Perfect substitutes Perfect substitutes for a person means the indifference curves will lose their convexity. In other words they will become straight lines. As an example let’s think about snack food and more specifically chips. Think about those little bags with like 3 chips in them. If the chips are regular or BBQ, it doesn’t matter to me. No matter how many BBQ bags I have I will always give up 1 for 1 bag of regular chips and I will be equally happy. Note, sometimes the trade-off will not be 1 to 1 but we have perfect substitutes. Say 1 glass of grapefruit juice is always worth the same as 2 glasses of orange juice. We still have straight line indifference curves, just the slope is different than -1.
X Y Perfect Substitutes u1 u2 u3 Here the budget line is the solid line. As such x is relatively expensive because you can see when you give up a unit of x you get a lot of y back. SO, if x is expensive and y is a perfect sub, just buy Y and have utility U2.
X Y u1 u2 u3 Here if the price of x falls a little the consumer stays at taking only y with utility u2, but if the price of x falls a lot the person will switch from buying only y to buying only x. Perfect Substitutes
Perfect complements for a person means the indifference curves will also lose their convexity. But, here the indifference curves become the left and bottom parts of a square or rectangle. As an example let’s think about a computer monitor and cpu box. If you have 1 of each you are probably happy. Having an extra cpu won’t make you any happier, or having an extra monitor won’t make you any happier. But having two of both makes you happier. Note, sometimes the complementarity will not be 1 to 1 but we have perfect complements. Say 1 monitor is a complement with 2 speakers.
Perfect Complements X Y u1 u2 u3 With given prices and income the consumer maximizes utility at U2.
X Y u1 u2 u3 With the same income, the prices of x and y could have several values, but one going up and one going down, and have the consumer take the same basket or bundle of goods. Perfect Complements