The 3Ps theory describes the forces that determine exchange rates in the long run. It states that a unit of any given currency should be able to buy the save quantity of goods in all countries.

The 3Ps theory is abased on a principle called the Law of one price. This law asserts that a good must sell for the same price in all locations. Otherwise, there would be opportunities for profit left unexploited. The law operates in domestic market in as much as it operates in international markets.

Let us illustrate how.

Suppose, a dollar could buy more almonds in the USA than in India. In this situation, international traders could make profit by buying almonds in the USA and selling them in India. This export of almonds form the USA to India would push up the price of almonds in the USA and drive down their price in India. In the end, the law of one price tells us that a dollar must buy the same amount of almonds in all the country.

This logic leads us to the 3Ps theory. According to this theory, a currency must have the same purchasing power in all countries. Thus, a dollar must buy the same quantity of goods in the USA and India, and a rupee must buy the same quantity of goods in India and the USA.

Parity means equability, and purchasing power refers to the value of money. Purchasing power parity states that a unit of all currencies must have the same real value in every country.

The 3Ps theory implies that the nominal exchange rate between the currencies of the two countries depends on the price level in those countries. If a dollar buys the same quantity of goods in the USA (where prices are measured in dollars) as in India (where prices are measured in rupees), then the number of rupees per dollar must reflect the prices of goods in the USA and India. For example, if a pound of butter costs Rs. 100 in India and $ in the USA, then the nominal exchange rate must be Rs. 100 = $2, or $1 = Rs. 50. Otherwise, the purchasing power of the dollar would not be the same in the two countries.

Suppose that P is the price of a basket of goods in the USA (measured in dollars), P is the price of the basket in India (measures in rupees, and e is nominal exchange rate. (The number of rupees a dollar can buy). Now consider the quantity of goods a dollar can buy at home and aboard. At home, the price level is P, so the purchasing power of $1 at home is 1/P. Abroad, a dollar can be exchanged into e units of foreign currency, which in turn have the purchasing power e/P*. For the purchasing power of foreign currency, which in turn have the purchasing power of a dollar to be the same in the tow countries, it must be the case that

1/P = e/P*

With rearrangement, this equation becomes

Notice that the left-hand side of this equation is a constant, and the right-hand side is the real exchange rate. Thus, if the purchasing power of the dollar is always the same at home and abroad, then the real exchange rate-the relative price of domestic and foreign goods-cannot change.

To see the application of this analysis for the nominal exchange rate, were can rearrange the last equation to solve for the nominal exchange rate:

e = P*/P

That is, the nominal exchange rate equals the ratio of the foreign price level (measured in units of the foreign currency) to the domestic price level (measured in units of the domestic currency). According to the 3Ps theory, the nominal exchange rate between the currencies of two countries must reflect the different price levels in these countries.

A key implication of this theory is that the nominal exchange rate changes when price level changes. The price level in any country adjusts to bring the quantity of money supplied and the quantity of money demanded into balance. because the normal exchange rate depends the price levels, it also depends on the money supply and money demand in each country. When a central bank in any country increases the money supply and causes the price level to rise, it also causes that coutnry’s currency to deprecate relative to other currencies in the world. In other words, when the central bank prints large quantities of money, that money loses value both in terms of the goods and service it can buy and in terms of the amount of other currencies it can buy.

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