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The conclusion that the purchasing power of a given money is the same in every location where the money can be exchanged for goods is a particular case of a general “law of one price.” If a good is divisible into homogeneous units, say troy ounces of pure gold, then each unit will sell for the same price in the same market at the same moment. If, to the contrary, gold was selling for $1,500 an ounce in London and $1,200 an ounce in New York today, then arbitragers could earn profit by buying in New York and selling in London. As they continued to do so the profit would shrink for additional arbitrage because they are increasing the demand in New York, driving the price up there, and increasing the supply in London, driving the price down there. The arbitrage will cease only when there is no additional profit to be earned, that is, when the prices in the two locations are the same, net of transaction costs.
Money is a nearly perfect example of the law of one price because every unit of money is homogeneous and the transaction costs of transferring money from one location to another is nearly zero. We can, therefore, infer that the purchasing power of a given money is the same in every location where it can be traded for goods.
It follows that if the price of a given good is higher in one location than another, then there must be a difference in the subjective value people place on the good in one location relative to the other.
Ludwig von Mises uses the following example to illustrate. The price of a room at a hotel on the top of a ski-resort mountain is higher than an equivalent room at a hotel at the bottom of the mountain. The purchasing power of money, however, is the same at the top and bottom of the mountain.
The price of goods is higher in Hawaii because the people who live there value living there more highly than living on the mainland. For that reason, they are willing to pay the costs for transportation to have the goods shipped to them.
Price inflation, however, does not refer to the prices of some goods being higher in one place and lower in another. It refers to changes in the purchasing power of money, that is, in the prices of goods rising all around both in places where they are higher and in places where they are lower. It is true that when the money supply is increased with a given money demand, the prices of some goods will increase more and the prices of other goods with increase less and the prices of some goods will increase sooner and the prices of other goods will increase later, however, price inflation refers to the circumstance that prices overall are higher. Think of the prices in an economy as a swarm of bees. Individual bees are constantly changing their positions relative to each other with some rising and others falling, whether the swarm is stationary, upward moving, or downward moving. Price inflation occurs when the swarm is moving up and price deflation when the swarm is moving down.