<p>Consider the budget line with 2 goods:
<span class="math-container">\begin{equation}
p_xx+p_yy=m
\quad\text{or}\quad 
y=\frac{m}{p_y}-\frac{p_x}{p_y}x,
\end{equation}</span>
where the relative price is <span class="math-container">$\frac{p_x}{p_y}$</span>. </p>

<p>Suppose now both goods become <span class="math-container">$10\%$</span> more expensive (e.g. due to a <span class="math-container">$10\%$</span> tax on them). Then the budget line becomes
<span class="math-container">\begin{equation}
1.1p_xx+1.1p_yy=m
\quad\Leftrightarrow\quad 
p_xx+p_yy=\frac{m}{1.1}
\quad\text{or}\quad 
y=\frac{m}{1.1p_y}-\frac{1.1p_x}{1.1p_y}x=\frac{m}{1.1p_y}-\frac{p_x}{p_y}x
\end{equation}</span>
where the relative price is still <span class="math-container">$\frac{p_x}{p_y}$</span>. From the equations, we see that a uniform percentage change in prices produces a pure income effect (<span class="math-container">$m$</span> drops to <span class="math-container">$m/1.1$</span>), but no substitution effect, since the relative price remain the same after the change. </p>

CC BY-SA 4.0
2019-05-03T23:32:46.093Z
2019-05-03T23:32:46.093Z
Herr K.
<p>I am trying to grasp the concept of income- and substitution effects.</p>

<p>The way, I've understood it, the decomposition bundle is found, at the original indifference curve, where the slope equals that of the new budget line.</p>

<p>Does this mean that if the price of both goods (assuming a simple model of 2 goods) change by the same percentage, the substitution effect is zero? As the slope of the budget line will remain unchanged.</p>

<p>This seems to intuitively make sense to me, but I would greatly appreciate a 100% confirmation, that this is correct.</p>

<p>Thank you!</p>

<microeconomics><consumer-theory><preferences>
Substitution effect when price of both goods change by the same percentage
dandan
# Substitution effect when price of both goods change by the same percentage

(Asked by: username_0 on 2019-05-03)

I am trying to grasp the concept of income- and substitution effects.

The way, I've understood it, the decomposition bundle is found, at the original indifference curve, where the slope equals that of the new budget line.

Does this mean that if the price of both goods (assuming a simple model of 2 goods) change by the same percentage, the substitution effect is zero? As the slope of the budget line will remain unchanged.

This seems to intuitively make sense to me, but I would greatly appreciate a 100% confirmation, that this is correct.

Thank you!

**Tags:** microeconomics, consumer-theory, preferences

---

## 1 answers

### Answer by username_1 on 2019-05-03. Score: 1 | Accepted answer

Consider the budget line with 2 goods:
\begin{equation}
p\_xx+p\_yy=m
\quad\text{or}\quad
y=\frac{m}{p\_y}-\frac{p\_x}{p\_y}x,
\end{equation}
where the relative price is $\frac{p\_x}{p\_y}$.

Suppose now both goods become $10\%$ more expensive (e.g. due to a $10\%$ tax on them). Then the budget line becomes
\begin{equation}
1.1p\_xx+1.1p\_yy=m
\quad\Leftrightarrow\quad
p\_xx+p\_yy=\frac{m}{1.1}
\quad\text{or}\quad
y=\frac{m}{1.1p\_y}-\frac{1.1p\_x}{1.1p\_y}x=\frac{m}{1.1p\_y}-\frac{p\_x}{p\_y}x
\end{equation}
where the relative price is still $\frac{p\_x}{p\_y}$. From the equations, we see that a uniform percentage change in prices produces a pure income effect ($m$ drops to $m/1.1$), but no substitution effect, since the relative price remain the same after the change.


---

