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## Real exchange rates

Some goods (eg cars, computers) are called tradable goods because they can be traded between countries, and consumers in one country have the choice of buying domestically produced goods or importing them from foreign firms. Other goods (eg tourism, haircuts) can’t be traded and so are non-tradable goods.

Usually smaller countries have higher percentages of their GDP that are made up of imports/exports, they must specialise in what they are good at and rely on imports for other products.

For consumers, the choice between buying domestic or foreign goods depends on the relative prices, any tariffs which distort the relative prices, and the real exchange rate (purchasing power in terms of goods of one currency in another).

The real exchange rate is the nominal exchange rate multiplied by the ratio of price levels:

Real exchange rate: $\epsilon = \frac{EP}{P*}$.

This notation is saying the real exchange rate is equal to the nominal exchange rate multiplied by the domestic price level, divided by the foreign price level.

The nominal exchange rate is simply the rate at which you trade one currency for another, eg £1:€1.13 is a nominal exchange rate saying you get 1.13 Euros to the Pound Sterling.

If the real exchange rate is high, foreign goods are relatively cheap and domestic goods are relatively expensive. If the real exchange rate is low, foreign goods are relatively expensive and domestic goods are relatively cheap.

Think in terms of one good, eg imagine the same type of car costs £8000 or €9000. The nominal exchange rate is £1=€1.14. So the real exchange rate is $\epsilon = \frac{1.14(8000)}{9000}=1.013$. In other words, we can exchange 1 British car for 1.01333 European cars. Now imagine a year later, the nominal exchange rate is £1=€1.26. The car sells in Britain for £8300 and in Europe for €9600. Now the real exchange rate is $\epsilon = \frac{1.26(8300)}{9600}=1.0894$. which means that now we can exchange 1 British car for 1.0894 European cars. The good in question (the car) now exchanges on better terms for British customers.

We can extend this principle to thinking of a generic basket of goods. Imagine a general basket of goods in the UK being given an ‘index’ of 100. If the same basket of goods in the US was 98 then we could conclude the basket was slightly cheaper in the US. Assume the nominal exchange rate is £1=$1.62. So the real exchange rate is $\epsilon = \frac{1.62(100)}{98}=1.653$. Because we are using index numbers, on its own this figure is arbitrary and uninformative. All it tells us is that in terms of the basket of goods we are comparing, £1 would buy$1.65306 worth of goods. Now imagine inflation in the UK is 4% and in the US is 2%, but a year later, the nominal exchange rate stays the same, £1=$1.62. Now the real exchange rate is $\epsilon = \frac{1.62(104)}{99.96}=1.685$. Now £1 would buy$1.685 worth of goods in the US, which sounds like it is a better deal for UK consumers, yet inflation has been higher here than in the US? This is because we kept the nominal exchange rate the same. We can consider what would happen if we assumed the real exchange rate stayed the same and the nominal exchange rate adjusted to reflect the differing levels of inflation in each country.

You can rearrange the real exchange rate formula to give $E = \frac{\epsilon P*}{P}$ so if we assume the real exchange rate in our example stayed the same, then $E = \frac{1.653(99.96)}{104}=1.588$. So as a result of the higher inflation in the UK compared to the US, the pound has fallen against the dollar. You now don’t get as many dollars for each pound as you did before, assuming the purchasing power in terms of goods has stayed the same in the two countries.

In practice there are likely to be shifts in both the nominal and real exchange rate.

If the real exchange rate appreciates or depreciates against another currency over time then that tells us that goods are less or more expensive in one country against another. The real exchange rate is basically a relative price and so it affects the demand for goods. If the real exchange rate is low then domestic goods are relatively cheaper so imports are likely to be lower and exports are likely to be higher. If the real exchange rate is high then foreign goods are relatively cheaper so imports are likely to be higher. In the example before of the cars, the rise in real exchange rate for British consumers means they will probably import more cars from Europe in the second year than they did in the first.