# real exchange rate formula doubt

Real exchange rate formula is the exchange rate multiplied by the ratio of two prices.

what does this ratio actually imply? What is the rationale behind taking the ratio?

The ratio of relative prices $$P^*/P$$, where $$P^*$$ is foreign and $$P$$ home price level respectively, is used in order to adjust the nominal exchange rate for changes in relative price levels in two countries. I think a good way of understanding it is to use analogy with real GDP. A real GDP $$Y_r$$ will be defined as: $$Y_r = Y_n/P$$ where $$Y_n$$ is nominal GDP where we would divide by $$P$$ in order to adjust for the effect of inflation (change in price level).

The real exchange rate is basically the same concept you are trying to adjust the nominal exchange rate for changes in price level, but you cannot just divide by $$P$$ because then you would be ignoring the changes in foreign price level.

You can see this more clearly if you look at the equation in terms of inflation (as in Copeland's Exchange Rates and International Finance textbook). Start with the definition for real exchange rate:

$$Q=S\frac{P^*}{P}$$

where, $$Q$$ is the real exchange rate and $$S$$ nominal exchange. Now take logs of the variables and to clean up the expression I will be using lowercase letters to denote logs (i.e. $$\ln X = x$$):

$$q = s + p^* - p$$

Now the above should hold across multiple time periods so lets examine the changes between $$t-1$$ and $$t$$ where $$\Delta x_t = x_{t}-x_{t-1}$$:

$$\Delta q_t = \Delta s_t + \Delta p_t^* - \Delta p_t$$.

Now finally by definition inflation ($$\pi_t$$) is the change in price level so $$\pi_t\approx \Delta p_t$$ so lets substitute that in:

$$\Delta q_t = \Delta s_t + \pi_t^* - \pi_t$$.

Hence the change in real exchange rate reflects the change in nominal exchange rate adjusted for inflation in foreign country and home country.

As a consumer the nominal exchange rate is arbitrary, £1 can get me $1.28, so what? What matters is how much the consumer can buy given this exchange rate. By incorporating the price level of the domestic and foreign economies the consumer can know how much they will be able to buy with this exchange of currency. Suppose, Domestic economy ~ U.K. Foreign economy ~ U.S.A. Nominal Exchange Rate ~$1.28/£

Assume that the price level of the U.S.A. is greater than the U.K.'s price level so that the foreign economy has a greater weighted average of prices relative to the domestic economy. For this given nominal exchange rate, my purchasing power would decline if I exchanged all my pounds to dollars, as U.S.A. goods are more expensive.

As the foreign price level is greater, the pound is overvalued in this case. There is not enough demand for U.K. goods to cause any inflationary pressure. By devaluing the pound, there will be a greater demand for U.K. goods as holders of the U.S. dollar can get more pounds per dollar. The result is an increase in the real exchange rate as the price ratio increases.

• "Assume that the price level of the U.S.A. is greater than the U.K.'s price level" measured in what currency? – Giskard Nov 27 '18 at 7:06
• Are you assuming that absolute purchasing power parity holds? If yes, can you explain why? – Giskard Nov 27 '18 at 7:07
• 1) Let's use our imagination and use the CPI – plim Nov 27 '18 at 9:37
• 2) PPP should hold, theoretically, due to simple demand dynamics, but I am open to be corrected. If you would so kindly volunteer. – plim Nov 27 '18 at 9:41
• 1) This is not what I asked, please read my question again. – Giskard Nov 27 '18 at 12:09