# Indifference curves and marginal rate ofÂ substitution

## Video transcript

In this video we're going to explore the
idea of an indifference curve. Indifference curve. What it is, is it describes
all of the points, all of 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 of the combinations that essentially give us
the same total utility. Let's draw a graph that tells us all of the
different combinations of 2 goods, to which we are indifferent. Like we've mentioned before, we're focusing on 2 goods, because if we did 3 goods we would have to do it in 3 dimensions and 4 goods would get very abstract. 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 2
things that we consume. This is going to be the
quantity of chocolate, in bars. In the horizontal axis, this is going to be the quantity of fruit, and this is going to
be in pounds of fruit. This will go ... Let's see, this is 10. This is 20. This is 10 and this is 20. This will be 15, 5. 5 and then 15. Let's say that right now, at some point, I am consuming 5 pounds of fruit per month and 15 bars of chocolate per month. That would put me right there. If someone were to ask, "Sal, how would you feel
if 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 am indifferent." I wouldn't care whether I have ... This right over here is ... 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 2. 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. 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, and 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. Then, keep going all
the way down like that. Any point on this curve right over here, I'm indifferent, relative
to my current predicament of 15 bars and 5 pounds of chocolate. That is my indifference curve. Indifference, indifference curve. Now let's think about it. Obviously, if I go all over here, 20 pounds of fruit and ... I don't know, that looks like about 2 bars of chocolate. To me, the same utility, based on my preferences, as where I started off with. If someone just swapped everything out, I would kind of just shrug my shoulders and say, "No big deal." I wouldn't be happy. I wouldn't be sad. I am indifferent. What about points down here? What about a point like this? That is clearly not preferable, because, for example, that point I just showed, I can show a point on
the indifference curve where I am better off. For example, that point that I just did, that's 5 pounds of fruit and about 5 bars of chocolate. Assuming that the marginal benefit of more chocolate is positive, in the way I've drawn this, the assumption is that it is, then I'm obviously getting more benefit if I get even more chocolate per month. Anything down here, below the indifference curve, is not preferred. Not preferred. Using the same exact logic, anything out here, well that would be good, because we're neutral between all of these points on the curve. 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. It looks like I have 11
or 12 pounds of fruit. Assuming that I'm getting marginal benefit from those incremental pounds of fruit, we will make that assumption, then this right over here, anything out here is going to be preferred. This whole area is going to be preferred to everything on the curve. Preferred. The whole area down here is obviously we've not preferred to anything on the curve. Just to show you that
it's not those points. Let me do that in a
different color, actually, because our curve is purple. Everything in blue, is not preferred. The last thing I want to
think about in this video, is what the slope of this of this indifference curve tells us. When I talk about the slope, and this is really kind of
an idea out of calculus. We're used to thinking
about slopes of lines. If you give me a line like that, the slope is, how much does my vertical axis change for every change in my horizontal axis. The typical algebra class, that axis is your Y axis, that is your X axis. When we think about slope we say, "Okay, when I have
a certain change in Y" "when I change in X by 1." 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. Delta Y, the change in Y over change in X, is equal to the slope. This is when it's aligned and the slope isn't changing. At any point on this line, if I do the same ratio between the change in Y and the change in X, I'm going to get the same value. On a curve like this, the slope is constantly changing. What we really do, to figure out the slope exactly to point, you can imagine it's really the slope of the tangent line at that point, a line that would just
touch at that point. For example, let's say
that I draw a tangent line. I'm going to 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 out starting predicament, just like that. It looks something like that. It looks something like that. Right where we are now, exactly at this point. If we veer away it seems like our slope is changing. When in fact it definitely is changing. It's becoming less deep as we go forward to the right. It's becoming more deep as we go to the left. Right there, the slope of the tangent line looks 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 â€¦" This looks like about ... "If we want an extra 2 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?" 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 5 bars. This is 5 and this is 2. What is your change in ... What is the slope here? The slope here is going to be your change in bars. I should actually say this is a 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. In this situation, it is negative 5 bars for every 2 fruit that you get. So, bars per fruit. Or, you can say this is equal to negative 2.5 bars per fruit. Bars per fruit. 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. Say, exactly where
you're sitting right now you would be indifferent only as you just slightly move, or for an extra drop of fruit an extra ounce of fruit, not even a whole pound, you would be willing to trade off 2.5 bars per fruit. What this says, so you're willing to give up, since it's negative you're giving up 2.5 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. Let me draw it in a color
we haven't used yet. Over here the tangent line looks something like this. It looks something like this. Let's say, when you calculate it, in order to get ... I don't know, this looks like about 5 pounds of fruit. In order to get 5 pounds of fruit, you're going to have to give up 2 bars. Once again, the slope is the change in the vertical axis, over the change in the horizontal axis. 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 2 bars for every 5 fruit. Bars per fruit. Bars per fruit. This right over here is negative, this is negative .4, negative 0.4. I'll say B for F. Over here you're willing to give up fewer bars for every incremental fruit. Up here you were willing to give many bars away for every fruit. That makes 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. Over here, you have many fewer bars. You're much more resistant to giving up bars for fruit. This number, how many bars you're willing to give up for an incremental fruit, at any point, at any point here, or you can 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. Right at that point, for a super, super small amount, how many bars are you willing to give up? Obviously it changes as we go along this indifference curve.