Can the Income Consumption Curve have a shape that is kinked?
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3$\begingroup$ Please ask separate questions separately. $\endgroup$ – Giskard Sep 13 '20 at 19:45
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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: $$ (x,y) = \left\{ \begin{array}{ll} \left( 0, \frac{I}{6} \right) & \text{ if } I \leq 30 \\ \left( \frac{2I}{10} - 6, 8 - \frac{I}{10} \right) & \text{ if } 30 < I \leq 80 \\ \left( \frac{I}{8}, 0 \right) & \text{ if } 80 < I \end{array} \right. $$
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$\begingroup$ 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! $\endgroup$ – Anshuman Singh Sep 14 '20 at 10:07
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1$\begingroup$ @DARE2ZLATAN Thank you but I don't like reading handwritten notes, I do enough of that at work. $\endgroup$ – Giskard Sep 14 '20 at 10:44
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1$\begingroup$ @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. $\endgroup$ – Giskard Sep 14 '20 at 10:49
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$\begingroup$ 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. $\endgroup$ – Anshuman Singh Sep 14 '20 at 10:55
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$\begingroup$ @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. $\endgroup$ – 1muflon1♦ Sep 14 '20 at 11:02
