"Incompatible" answer
"Last lecture, a student asked an interesting question concerning about the satiation effect of the indifferent curve in the perfect substitute and perfect complement case. Is he here now? Please raise up your hand." He then looked around.
I did so, and everyone stared at me.
He approached me and asked quietly, "have you got the answer now?" Without a second of thought, I replied, "no".
He then drew two diagrams, let me reproduce here,


That is his final answer so far, I don't quite agree with him, what do you think?
I did so, and everyone stared at me.
He approached me and asked quietly, "have you got the answer now?" Without a second of thought, I replied, "no".
He then drew two diagrams, let me reproduce here,


That is his final answer so far, I don't quite agree with him, what do you think?

3 Comments:
Oh I quite agree with him.
Agree with the perfect sub. case.
Refinement: For the perfect sub. case, the bottom-left line implies a fixed ratio between the two goods, say $2 coins and $1 coins.
Suppose at a certain point you find $1 coins disgusting. Now you are willing to give up $2 coins in order to give up $1 coins. Now, in order to stick with the concept of perfect sub., you should get a straight line again. But now the ratio may NOT be 1 to 2 again. It can be any number. To keep the four straight lines "connected", either the top-left or bottom-right, but not both, should be a number different from 1 to 2. The top-right one should have a slope of negative the one that differs from 1 to 2.
For the perfect comp. case, the answer is clearly wrong (or nonsense)! Look at a "corner" in the bottom-left area. Now you keep increasing good Y, say. According to the graph, you will keep following a straight line until you reach another "corner" in the top-left area. That does not make sense. It means you are having more and more Y and it does not hurt you even when you have passed the "boundary". But all of a sudden (when you go beyond the new "corner")...oops...it reduces you utility! What the hell is that?
So, Byron, what do you think it will be like then? I think I need to brush up myself on this stuff. Lost in the technicality.........
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