The theory of PPP has been around as long as paper money. It is one of the oldest theories of exchange rate determination. Hence we present it first.
It was discussed in 16 th Century Spain, for example.
It was last resurrected by Gustav Cassel in the period between WWI and WWII. He used it in discussions of how much European countries would have to either change their exchange rates or their domestic price levels, given that WWI had changed the relative prices in the countries (causing different inflation rates in the countries).
“ In a competitive market, if two goods are identical, then they should sell for the same price.”
If the two goods were in the same place and both available to customers, then customers would always choose the cheaper of the two goods, forcing the sellers of the more expensive one to lower their price.
Carrying (storage) costs reduce the profits from speculation, and
Transportation costs reduce the profits from arbitrage.
Transactions costs are other costs associated with a transaction, over and above the cost of the good which actually changes hands. These also reduce the profits associated with arbitrage and speculation.
All three of these can result in deviations from the LOOP.
When we add the complication of (flexible) exchange rates, we have to restate the law of one price for international trade:
“ In a competitive market, similar goods in different countries should sell for the same price when the prices are stated in the same currency.” In effect, this means that we have to apply the exchange rate to translate the prices of the goods to a common currency. After doing so, the prices should be equal.
Thus if p d is the domestic price and p f is the foreign price of the same good, and e is the spot price of the foreign currency in the domestic currency, then p d = e p f and ep f / p d = 1 and e = p d / p f
“ The percentage change in the exchange rate between two currencies over any period equals the difference between the percentage changes in national price levels.” This amounts to: rate of appreciation of the foreign currency = π d – π f , which implies that an increase in the domestic inflation rate will raise the spot exchange rate proportionately.
Notice that interest parity is essentially an extension of relative PPP.
Interest is the price of borrowing, and interest parity arguments (covered interest parity and uncovered interest parity) argue that changes in these special prices will cause adjustments in the exchange rate.
A major difference between interest parity and PPP is that interest parity is related to financial assets whose prices adjust very quickly, and that have substantially lower transactions costs, transportation costs, etc.