# How inflation affects exchange rates?

I have a question regarding the impact of inflation on exchange rate between trading countries.

Let's assume a hypothetical situation where the UK and the USA trade with each other. The USA import goods from the UK and the UK exports goods to the USA.

Assume the exchange rate £1=$5 at the beginning. The UK is selling one widget to the USA for £10. Now let's imagine an inflation of 100% happened so that the UK prices this widget £20. Now, my reasoning is that £ should weaken against dollar so that £1 = \$2.5. So inflation weakens country's currency. My reasoning is that this is logical that this should happen because now £1 is worth less than it was before the inflation (with the same amount of pounds you could buy twice as much before the inflation than you can now) so £1 should cost \$2.5 instead of \$5. Is my reasoning correct?

• Which is why we look at real exchange rates... Jan 24 '16 at 21:41

Consider two standard relations that tend to hold:

$$i_t = r_t + \pi^e_{t+1} \tag{1}$$

where $i_t$ is domestic nominal interest rate, $r_t$ is domestic real interest rate, and $\pi^e_{t+1}$ is expected domestic inflation. The expression is known as the Fisher equation.

Also, we have the uncovered interest rate parity

$$i_t = i^*_t - [s^e_{t+1} - s_t] \tag{2}$$

where $i^*_t$ is "foreign" nominal interest rate, and $[s^e_{t+1} - s_t]$ is expected appreciation of domestic currency in percentage terms ($s$ is the natural logarithm of "foreign currency per unit of domestic currency" exchange rate). Combining the two and re-arranging we have

$$[s^e_{t+1} - s_t] = i^*_t - r_t - \pi^e_{t+1} \tag{3}$$

Assume that inflation is monetary, and keep $i^*_t,r_t$ constant. Then expectations for domestic inflation will tend to reduce expected appreciation of domestic currency, and may even turn it into an expected depreciation, especially if expected domestic inflation is high. Shortening the length of the time periods, this tendency becomes more of "actual" inflation and "actual" exchange rate.

The fundamental reason is of course what the OP was thinking: if we think of USD as another good (which it is since it is a store of value and can be exchanged for goods), then, if English pound loses value due to inflation and can buy less goods, why should it be still able to buy the same amount of the good "USD"?

Someone can probably answer that question better than I could., but let us give a try nonetheless.

Let us consider that we have an independent market between the US and the UK and that the values of their respective money is only depending on that market. That is no influence outside those two countries will be considered.

At this market, the exchange rate between the pounds and the dollars is a consequence of the buying and selling of dollars against pounds. If we further simplify, supposing that no government, currency speculation, or otherwise take place, we can reduce the exchange rate to be a consequence of the commercial balance between those two countries. The more the US import, the more the pound/dollar ratio increases. And the more they export, the more the ratio decreases.

Now, we consider that the prices in the UK rises as an effect of the inflation. The US inflation on the same period is 0.

At first, the exchange rate was unchanged. Export goods are kept at the same price (no inflation in the US and constant exchange rate). However import goods are more expensive due to the inflation. This favours the US export in comparison to its import. As a consequence, there is a higher demand of US goods in the UK (cheaper) and a lower demand of UK goods in the US.

The effect is a fall of the pound in comparison to the dollar.

It can be seen in another way, the acquisition power of the pound has lowered due to the inflation, and the exchange rate reflects that against the non-inflated dollar.

As a consequence, the prices of the US exported goods will rise, whereas the prices of the UK exported goods will lower. This will re-establish the variation of demand and offer caused by the inflation to what it was before, but with a new echange rate, reflecting the new acquisition power of the pound.

This is a theoretical illustration of the self-regulation of the market.