Tutorial on Purchasing Power Parity

* with calculation from Big Mac article

Prices create a veil behind which the real goods and services are transacted. Prices themselves have no intrinsic meaning because they have to be considered in a relative context. That is, a price of $200 means one thing if your income is $2000 and another if it is $20,000. It is these relative prices that convey meaning about the value of things. When it comes to the international economy, there is a double veil. Not only are we concerned with the relative prices of goods and services within an economy, but we are also concerned with their relative value across countries divided by national currencies. To help us think about this, economists have conjured up a simple proposition called Purchasing Power Parity [PPP], which helps us to consider how we expect currencies to be valued one to the other.

Before we consider PPP, it helps to understand a little bit about how currencies are valued and their relationship to the balance of payments. Currencies, like all traded goods have prices. The price of a currency is its exchange rate. The British pound trades for about $1.49 cents, meaning that that American must spend $1.49 to purchase one pound. It also implies that .67 pence buys one dollar. In short there are two exchange rates: One that expresses cost of one dollar in terms of British pounds

and the other which expresses the cost of one pound in terms of American dollars

As in our tutorial on comparative advantage it is important not to mix the two exchange rates and to be clear which price we are using.

More important, however, is the question where this exchange rate comes from. Like all traded goods it is determined by supply and demand. The demand for a currency comes typically from foreigners who want to buy goods and services (Exports), or to lend and invest. The supply of a currency typically comes from locals who want to sell their currency in order to buy goods and services abroad (Import), or who want to borrow or repay investments. If we think about lend and investing as the trade in assets (bonds, stocks and physical capital), then these can also be thought of as exports. That is, if foreigners lend money, they are importing assets (an IOU), while the country receiving selling the IOU is exporting those IOUs.

Sales of goods and services are referred to as current account activities, while sales of IOU and physical capital are typically considered capital account activities. Putting these together we can construct the supply and demand for currencies.

Demand for a currency largely consists of

1. Exports to foreigners of Goods and Services (the Current Account)
2. Exports to foreigners of Assets like Bonds, Stock and Direct Ownership of Assets (the Capital Account)

Supply for a currency largely consists of

1. EXPORTS by citizens of Goods and Services (the Current Account)
2. EXPORTS by citizens of Assets like Bonds, Stock and Direct Ownership of Assets (the Capital Account)

Assuming that markets are allowed to function (i.e., exchange rate controls are not in place and the government of a nation is not manipulated the market through its own purchases and sales of its currency), then the exchange rate is determined through when the following relationship is determined.

This equation is called the balance of payments (not the balance of trade: that is simply exports of goods - imports of goods). If markets are allowed to operate than without controls then demand must = supply and it is the exchange rate the changes until this balance is achieved.

We are now in a position to consider what PPP means. If an economy had only one good, and if there were no barriers to trade (no tariffs, no transportation costs, nothing which made one market preferable to another), then we would expect exchange rates would adjust until there was no difference in the price of the good. The prices in local currencies would be different, but after conversion through the exchange rate an individual would find no financial reason to prefer the either the domestic or the foreign market. For example, if chocolate was the only good produced in the two countries, and if that chocolate could be costlessly shipped through a transporter like those in StarTrek, then chocolate should not be cheaper in one place than another. If Country A's currency was called ABUCK, and Country B's currency was called BBUCK we can see how their exchange rate would change. If chocolate sold in A for 5 ABUCKS, and in B for 10 BBUCKS, any exchange rate other than 1 ABUCKS per 2 BBUCKs would make chocolate more expensive in one country than another. At 2 BBUCKS per ABUCK citizens of B could exchange 10 BBUCKS for 5 ABUCKS, and would be able to buy exactly the same amount of chocolate. If the exchange rate were 3 BBUCKs per ABUCK, however, then when citizens of B exchanged 10 BBUCKS they would only get 3.33 ABUCKS and be worse off (the exchange rate have depreciated for citizens of B--it now takes 3 BBUCKs to buy an ABUCK where it formerly cost 2). So citizens of B would find that the price of chocolate in A now required them to exchange more than the 10 BBUCKs when the exchange rate was 2 for 1 (it now costs them 15 BBUCKS).

The consequence of this example is that the demand and supply for currencies in A and B would change with different prices for chocolate. When prices in one country are lower than prices in another after currency exchange rates are considered, then demand for chocolate in that country rises from the citizens of the other country. However, those citizens can not purchase chocolate without first purchasing the currency of the county. This would raise demand for that currency and increase its exchange rate until perfect purchasing power parity (PPP) was established.

The example given assumes that there is only one good and that there are no barriers to trade (see Short Economist link on Big Mac). When there are more one good, and particularly when there are barriers to trade, we will not expect perfect purchasing power parity. Still, if it were systematically possible to buy everything in one country at a rate cheaper than that found in another, then we would expect the exchange rate for that country to rise.

Some goods, like in person services, like those of baby-sitters or domestics, are difficult to trade across international barriers. Thus, when PPP motivates changes in exchange rate levels, we expect that it does so most fully for those goods that can be traded relatively costlessly. The prices of baby-sitters, however, may not converge much. Thus, the overall exchange rates can not achieve PPP for all goods. Though, in the case cited above, we might expect that in countries where service providers have higher wages, there will be incentives to migrate (see article on Electronic Reserve by Arlie Hochild on the Global Nanny Chain).

Clearly the PPP theory becomes more complicated as we add more goods and more barriers to trade, but we should consider one final wrinkle. As noted earlier, supply and demand for currencies reflect current (goods and services) and capital accounts (assets like bonds, stocks and land).

How did the the Economist Magazine decide whether Japan's currency was overvalued or undervalued.

First, they found the price of a Big Mac in Japan in terms of Yen. That was 294 Yen.

Second, they divided that by the exchange of Yen per Dollar. That was 124 Yen per dollar.

Third, from this they calculated the price of a Big Mac in Japan in terms of Dollars. This was $2.38.

Fourth they compared this to the price of a Big Mac in dollars in the United States. This was $2.54.

Thus the 2.38 price in Japan is 94% of the 2.54 price in the U.S.

So Japan's currency is undervalued by 6%.

To review

294Yen/124Yen per dollar=$2.38

2.38/2.54 = 94 %

So Japan's price after conversion to dollars is 94% of the U.S. dollar price.