<p>The ratio of relative prices <span class="math-container">$P^*/P$</span>, where <span class="math-container">$P^*$</span> is foreign and <span class="math-container">$P$</span> 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 <span class="math-container">$Y_r$</span> will be defined as: <span class="math-container">$Y_r = Y_n/P$</span> where <span class="math-container">$Y_n$</span> is nominal GDP where we would divide by <span class="math-container">$P$</span> in order to adjust for the effect of inflation (change in price level).</p>
<p>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 <span class="math-container">$P$</span> because then you would be ignoring the changes in foreign price level.</p>
<p>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:</p>
<p><span class="math-container">$$Q=S\frac{P^*}{P}$$</span></p>
<p>where, <span class="math-container">$Q$</span> is the real exchange rate and <span class="math-container">$S$</span> 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. <span class="math-container">$\ln X = x$</span>):</p>
<p><span class="math-container">$$q = s + p^* - p$$</span></p>
<p>Now the above should hold across multiple time periods so lets examine the changes between <span class="math-container">$t-1$</span> and <span class="math-container">$t$</span> where <span class="math-container">$\Delta x_t = x_{t}-x_{t-1}$</span>:</p>
<p><span class="math-container">$$\Delta q_t = \Delta s_t + \Delta p_t^* - \Delta p_t$$</span>.</p>
<p>Now finally by definition inflation (<span class="math-container">$\pi_t$</span>) is the change in price level so <span class="math-container">$\pi_t\approx \Delta p_t$</span> so lets substitute that in:</p>
<p><span class="math-container">$$\Delta q_t = \Delta s_t + \pi_t^* - \pi_t$$</span>.</p>
<p>Hence the change in real exchange rate reflects the change in nominal exchange rate adjusted for inflation in foreign country and home country.</p>

CC BY-SA 4.0
2020-08-17T23:50:08.127Z
2020-08-17T23:50:08.127Z
1muflon1
<p>As a consumer the nominal exchange rate is arbitrary, £1 can get me $1.28, so what?</p>

<p>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. </p>

<p>Suppose, </p>

<p>Domestic economy ~ U.K.</p>

<p>Foreign economy ~ U.S.A.</p>

<p>Nominal Exchange Rate ~ $1.28/£</p>

<p>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. </p>

<p>As the foreign price level is greater, the pound is overvalued <em>in this case</em>. 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.  </p>

CC BY-SA 4.0
2018-11-27T07:06:14.717Z
"Assume that the price level of the U.S.A. is greater than the U.K.'s price level" measured in what currency?
Giskard
CC BY-SA 4.0
2018-11-27T07:07:00.187Z
Are you assuming that absolute purchasing power parity holds? If yes, can you explain why?
Giskard
CC BY-SA 4.0
2018-11-27T09:37:51.497Z
1) Let's use our imagination and use the CPI
plim
CC BY-SA 4.0
2018-11-27T09:41:11.050Z
2) PPP should hold, theoretically, due to simple demand dynamics, but I am open to be corrected. If you would so kindly volunteer.
plim
CC BY-SA 4.0
2018-11-27T12:09:26.200Z
1) This is not what I asked, please read my question again.
Giskard
CC BY-SA 4.0
2018-11-27T12:11:55.640Z
2) It is my understanding that absolute PPP does not hold in practice. There are several explanations, such as non-tradeable goods. See the Balassa-Samuelson model for details. There is some evidence that the weaker relative PPP holds in the long run. (But not in the short run.)
Giskard
CC BY-SA 4.0
2018-11-26T20:55:37.017Z
2018-11-26T20:55:37.017Z
plim
<p>Real exchange rate formula is the exchange rate multiplied by the ratio of two prices.</p>

<p>what does this ratio actually imply? What is the rationale behind taking the ratio?</p>

<macroeconomics><inflation>
real exchange rate formula doubt
user585380
# real exchange rate formula doubt

(Asked by: username_0 on 2018-11-26)

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?

**Tags:** macroeconomics, inflation

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## 2 answers

### Answer by username_1 on 2020-08-17. Score: 1

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.


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### Answer by username_2 on 2018-11-26. Score: 0

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.

> **Comments:**
> **username_3**: "Assume that the price level of the U.S.A. is greater than the U.K.'s price level" measured in what currency?  
> **username_3**: Are you assuming that absolute purchasing power parity holds? If yes, can you explain why?  
> **username_2**: 1) Let's use our imagination and use the CPI  
> **username_2**: 2) PPP should hold, theoretically, due to simple demand dynamics, but I am open to be corrected. If you would so kindly volunteer.  
> **username_3**: 1) This is not what I asked, please read my question again.  
> **username_3**: 2) It is my understanding that absolute PPP does not hold in practice. There are several explanations, such as non-tradeable goods. See the Balassa-Samuelson model for details. There is some evidence that the weaker relative PPP holds in the long run. (But not in the short run.)  

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