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## Utility maximization with indifference curves

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# Types of indifference curves

## Video transcript

I've been drawing my
indifference curves to look something like this. So that's the vertical axis. That's one good. So this is the
quantity of good A. This is the quantity of good B. And I've been drawing the
indifference curves like this. So it might look like that. That's one indifference curve. Then another indifference
curve would look like that. And I could keep drawing
indifference curves. And it this is what
a indifference curve would look like for
two normal goods. So let me write that down. These are normal goods. And the reason why normal goods
indifference curves would look like that or what I'm
trying to figure out the combinations
of two normal goods is because if I
have a lot of one good-- so this point right over
here-- I have a lot of good A and I have very
little of good B. I would be willing to trade off
a lot of A to get one extra B. But if all of a sudden I have
a lot of B and a lot less A, I would be willing to
trade off very little A to get an incremental B.
So that's why we have kind of this inward bow-shaped
curve right over here. Or mathematically, it looks
like it's part of a hyperbola. And that's what normal goods,
the indifference curves if you're trading off between
normal goods would look like. Now let's think about
the indifference curves. So it would be this
kind of curved thing. The marginal rate
of substitution would constantly be changing. Now let's think about
different types of goods. Let's say that this is
the quantity of $5 bills. And let's say that this is
the quantity of $10 bills. And we're talking
about the good now is actually the dollar bills. So let's say that this right
over here is 10 $5 bills. Well, that's $50. I'd be indifferent between
that and 5 $10 bills. So this is 5 right over here. And any point in between,
I would be indifferent because I'm always willing
to trade off 2 $5 bills for 1 $10 bill. So my indifference curve
would be linear in this case. So no matter what, on
this indifference curve, I'm always willing, if I want
to get to 1 extra $10 bill, I'm always willing to
give up 2 $5 bills, which makes complete sense because
2 $5 bills are completely equivalent to 1 $10 bill. Now we could take it
to another extreme. Let's say I have an
indifference-- well, let me draw the quantity of,
I don't know, M&Ms. Let's say, red M&Ms. And I should have
done that in red, but I won't. And then let's say this is
the quantity of blue M&Ms. And let's say that I actually
am indifferent between red and blue M&Ms.
Some people aren't. Red M&Ms and blue M&Ms. So having 10 red M&Ms is to
me is completely equivalent of having 10 blue M&Ms. So I am
willing to trade them off one for one. I don't care. I get the same total utility. So in this case, assuming
that I really don't we care the color of my
M&M, I'm completely indifferent as I swap them out. And so this is a case
of perfect substitutes. Now I'd always be happy
to have more M&Ms. So another indifference curve
might look something like this. But it's always going to
have a slope of negative 1. I was giving up 1 red
M&M to get 1 blue M&M, then I would be indifferent. And likewise, over here, you
could another indifference curve between $5 bills and $10
bills that looks like this. But the slope would be
the exact same thing. Now the last situation
I want to think about is what we'll call
perfect complements. So goods that if you
have one of them, you really need the other one. Otherwise, one of the
two is somewhat useful. And maybe the most pure version
of perfect complements-- let me write it over here. So let's say this is the
quantity of right shoes. And this is the
quantity of left shoes. So obviously, if we're
talking about just one pair, you have one of each. Now, do you care if you
really get more left shoes? No. You have the exact
same preference. It doesn't really
change your life. You have the same total utility. In fact, it might
even be negative because you have
to store them all. But let's just assume you
have the same total utility and you don't get
any benefit of having those spare shoes in
case your shoe gets destroyed or anything like that. In terms of what you can get
out it, what you can wear, you get the same utility. And so you're really
indifferent no matter how many extra left
shoes someone gives you. And you'd also be
indifferent no matter how many extra right
shoes someone gives you. Now, you would be happier if
you had maybe two right shoes and two left shoes because
now you have two pairs. So this would be another
indifference curve. And once again, if you
have two right shoes, you really don't care
how many more than two left shoes you get. And if you have two
left shoes, you really don't care how many more
than two right shoes you get. So this indifference
curve in green is clearly preferable
to the one in white, but along each
indifference curve it doesn't benefit you to
have three left shoes and only two right shoes. So this is what perfect
complements would look like. This is perfect substitutes. And this is normal goods.