Indifference curves and marginal rate of substitution | Microeconomics | Khan Academy

In this video, we're going to explore the idea of an indifference curve. Indifference curve, and what it is, it describes all of the points, all the combinations of things to which I am indifferent. In the past, we've thought about maximizing total utility. Now we're going to talk about all the combinations that essentially give us the same total utility.

So let's draw a graph that tells us all of the different combinations of two goods to which we are indifferent. Like we've mentioned before, we're focusing on two goods because if we did three goods, we would have to do it in three dimensions, and four goods would get very abstract. So let's say in this axis, the vertical axis, this is going to be the quantity. We’ll stay with the chocolate and the fruit tradeoff; those are the only two things that we consume.

So this is going to be the quantity of chocolate in bars, and in the horizontal axis, this is going to be the quantity of fruit, and this is going to be in pounds of fruit. And this will go... see, this is 10, this is 20, this is 10 and this is 20, and this would be 15, five, five, and then 15.

Let's say that right now, at some point, I am consuming five pounds of fruit per month and 15 bars of chocolate per month. So that would put me right there. And if someone were to ask me how I would feel if, instead of that, instead of that, I were to give you, let's say, 10 bars of chocolate and 7 pounds of fruit, I would say, "You know what? I'm indifferent. I wouldn't care whether I have 15 bars of chocolate and 5 pounds of fruit or whether I have 10 bars of chocolate and 7 pounds of fruit."

I am indifferent between these two. I've introspected on what I like and what I derive benefit and satisfaction out of, and I get the same total utility out of either of these points. So both of these are on the same indifference curve. In general, I could plot all of the different combinations that give me the exact same total utility.

It might look something like this; let me try to draw it as neatly as possible. I'll do it in magenta. It might look something like this and then keep going all the way down like that. So any point, any point on this curve right over here, I'm indifferent relative to my current predicament of 15 bars and 5 pounds of chocolate.

So that is my indifference curve, indifference curve. Now let's think about... so obviously, if I go all over here, 20 pounds of chocolate, 20 pounds of fruit, and I don't know, that looks like about two bars of chocolate to me, the same utility based on my preferences as where I started off with. So if someone just swapped everything out, I would just kind of, you know, shrug my shoulder and say, "Yeah, no big deal."

I'm exact; I wouldn't be happy. I wouldn't be sad. I am indifferent. Now what about points... what about points down here? What about a point like this? Well, that is clearly not preferable because, for example, that point I just showed; I can show a point on the indifference curve where I'm better off. For example, that point that I just... that's five pounds of fruit and about five bars of chocolate.

But assuming that the marginal benefit of more chocolate is positive, and the way I've drawn this, or the assumption is that it is, then I'm obviously getting more benefit if I get even more chocolate per month.

So anything down here below the indifference curve is not preferred, not preferred. Using the same exact logic, anything out here... anything out here, well, that would be good because we're neutral between all of these points on the curve. But this green point right over here, I have the same number of bars as a point on the curve, but I have a lot more pounds of fruit.

Looks like I have 11 or 12 pounds of fruit, so assuming that I'm getting marginal benefit from those incremental pounds of fruit, and we will make that assumption, then this right over here, anything out here is going to be preferred. So this whole area, this whole area is going to be preferred to everything on the curve.

Preferred, and the whole area down here is obviously not preferred to anything on the curve. And let me just show you this, not those points, so all of this, and let me do that in a different color actually because our curve is purple. Everything in blue, everything in blue is not preferred.

Now, the last thing I want to think about in this video is what the slope of this indifference curve tells us. When I talk about the slope, this is really kind of an idea out of calculus because we're used to thinking about slopes of lines. So if you give me a line like that, the slope is how much, how much does my vertical axis change for every change in my horizontal axis?

So in a typical algebra class, that axis is your y-axis; that is your x-axis. And when we think about slope, we say, "Okay, when I have a certain change in y, when I change in x by one," so we have something like this. When I change, I get a certain change in y. The triangle means change in Delta; change in y when I get a certain change in x, when I get a certain change in x.

And delta y, the change in y over change in x is equal to the slope. But this is when it's a line, and the slope isn't changing at any point on this line. If I do the same ratio between a change in y and a change in x, I'm going to get the same value. On a curve like this, the slope is constantly changing.

So what we really do to figure out the slope exactly at a point you can imagine, it's really the slope of the tangent line of that point, a line that would just touch at that point. So for example, let's say that I draw a tangent line. I'll draw my best attempt at drawing a tangent line; I'll do it in pink.

Let's say I have a tangent line right from our starting predicament just like that, and it looks something like that. And so right where we are, right where we are now, exactly at this point, if we veer away, it seems like our slope is changing. In fact, it definitely is changing; it's becoming less deep as we go forward to the right.

It's becoming more steep as we go to the left, but right there, the slope of the tangent line looks just like that, or you can view that as the instantaneous slope right there. We can measure the slope of the tangent line; we could say, "Look, if we want an extra, extra..." Let's see, this looks like about if we want an extra two.

If we want an extra two pounds of fruit, how many bars are we going to have to give up? How many bars are we going to have to give up? Well, it looks like we're going to have to give up, based on the slope right over there, it looks like we're going to have to give up five bars. So this is five, and this is two.

So what is your change in... what is the slope here? The slope here is going to be that your change in bars, and I should actually say this, this is negative right over there. It's going to be your change in bars, your change in chocolate bars over your change in fruit, over your change in fruit.

And in this situation, it is five bars for every two fruit, so bars per fruit, or you can say this is equal to -2.5 bars per fruit. Bars per fruit. So it's essentially saying exactly at that point how are you willing to trade off bars for fruit. Exactly at that point, it's going to change as things change along this curve, but it's saying exactly where you're sitting right now, you would be indifferent.

But it's only as you just slightly move or for an extra drop of fruit, an extra ounce of fruit, not even a whole pound, you'd be willing to trade off two and a half bars per fruit. And what this says, so you're willing to give up, since it's negative, you're giving up 2 and 1/2 bars of chocolate for every pound of fruit.

Now, it's going to be different once you have a lot more fruit. You're going to be much less willing to give up bars of chocolate. Over here, you have a lot of bars and not a lot of fruit, so you're willing to give up a lot of bars for fruit. Over here, if we go over here, the slope looks a little bit different.

Over here, it is much flatter. It is much flatter. So let me draw it in a color we haven't used yet. So over here, the tangent line looks something like this. It looks something like this. And let's say when you calculate it, when you calculate it, in order to get, I don't know, this looks like about five pounds of fruit, in order to get five pounds of fruit, you are going to have to give up, you're going to have to give up two bars.

So once again, the slope is the change in the vertical axis over the change in the horizontal axis. So over here, at this point, your change in bars over your change in fruit is going to be... well, you're going to give up two bars for every five fruit. So every five fruit, bars per fruit. Bars per fruit.

So this right over here is negative; this is 0.4. I’ll say B for F. So over here, you're willing to give up much fewer bars for every incremental fruit. Up here, you were willing to give many bars away for every fruit, and that made sense.

Over here, you had a lot of chocolate bars, not a lot of fruit, so you were willing to give up more bars for your fruit. And over here, you have many fewer bars, so you're much more resistant to giving up bars for fruit. But this number, this number, how many bars you're willing to give up for an incremental fruit at any point, at any point here, or you could view it as the slope of the indifference curve, the slope, or the slope of a tangent line at that point of the indifference curve—this right over here is called our marginal rate of substitution.

Marginal rate of substitution; it's a very fancy word, but all it's really saying is how much you're willing to give up of the vertical axis for an increment of the horizontal axis right at that point. It changes as soon as you move because this is a curve. It changes a little bit, but right at that point, for a super, super small amount, how many bars are you willing to give up for fruit?

And obviously, it changes as we go along this indifference curve.