<p>An easy example:</p>
<p>When the utility function is
<span class="math-container">$$
U(x,y) = \ln x + y
$$</span>
and the prices are
<span class="math-container">$p_x = p_y = 1$</span>, the IOC is kinked at income level <span class="math-container">$I=1$</span>:
<span class="math-container">$$
(x,y) = \left\{
\begin{array}{ll}
\left( I, 0 \right) &amp; \text{ if } I \leq 1 \\
\left( 1, I-1 \right) &amp; \text{ if } 1 &lt; I
\end{array}
\right.
$$</span></p>
<hr />
<p>A more complicated example:</p>
<p>When the utility function is
<span class="math-container">$$
U(x,y) = \min\left(2x+2y,x+10\right)
$$</span>
and the prices are
<span class="math-container">$p_x = 8$</span>, <span class="math-container">$p_y = 6$</span>,
the good <span class="math-container">$y$</span> exhibits inferior (and Giffen) behavior. The IOC is kinked at income levels 30 and 80:
<span class="math-container">$$
(x,y) = \left\{
\begin{array}{ll}
\left( 0, \frac{I}{6} \right) &amp; \text{ if } I \leq 30 \\
\left( \frac{2I}{10} - 6, 8 - \frac{I}{10} \right) &amp; \text{ if } 30 &lt; I \leq 80 \\
\left( \frac{I}{8}, 0 \right) &amp; \text{ if } 80 &lt; I
\end{array}
\right.
$$</span></p>

CC BY-SA 4.0
2020-09-14T10:07:52.633Z
thank you, I posted a similar question which for some reason was down voted even though I wasn't seeking homework help. Can you help me with the question https://economics.stackexchange.com/questions/39696/income-consumption-curve-to-find-preferences , I only needed to understand if my concept with respect to the ICC was correct or not in deriving that result!
ghghghghghg
CC BY-SA 4.0
2020-09-14T10:44:49.107Z
@DARE2ZLATAN Thank you but I don't like reading handwritten notes, I do enough of that at work.
Giskard
CC BY-SA 4.0
2020-09-14T10:49:20.087Z
@DARE2ZLATAN Also, the question seems very specific. As such, it is unlikely to be useful for future visitors of the site, which is ultimately the goal of SEs.
Giskard
CC BY-SA 4.0
2020-09-14T10:55:43.800Z
The question that I asked in this thread was very general and I cannot present what I'm trying to think or implement without showing my working or the question which is why I thought you could understand what it is that I'm trying to ask exactly by referring to the original question.
ghghghghghg
CC BY-SA 4.0
2020-09-14T11:02:58.313Z
@DARE2ZLATAN you can show your work by typing out the equations and text using markdown/Mathjax. Pictures should be reserved for graphs not equations and text.
1muflon1
CC BY-SA 4.0
2020-09-14T14:01:27.407Z
ok, will keep that in mind.
ghghghghghg
CC BY-SA 4.0
2020-09-14T05:37:59.157Z
2020-09-14T08:33:59.700Z
2020-09-14T08:33:59.700Z
Giskard
<p>Can the Income Consumption Curve have a shape that is kinked?</p>

CC BY-SA 4.0
2020-09-13T19:45:32.937Z
Please ask separate questions separately.
Giskard
<microeconomics>
Can the Income Consumption Curve have a non smooth shape?
ghghghghghg
# Can the Income Consumption Curve have a non smooth shape?

(Asked by: username_0 on 2020-09-13)

Can the Income Consumption Curve have a shape that is kinked?

**Tags:** microeconomics

> **Comments:**
> **username_1**: Please ask separate questions separately.  

---

## 1 answers

### Answer by username_1 on 2020-09-14. Score: 3

An easy example:

When the utility function is
$$
U(x,y) = \ln x + y
$$
and the prices are
$p\_x = p\_y = 1$, the IOC is kinked at income level $I=1$:
$$
(x,y) = \left\{
\begin{array}{ll}
\left( I, 0 \right) & \text{ if } I \leq 1 \\
\left( 1, I-1 \right) & \text{ if } 1 < I
\end{array}
\right.
$$

---

A more complicated example:

When the utility function is
$$
U(x,y) = \min\left(2x+2y,x+10\right)
$$
and the prices are
$p\_x = 8$, $p\_y = 6$,
the good $y$ exhibits inferior (and Giffen) behavior. The IOC is kinked at income levels 30 and 80:
$$
(x,y) = \left\{
\begin{array}{ll}
\left( 0, \frac{I}{6} \right) & \text{ if } I \leq 30 \\
\left( \frac{2I}{10} - 6, 8 - \frac{I}{10} \right) & \text{ if } 30 < I \leq 80 \\
\left( \frac{I}{8}, 0 \right) & \text{ if } 80 < I
\end{array}
\right.
$$

> **Comments:**
> **username_0**: thank you, I posted a similar question which for some reason was down voted even though I wasn't seeking homework help. Can you help me with the question https://economics.stackexchange.com/questions/39696/income-consumption-curve-to-find-preferences , I only needed to understand if my concept with respect to the ICC was correct or not in deriving that result!  
> **username_1**: @DARE2ZLATAN Thank you but I don't like reading handwritten notes, I do enough of that at work.  
> **username_1**: @DARE2ZLATAN Also, the question seems very specific. As such, it is unlikely to be useful for future visitors of the site, which is ultimately the goal of SEs.  
> **username_0**: The question that I asked in this thread was very general and I cannot present what I'm trying to think or implement without showing my working or the question which is why I thought you could understand what it is that I'm trying to ask exactly by referring to the original question.  
> **username_2**: @DARE2ZLATAN you can show your work by typing out the equations and text using markdown/Mathjax. Pictures should be reserved for graphs not equations and text.  
> **username_0**: ok, will keep that in mind.  

---

