Purchasing Power Parity

Law of one price says that if two goods are identical, they must sell at the same price. This happens due to arbitrageurs. If prices differ arbitrage tries to close the gap. If transaction costs are small then the prices become identical, however, if transactions cost is significant then prices would differ (obviously). Transaction costs are all costs associated with a transaction over and above the cost of the item that actually changes hands. 

Purchasing Power Parity is based on the law of one price for an open economy. The only difference is the law of one price holds for each individual good but PPP comments on the general basket of good. It says that in long run exchange rates of countries should adjust such that the cost of an identical basket of good is the same across countries i.e. P = S.P*; where P is the price level in home country, P* is the price level in foreign country and S is the exchange rate of home currency to foreign currency.

The real exchange rate is the price of foreign basket relative to the domestic basket. Real exchange rate = nominal exchange rate * (Price of good X in the foreign market)/(Price of good X in the home market). Through this, we can know how much of 1 unit of the good in the foreign market be equivalent to in our home market. If PPP holds then the real exchange rate would be 1. If the real exchange rate is less than 1, then foreign goods are cheaper.

Another way of thinking PPP is relative PPP which says that the difference in inflation rates is equivalent to percentage difference in appreciation or depreciation of the exchange rate i.e. DP - DP* = DS; where P is the price level in home country, P* is the price level in a foreign country and S is the exchange rate.

For any two countries A & B, the market exchange rate tells you how many units of currency from country B you can buy with a unit currency A. PPP conversion factor takes relative prices in the two countries into account. The exchange rate does affect the prices of goods, but only of which are tradable. There are several non-tradable goods, whose prices do affect the price level of the country but their prices are determined by domestic dynamics. Due to this PPP and exchange rates differ.

Problems with PPP:

1. Contrary to the assumptions of the LOOP, transport costs and restrictions on trade do exist; costs can be so high that some goods and services are never traded internationally. The price of non tradables are determined by domestic demand and supply curves.

2. Firm might sell same product for different prices in different markets depending on the demand condition in different countries.

3. Different commodity basket in different countries