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

In this video we will examine the idea of ​​an indifference curve. Indifference curve. What is it? Describes all points all combinations of things against which I am indifferent. In the past, we considered maximizing the overall benefit. We will now talk about all the combinations which give us essentially the same overall benefit. I will draw a graph, which shows us all the different combinations 2 goods we are indifferent to. As we mentioned before, we focus on 2 types of goods, because if it were 3 types of goods, we would have to do it in three dimensions and with 4 types of goods it would be very abstract. Let's say that on this axis, the vertical axis, there will be a quantity.

We will stick to the comparison of chocolate and fruit. These are the only 2 things we consume. This will be the amount of chocolate in sticks. On the horizontal axis it will be the amount of fruit and it will be in pounds. This will be … 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 now at some point I consume 5 pounds of fruit a month and 15 bars of chocolate per month. That will get me right here. If someone asked: "Sale, how would you feel if I told you instead put, say, 10 bars of chocolate and 7 pounds of fruit? " I would say, “You know what? I'm indifferent. I don't care if I have … This is here … I wouldn't care if I had 15 bars of chocolate and 5 pounds of fruit or if I have 10 bars of chocolate and 7 pounds of fruit.

I'm indifferent between the two. I found out what I like and what benefits me and satisfies me and I get the same overall benefit at any of these points. Both of them are on the same indifference curve. In general, I can sketch all different combinations, which bring me exactly the same overall benefit and it might look something like this. I will try to draw it as best I can. I'll make it purple. It might look something like this. Then I will continue down this way. At any point on this curve here I am indifferent to my current dilemma 15 bars and 5 pounds.

This is my indifference curve. Indifference, indifference curve. Now let's think about it. Of course when I move here for 20 pounds of fruit and … i don't know it looks like about 2 bars of chocolate. The same benefit for me based on my preferences, where I started. If someone exchanged everything, I would just shrug and said, "No big deal." I wouldn't be happy. I wouldn't be sad. I'm indifferent. What points down here? How about a point like this? This is clearly disadvantageous, because for example the point I just showed … I can show a point on the indifference curve, where I'm better at it. For example, the point I just showed is 5 pounds of fruit and about 5 chocolate bars. Assuming marginal utility more chocolate is positive, the way I drew it here, is the assumption that of course I get more benefits, when I get more chocolate a month. Anything down here under the indifference curve not advantageous.

It is not advantageous. Using the same logic anything here will be good because we are neutral between all these points on the curve. At this green point here I have the same number of bars both at a point on the curve, but I have far more pounds of fruit. Looks like I have 11 or 12 pounds of fruit. Assuming I get a marginal benefit of these additional pounds of fruit, we will assume that this here, anything here will be advantageous.

This whole area is preferred before what's on the curve. Preferred is. This whole area downstairs of course we do not prefer before anything on the curve. Just to show you that these are not the points. I'll do it in a different color, because our curve is purple. To all blue we do not prefer. One last thing I want to think about in this video is what tells us the inclination of this indifference curves. When I talk about inclination … and this is really kind of a computational idea. We are used to thinking about the slopes of the lines. If you give me a line like this, her inclination is how much my vertical axis changes every time I change on my horizontal axis.

In a typical algebra class this axis is your Y axis, this is your X axis. When we think of inclination we say, "When I have some change in Y, when I change X by 1. " We have something like that. When I change … I get some change in Y. That triangle is a delta and means change. Change Y, when I get some change X. … Delta Y, change Y angled change X equals the slope. This is when it's balanced and the inclination does not change. At any point on this line, when I make the same ratio between change Y and change X, I get the same value. On a curve like this the inclination is constantly changing. What we really do to find the slope exactly at the point … You can imagine that it's really a slope tangent at a given point, a line that just touches at that point. For example, let's say I drew a tangent. I will do my best, to draw a tangent. I'll make it pink. Let's say I have a tangent right from our initial claim exactly like that.

It looks something like this. … Right where we are now exactly at this point. When we turn away, it seems that our inclination is changing. Actually is definitely changing. It's less steep, as we move to the right. It becomes steeper, as we move to the left. Right here inclination on the tangent it looks like this or you can look at it as a momentary inclination here. We can measure the tendency to be tangent. We could say: "If we want extra … This looks like … If we want 2 extra pounds of fruit, how many sticks will we have to give up? How many sticks will we have to give up? " Looks like we're going to have to give up based on the slope here it looks like we're going to have to give up 5 sticks.

This is 5 and this is 2. What is your change in … What is the inclination here? The slope will be here your change in sticks. Actually, I should say this is negative here. It will be your change in the sticks, your change in chocolate bars broken your change in fruit. … In this situation that's minus 5 bars angled every 2 fruits you get. Fruit chopsticks. Or you can say it's equal minus 2.5 sticks broken fruit. Fruit chopsticks. It basically tells us exactly at this point how are you willing to exchange fruit sticks. Exactly at this point that will change as things change along this curve. Let's say exactly where you are right now, you would be indifferent if you move slightly or there would be a significant drop in fruit.

ounces of extra fruit not even a whole pound, you would be willing to exchange 2.5 sticks broken fruit. This says that you are willing to give up because it's negative give up 2.5 bars of chocolate for every pound of fruit. Now it will be different. Once you have a lot more fruit, you will be far less willing give up chocolate bars. You have a lot of sticks here and not a lot of fruit, so you are willing to give up many sticks for fruit.

Here, when we move here the slope looks a little different. It's much flatter here. It's much flatter. I'll draw it with a color we haven't used yet. Here the tangent looks something like that. It looks something like this. Let's say when you calculate it, to get … i don't know this looks like about 5 pounds of fruit. To get 5 pounds of fruit, you will have to give up 2 sticks. Once again inclination is change on the vertical axis angled change on the horizontal axis. Here at this point your change in sticks broken your change in fruit will be… You give up 2 sticks for every 5 pounds of fruit. Fruit sticks. … This here is negative this is minus 0.4 … I will say T divided by L. Here you are willing give up fewer sticks for each additional fruit. You're willing up here Give up many sticks for each fruit.

That makes sense. You had a lot of chocolate bars here, not much fruit so you were willing to give up more sticks for your fruit. Here you have far fewer bars. You are far resistant give up fruit sticks. This number, how many sticks are you willing to give up for more fruit at a given point, at that point here or you can look at it as on the slope of the indifference curve. Tilt or the slope of the tangent at a given point in the indifference curve. This here is called the marginal rate of substitution. Marginal rate of substitution. It sounds sublime, but it just really says how much you are willing to give up something on the vertical axis for the increment on the horizontal axis. It is at this point that this changes. Once you move, because this is a curve, it changes a bit. Right at this point for a very small amount how many sticks are you willing to give up? Of course, that is changing, as we move along the indifference curve..