# Can the Income Consumption Curve have a non smooth shape?

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

• Please ask separate questions separately. – Giskard Sep 13 '20 at 19:45

## 1 Answer

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: $$(x,y) = \left\{ \begin{array}{ll} \left( 0, \frac{I}{6} \right) & \text{ if } I \leq 30 \\ \left( \frac{2I}{10} - 6, 8 - \frac{I}{10} \right) & \text{ if } 30 < I \leq 80 \\ \left( \frac{I}{8}, 0 \right) & \text{ if } 80 < I \end{array} \right.$$

• 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 economics.stackexchange.com/questions/39696/… , I only needed to understand if my concept with respect to the ICC was correct or not in deriving that result! – Anshuman Singh Sep 14 '20 at 10:07
• @DARE2ZLATAN Thank you but I don't like reading handwritten notes, I do enough of that at work. – Giskard Sep 14 '20 at 10:44
• @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 Sep 14 '20 at 10:49
• 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. – Anshuman Singh Sep 14 '20 at 10:55
• @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 Sep 14 '20 at 11:02