# The Real Exchange Rate

## The Real Exchange Rate

If you put 100 pounds in a bank, and earn 8% interest over the year (eight pounds interest), this is only the nominal rate of interest. What you really get - the real rate of interest - depends on the rate of inflation as well. If inflation was running at 5% over the year, then the real rate of interest was only 3% (8% − 5%). Your 100 pounds became 108 pounds, but goods and services costing 100 pounds a year ago now cost 105 pounds. In real terms you have only really made 3 pounds.

The nominal exchange rate between, say, the pound and the dollar is simply the amount of dollars you can buy for each pound as dictated by the price in the foreign exchange markets. To find the real exchange rate, we have to allow for relative inflation rates in the two countries, just as you do with interest rates, of growth, or spending, or incomes or anything where the price rises distort the picture.

In this case, the picture that is being distorted is the UK's competitiveness, in terms if trade, with other countries. If the trade weighted index for sterling fell by, say, 5% over a given year, this would make UK manufacturers' exports 5% cheaper in foreign countries. If sterling falls, UK manufacturers are happy! But if, over the same period of time, prices in the UK rose by 5%, the benefit in terms of the reduced value of the pound for UK manufacturers would be cancelled out by the higher domestic prices.

The real exchange rate tries to take relative changes in countries' inflation rates into account. Look at the formula below:

In this formula, the 'world' price level is an average of the price levels of the sixteen countries that are included in the trade weighted effective exchange rate. Assume that the UK's effective exchange rate stays constant over a given year. If UK inflation is 10% over that year, and world inflation is only 7%, then the real exchange rate will rise by roughly 3% (10% − 7%). The exact rise would be 2.8%. See if you can work out why it is not exactly 3%. Read through the following example, trying to understand the principles,click to reveal answer when you have finished.

Assume that the RPI in the UK is 100 and the RPI for the rest of the world also happens to be 100. Hence:

In the example above, we said that UK inflation was 10% over the given year. This gives a new RPI of 110. In the same way, the new RPI for the rest of the world will be 107. So the new ratio of price levels will be:

So the ratio has risen by 0.028. As a percentage (multiplying by 100) this is 2.8%.

The problem for the UK during the 70s and 80s was that, regardless of how low the effective exchange rate was, its inflation rate tended to be higher than the world average. This caused the real exchange rate to rise (for a given effective exchange rate), making UK exports relatively more expensive abroad and so less competitive pricewise. For a detailed discussion on the competitiveness of UK industry, see the topic called 'Why trade?'

This is not an official measure of the exchange rate, but is often used to assess at what level the exchange rate ought to be. PPP gives a 'parity', or exchange rate, based on the prices of a given basket of goods and services in two different countries.

For example, let us assume that this basket of goods and services contained the price of a bottle of lager, a pound of cheddar cheese, a litre of petrol and a visit to the cinema. Look at the table below.

Items Britain USA France
One bottle of lager £2.20 \$2.90 25 francs
One pound of cheese £2.50 \$3.60 20 francs
One litre of petrol £0.80 \$0.70 7 francs
A visit to the cinema £4.50 \$6.80 53 francs
Totals £10.00 \$14.00 105 francs

The four items in question cost £10 in the UK. The same items cost \$14 in the USA and 105 francs in France. So if the exchange rate between the UK and the USA was based on the price of these four goods and services, it would be £1 = \$1.40. The PPP between the UK and France would be £1 = 10.50 francs.

It is often felt that the actual market exchange rates should match these PPPs as closely as possible. The pound is felt to be overvalued at the moment by around 10% against the euro. Paris always used to be the most expensive European city in which to spend a weekend. This dubious honour now belongs to London.