rational pricing.

Example in formal financial markets
Commodities can be traded on financial markets, where there will be a single offer price (asking price), and bid price. Although there is a small spread between these two values the law of one price applies (to each).

No trader will sell the commodity at a lower price than the market maker’s bid-level or buy at a higher price than the market maker’s offer-level. In either case moving away from the prevailing price would either leave no takers, or be charity.

In the derivatives market the law applies to financial instruments which appear different, but which resolve to the same set of cash flows; see Rational pricing. Thus:

“A security must have a single price, no matter how that security is created. For example, if an option can be created using two different sets of underlying securities, then the total price for each would be the same or else an arbitrage opportunity would exist.”
A similar argument can be used by considering arrow securities as alluded to by Arrow and Debreu (1944).

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