Main content

## Microeconomics

### Course: Microeconomics > Unit 5

Lesson 3: Utility maximization with indifference curves# Types of indifference curves

Indifference curves for normal goods, substitutes and perfect complements. Created by Sal Khan.

## Want to join the conversation?

- You talked about normal goods in this video, what if it is a Inferior good? Could you connect this with Substitution effect and Income effect. :)(22 votes)
- An inferior good can still have indifference curves that bow inward (convex to the origin). What's important is that the income effect is negative.(4 votes)

- What would the indifference curve look like if someone could only buy good x and never buy good y? For instance, a person who is Hindu will alway prefer a soy burger to a regular burger. What would the indifference curve look like then?(8 votes)
- If soy burgers are on the x axis, and beef burgers are on the y axis, then the indifference curve will be a flat line along the x axis, as any amount of x will always be completely preferred to y.(13 votes)

- Explain why indifference curves can never cross(4 votes)
- Each point on an indifference curve is a combination of two goods that would provide the same utility.

Consider the indifference curve of ice creams and cold coffee. Let us consider two indifference curves for the same. I'll try to explain this concept by contradiction.

By definition, in economics when we consider indifference curves, we say "more is better", that is the farther of the indifference curve is, the better. So we would always chose the one that is farthest given a choice.

Now back to the example, cold coffee and ice cream. If the two indifference curves crossed, they would have a common point, say A. 'A' has the same utility as any of the points on curve 1 and curve 2. But this cannot be true, as more is always better. The curve which is farther IS better than the one closer to the origin. Thus, they could not have crossed, else the utility from both the curves would have been the same.(18 votes)

- Is there a indifference curve that curves out? (opposite of the first example) What would a scenario be that uses one?(3 votes)
- You will get a concave indifference curve (curving out not in) whenever it's better to have a lot of one thing rather than a mix of two things. That is, rather than complementary goods, you have incompatible goods*.

Here's a good example: Suppose you can either buy brand A hand-held radios or brand B hand-held radios for your company, but that brand A is only compatible with brand A, and brand B is only compatible with brand B. In this case, you might be indifferent between "20 radio sets of brand A and 0 of brand B" and "0 of brand A and 20 of brand B", so these two points would lie on your indifference curve. Now think what happens in between: Having 10 of each brand would clearly be LESS useful than either of these cases, so that would NOT lie on the same curve. However,*perhaps*having 15 of each brand might be as useful, if two groups of 5 employees never need to communicate directly (10 people carry both brands, 5 carry just brand A, 5 carry just brand B). You could then fill in the rest of the curve - you will see that it is concave rather than convex.

You could also extend this concept to "perfect incompatibility", where you would get a 90 degree angle with straight lines, again convex. (For example with the radios above, if every employee needed to be able to communicate with every other employee, then "20 of A and 20 of B" is no more or less useful than "20 of A and 0 of B" or "0 of A and 20 of B".)

* This idea of incompatibility assumes that it is costly or troublesome to trade goods of one kind for another once you have them.(4 votes)

- But how do you actually calculate the optimum point?

I miss a video explaining how to use algabra to calc this point..(3 votes)- You need to know a little calculus to calculate the optimum point. The trick is that at the optimum point the slope of the budget line and the slope of the indifference curve is the same.

Thus, you can calculate the slope of the budget line by dividing Px by Py.

You can calculate the slope of the indifference curve at a given point by dividing the marginal utility of x by the marginal utility of y (=taking the derivative of the utility function by x and by y, and divide them).

Thus the optimum point is:

Px/Py = MUx / MUy

I hope I could help you.(1 vote)

- You already talked about Normal Goods; why don't you also discuss Indifference Curve for Inferior Goods ? It's quite interesting to learn the Indifference Curve for goods whose quantity demanded goes down as the budget line for that good expands.(3 votes)
- Sal can u pls explain sub and income effect for perfect substitutes?? I have a final in it tomorrow!(1 vote)
- If good X and good Y are perfect substitutes, then the increase/decrease in the price of X will have an effect on the quantity consumed of good Y and of good B.

Lets say the Price of Good X Increases. Quantity consumed of good X decreases. And because they are perfect substitutes, if Qc of Good X reduced by 20, Qc of Good Y increased by 20. Next I will explain how the Sub and Income effects come in.

For the Substitution effect, When the price decreased, your level of satisfaction remained the same (your new budget line is also tangent to the original indifference curve, just not at the same point that the old budget line was on). Your Qc for good Y increased by the same amount that your Qc for good X did.

For the income effect, your income decreased while prices remained constant. This results in not a shift in Price ratio, but in satisfaction. (Your new budget line is tangent to a lower indifference curve) Because the price ratio remains the same however, the new budget line is parallel (but to the left of in this case) to the previous one that was created by the Substitution effect.

The new Quantity consumed for good x is smaller because of the additional income effect. And whatever the EXACT amount of consumption that is reduced of good x is seen as a gain in consumption for Good y.

Hope this helps

-Economics Major(5 votes)

- what is the compinations of 2 normal goods?(2 votes)
- I scrolled down quite a bit but could not find the answer to how a set of indifference curves for two bads would look like?

Let's assume someone hates fast food and we plot the quantities of burgers and wings. Shouldn't indifference curves be concave towards the origin and the utility increase as one approaches the origin?

When I got it right the indifference curve shows how I should be compensated for an increase or decrease in the other good. In this case, if I go to the right and increase my numbers of wings, this decreases my utility. In order to offset that and hold my utility constant, I would have to reduce my quantity of hamburgers as well, am I right?

So that would gave you concave indifference curves towards the origin, which is also the preferred point on the diagram.(2 votes)- Yes, I think you have it. If you have two things that are "bads", the utility curves are concave (bowed out), and lower curves are preferred to higher ones.(1 vote)

- Is the Marginal Rate of Substitution always equal to 1 for subsitute goods ?(1 vote)
- No, the marginal rate of substitution is not always equal to zero, this is reflected in the numbers of the two goods you are producing as an economy, if you are producing different numbers of goods in each one then the MRS will not be 1.(2 votes)

## 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.