<p>Dimensional analysis is useful here.</p>
<p><span class="math-container">$$\text{RER}=1.58\frac{\text{Euro}}{\text{Sterling}}\cdot\frac{110\text{ Euro}}{118\text{ Sterling}}=1.47\frac{\text{Euro}^2}{\text{Sterling}^2}$$</span></p>
<p>where the unit of measurement is very strange indeed, since the real exchange rate should be a number without a unit of measurement. (Well, technically it is basket of British goods/basket of Euro goods.) This indicates that there is an error in the calculation above, and rereading the <em>logic</em> behind RER calculation is probably useful.</p>

CC BY-SA 4.0
2020-09-06T05:37:20.947Z
1muflon1 seems to be correct in their assessment, since flipping the price index from a euro to sterling ratio to sterling to euro ratio would cancel out all the units.
H Huang
CC BY-SA 4.0
2020-09-06T05:40:20.723Z
@HHuang Indeed. My answer is just meant to provide a simple control mechanism for students to see if they have "accidentally flipped" the price ratios.
Giskard
CC BY-SA 4.0
2020-09-05T13:58:19.297Z
2020-09-05T13:58:19.297Z
Giskard
<p>What will be the real value of the Euro/Sterling exchange rate if:</p>
<p>Given that:</p>
<p>Index of UK prices<span class="math-container">$=118$</span>, Index of Euro-area prices<span class="math-container">$=110$</span>, Nominal Euro/Sterling exchange rate<span class="math-container">$=1.58$</span> and UK marginal tax rate<span class="math-container">$=0.15$</span>.</p>
<p>My attempt,
<span class="math-container">$\text{RER}=\text{NER}\cdot\frac{
{\text{Price of domestic goods}}}{\text{Price of foreign goods}}$</span></p>
<p><span class="math-container">$$\text{RER}=1.58\cdot\frac{110}{118}=1.47$$</span></p>
<p>But the given answer is <span class="math-container">$1.69$</span>. Why?</p>

CC BY-SA 4.0
2020-09-05T13:28:47.597Z
I think your textbook wants you to treat UK as a home country if you do that you get 1.69 since 1.58*(118/110) is approximately 1.69
1muflon1
CC BY-SA 4.0
2020-09-05T13:33:04.360Z
But the question stated Euro/Sterling. Wouldn’t it be treating Euro is a home instead of U.K.? And why the UK marginal rate appeared in this question ?
Mathxx
CC BY-SA 4.0
2020-09-05T13:41:05.900Z
no exchange rate can be quoted in direct or indirect way. Both are valid exchange rate quotations - in your class teacher should be clear which one you should follow see here https://www.toppr.com/guides/economics/open-economy-macroeconomics/exchange-rate/ . The marginal tax rate might be something to throw you off it’s a standard teacher tactic to include some unrelated number to test if student can determine what information is important
1muflon1
CC BY-SA 4.0
2020-09-05T13:43:27.550Z
It's actually a multiple choice question. 

A)1.69
B)1.47
C)1.23

The given answer is A.
Mathxx
CC BY-SA 4.0
2020-09-05T13:44:37.077Z
yes in that case still my first comment applies
1muflon1
<macroeconomics><exchange-rates>
Real Exchange Rate (Euro/Sterling)
Mathxx
# Real Exchange Rate (Euro/Sterling)

(Asked by: username_0 on 2020-09-05)

What will be the real value of the Euro/Sterling exchange rate if:

Given that:

Index of UK prices$=118$, Index of Euro-area prices$=110$, Nominal Euro/Sterling exchange rate$=1.58$ and UK marginal tax rate$=0.15$.

My attempt,
$\text{RER}=\text{NER}\cdot\frac{
{\text{Price of domestic goods}}}{\text{Price of foreign goods}}$

$$\text{RER}=1.58\cdot\frac{110}{118}=1.47$$

But the given answer is $1.69$. Why?

**Tags:** macroeconomics, exchange-rates

> **Comments:**
> **username_1**: I think your textbook wants you to treat UK as a home country if you do that you get 1.69 since 1.58*(118/110) is approximately 1.69  
> **username_0**: But the question stated Euro/Sterling. Wouldn’t it be treating Euro is a home instead of U.K.? And why the UK marginal rate appeared in this question ?  
> **username_1**: no exchange rate can be quoted in direct or indirect way. Both are valid exchange rate quotations - in your class teacher should be clear which one you should follow see here https://www.toppr.com/guides/economics/open-economy-macroeconomics/exchange-rate/ . The marginal tax rate might be something to throw you off it’s a standard teacher tactic to include some unrelated number to test if student can determine what information is important  
> **username_0**: It's actually a multiple choice question.   A)1.69 B)1.47 C)1.23  The given answer is A.  
> **username_1**: yes in that case still my first comment applies  

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## 1 answers

### Answer by username_2 on 2020-09-05. Score: 2

Dimensional analysis is useful here.

$$\text{RER}=1.58\frac{\text{Euro}}{\text{Sterling}}\cdot\frac{110\text{ Euro}}{118\text{ Sterling}}=1.47\frac{\text{Euro}^2}{\text{Sterling}^2}$$

where the unit of measurement is very strange indeed, since the real exchange rate should be a number without a unit of measurement. (Well, technically it is basket of British goods/basket of Euro goods.) This indicates that there is an error in the calculation above, and rereading the *logic* behind RER calculation is probably useful.

> **Comments:**
> **username_3**: username_1 seems to be correct in their assessment, since flipping the price index from a euro to sterling ratio to sterling to euro ratio would cancel out all the units.  
> **username_2**: @username_3 Indeed. My answer is just meant to provide a simple control mechanism for students to see if they have "accidentally flipped" the price ratios.  

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