Two special cases might result in indifference curves that look a little different from the ones discussed in the text.

a. If two goods are perfect substitutes, that means the consumer would always be willing to trade one for the other in a certain, fixed proportion. In this case, the MRS would be constant, which means that indifference curves would be straight lines.

Suppose a consumer's MRS between two goods X and Y is a constant 2.5, which means that the consumer is always willing to give up 1 unit of good X for 2.5 units of good Y.

If the consumer has $180 in income to spend, the price of good X is $20 per unit, and the price of good Y is $10 per unit, what is this consumer's utility-maximizing bundle of X and Y?

Answer the question by thinking it through and then show with a diagram (including a budget constraint and an indifference curve) why your answer works.

b. If two goods are perfect complements, indifference curves have a very unusual shape. Let's see if you can reason through this one. Consider left and right shoes.

For most people, having left shoes alone (or right shoes alone) does not really provide any utility; rather, people get utility from having a pair of shoes that they can wear. In this case, left and right shoes are perfect 1:1 complements. Can you figure out what indifference curves would look like in such a case?

To do this, it might be helpful to think about questions like the following: If someone has 4 right shoes and 4 (matching) left shoes, what's the marginal utility of an extra right shoe?

If a consumer had to compare the bundles (4 left shoes, 4 right shoes), (4 left shoes, 5 right shoes), and (7 left shoes, 4 left shoes), how would these bundles rank? Would any of these bundles be better than the others?