Shapes of indifference curves
Most indifference curves that follow normal preferences have a convex shape:
However you will come across some different shapes:
Perfect substitutes are like this:
Here the consumer only cares about the total number of X + Y that they have, not whether they are getting more of X or Y, so the indifference curves are straight lines.
Perfect complements are like this:
This is a bit like the case where X is a left shoe and Y is a right shoe. If you have 3 left shoes and 4 right shoes, then you are no better off than having 3 left shoes and 3 right shoes as you need the pair together. In fact you are no better off even if you have 3 left shoes and 100 right shoes. So having more Y does not increase your utility unless you increase X as well.
Bads are like this:
Here the consumer doesn’t like good Y, so if you are making him have more of good Y, he has to have more of good X to compensate for it, otherwise his utility level falls.
Neutral goods are like this:
Here the consumer likes good X but does not have any opinion (good or bad) about good Y, so all that matters is the amount of good X he has, his utility doesn’t increase by having more Y.