Indifference Curves - Video Tutorials & Practice Problems

Indifference Curves

now let's see how different consumption bundles different amounts of goods can lead to the same amount of happiness or satisfaction for the consumer. Alright, these are going to show us our indifference curves. So we talked about budget constraints and budget constraints show us consumption bundles that we can afford with our income. Okay, So we're talking about we have a certain amount of income, what can we buy with that income? Regardless of how happy that's gonna make us. Okay. And indifference curve, it disregards money. Now, we're not considering how much money things cost, we're just gonna think about the satisfaction. Alright? Shows consumption bundles that give the same amount of satisfaction. Or we use this term in economics utility for satisfaction. Okay. We're gonna define it right down here, utility one more time is the satisfaction or happiness that one receives from consuming from the consumption of goods. Okay. So you can imagine this is gonna be kind of an abstract topic, right? When we talk about utilities, we're gonna talk about the unit of utility is the util the utility, the measurement of utility. And we use this you to measure it. A U. For utility. But let's think about this like it's gonna be really hard to quantify how much utility you get from something, right? When you eat a slice of pizza, it's not like you're saying um I'm getting 150 you tills of satisfaction out of this or right that we can't really talk about it like that. It's pretty abstract but it does help us in these situations because we can quantify different levels of happiness or satisfaction based on our consumption. Alright, so we've got this utility concept and of course, whenever we talk about a new concept, we're gonna talk about marginal of that concept. So we've got marginal utility right here. And what is that? Gonna tell us? We should be pretty used to marginal at this point, we're gonna see that marginal utility is the additional right, marginal being additional. Right? What do we get additional satisfaction from consuming one more of the good? Right, marginal. That's the whole thing with marginal we add one more. How much extra satisfaction. How many extra you tills am I getting out of this extra consumption? Okay. And what we're gonna see is that utility follows that law of diminishing returns, right? We've seen diminishing returns before, and that's the idea of the more you consume the less marginal utility you're gonna get. So you can imagine the first slice of pizza you eat, you're gonna get tons of utility. Thousands of utility from that first first slice, the second slice of pizza, maybe 500 utility. Right? Third slice, 200 now you're starting to get full. You're not satisfied by the pizza as much so that utility keeps going down, right? It keeps decreasing as we eat more and more of the same good. Okay, so we have those diminishing returns. Let's go ahead and see indifference curves on the graph. Let's continue with our example of party boy paul. So party boy paul gains the same amount of utility from the consumption bundles shown in the table graph the indifference curve for P. B. P. S consumption of vodka and beer. So quick note we have to make about utility. There's no way that you could have figured this out, right? There's no way you could have known how much vodka and how much beer gives him a certain level of satisfaction. This kind of information has to be given to you. Okay? So let's look at this first table where we have utility of 500 right? Notice the utility is staying constant. The amount of satisfaction we get from all these different bundles A. B, C. And D. It's the same. So we would be indifferent if we had one Vodicka and nine beers or if we had two vodkas and four beers, four vodkas and two beers. All of these would provide the same amount of satisfaction uh to party boy Paul in this case. So let's start with this first indifference curve. Right? Where no matter what consumption we do along this curve, it will provide us 500. You tales of utility of satisfaction. So remember we still got vodka on this axis and the quantity of beer on this axis. Okay, so that our graph hasn't changed, right? We're still showing quantity and quantity on the axes. And now we've just got different bundles here. So let's start with bundle A. Where we have one vodka and nine beers. So one vodka and nine beers is gonna put us somewhere out here. Now put an A. Right there. Let's go on to be so be we have to vodka and four beer. So two vodkas and four beers puts us right around there. And that's B. How about C, bundle C. Has four vodka and two beers right here and finally D. Has seven vodka and one beer. So 56. This is seven right here one beer. There we go. These are our points. So that was point C. This is point D. Alright let's go ahead and connect these points and make our first indifference curve here. So it's gonna look something like this, right? That was pretty good. That's our first indifference curve. And this represents all of the possible combinations of vodka and beer that provide 500 you tails. Right? So this indifference curve shows us all the combinations where party boy paul will get 500 you tales of satisfaction. Now what about this crew? Where utility is 7 50. So he's getting more satisfaction from these bundles. Right? So you can imagine if he could pick from bundle A versus bundle C. He would be indifferent but if we told him you could pick from bundle A. And bundle F. He would want bundle F. Because it has more utility, right? He's gonna get more satisfaction out of that bundle. So let's go ahead and mark these in. I'm gonna draw this one in blue. So we've got bundle E. With two vodka and nine beer. That's gonna be right here. E. F. Is gonna have three vodka and five beer right there and notice these points where they are they're all further away right there, further out from the origin because they're providing more utility, Right? So we would imagine we want more, we're gonna consume more to get more utility. That's the idea here uh higher consumption is higher utility. So let's kind of see it continue. So how about five vodka and three beer. And then finally eight vodka up here. This was eight and two beers. So any of these combinations Would provide 750 you tills uh to party boy Paul, right? And anywhere else along the curve also provides that amount of utility. So we just picked out some key points here but there is a whole curve with all the different utility that party boy Paul can get. Man, that was pretty good too. So this one is our 750 you tails curve right there, right? So that's how we graph our indifference curves. And once what we've started to build here is what we call an indifference curve map. Okay, so the indifference curve map. It's basically a collection of indifference curves. So it's gonna be a bunch of different indifference curves representing the consumer's utility function, right? We've got different levels of utility and that's based on different levels of consumption. So you can imagine there's more than just these two curves we just represented to situations where he's gonna have 500 utility or 7 50. But what about a situation where you have 600 utility or 800 utility? 1000 utility. 100 utility. Right, There's gonna be all these different curves. And you could imagine that there would be infinite curves just like this going all the way up and all the way down here, right? There would be curves everywhere based on different levels of utility. And that is the indifference curve map. Alright, so each person is gonna have all these different indifference curves based on their uh joy the utility that they get from the consumption. Okay, so one last concept here is the marginal rate of substitution. Okay, so this marginal rate of substitution, it's the amount of a good the consumer is willing to give up for one unit of the other good. Okay, and when we talk about marginal rate of substitution, the easy way to think about it is is just the slope of the indifference curve at any point, at whatever point we choose. Okay, so when we do the slope, it can be tricky to find the slope at a point because it's constantly changing. When we have a curve like this, the slope is constantly changing compared to a straight line. If we had a straight line, the slope is constant and it would be one number the whole time. But here the slope is changing right, we see it change and it's steep at the beginning and then it starts to weigh and then it becomes very shallow, right? So if you don't remember, here is our formula for slope where we take the change in Y. Over the change in X. Right? How much did the Y. Change divided by? How much did the exchange? And you might remember this from algebra as the rise over the run, right, we're gonna see how much the up down change. That's the rise and the run is the left or right change. Now with the M. R. S marginal rate of substitution? It's always gonna be positive. We just want a positive number. Right? How many of these units are we giving up for the other? So it's not gonna be you know, which is a positive or negative. We just want the absolute value. We just want the number. So let's go back to this idea where we're talking about him getting 500 you tills right? The utility the indifference curve for the 500, you tills. And let's see what the marginal rate of substitution is when he's consuming seven vodkas. So when he's consuming seven vodkas, right? How many vodkas is he willing to give up for another beer if he wants one more beer? Well, he's currently got one beer right? When he's got seven vodkas. But he wants to get over to two beers. So what is that marginal rate of substitution? Well, he's gonna give up from seven down to four. So he's willing to give up three vodkas there for one more beer at this point. Right? Because he doesn't have that much beer. He only has one beer and he's got a ton of vodka. So you can imagine all those vodka shots. It gets a little boring after a while he wants a beer clears throw chill out a little bit. Right? So that beer is very valuable to him at this point because he doesn't have a lot of beer yet. So let's go on and see what that means. So, we had a rise, right? Sorry. We had the rise in that situation. Is this three? Right? We had three vodkas less. Our change in Y. Is three and our change in X. Is one. Right? The run right here goes from 1 to 2. We have one extra beer. So our rise over run is three divided by one M. R. S marginal rate of substitution is going to equal three in that case, but it's not constant. Remember we've got a curve. It's gonna be changing. So let's see how about when he's consuming four vodkas? What is his marginal rate of substitution? So let's do the same thing notice? So to get from one point to the next. We have to go down by two here and over by two. Right? So we went over by to hear from one point to the next. Because it's curved, right? It doesn't necessarily cross at this point right there. It can be curved and it could be crossing somewhere else. So what we're kind of doing is taking the average slope over this region. So the average slope over this region. This one up here, I'm gonna put the one up here. Right? So um over this region we decreased by two. And we also the rise was two. And the run was too as well. So we're gonna have to divide by two. R. M. R. S. Is equal to divided by two, which is equal to one. Notice. It changed right at this point. Since we already have some beer, were less willing to give up vodka. Right? We still want to keep some of our vodka. So we would only trade one vodka away from one more beer at this point. To stay indifferent and keep our satisfaction the same. Now, what about when we only have two vodkas behind me here. Right. What's gonna be the marginal rate of substitution when we're down to just two vodkas? You can imagine that he's going to be pretty possessive of these. He doesn't want to give up those vodkas really easily because he's only got a few left. Alright, So let's see what happens when he's in a situation where he's got two vodkas here. Well um to give up that vodka right? To give up that vodka, he's gonna have to get five beers, right? This is all the way out here is nine. So he'd have to get five beers to give up that one vodka at that point. So you can see that it takes a lot once we get to those edges, just like we saw at the beginning, he was willing to give up a lot of vodka to get a little more beer. Well now he's not willing to give up much vodka because he doesn't have so much left. Alright. So our rise was one the rise over run, right? The rise was one the run was five in this case, and it doesn't matter positive or negative. Remember we just want the absolute value. We want the number here. So the M. R. S. Is going to equal the rise of one, divided by five. The run which is just 1/5. So he would only be willing to give up 1/5 of vodka for another beer. Right? So just let's put it in in in words, in the in this first situation, the idea is that he would be willing to give up three vodka for one beer, right? And the same thing for the next one in the second box. He'd be willing to give up one vodka for one beer. And then in that final situation he'd only be willing to give up 1/5 of a shot of vodka for the next beer. Right, So that's about it here. Let's go ahead and move on to the next video.

Properties of Indifference Curves

So now that we've seen what indifference curves are, let's discuss some of the properties of indifference curves. So the first property is that higher indifference curves are preferred to lower indifference curves? Okay. And we saw that when we built our indifference curves, we saw that the utility was higher as we went further out, we were gonna be consuming more, so our utility was higher. So what we saw here This was the party boy Paul's utility indifference curves here, and this was 500 you tails. He got from this curve 750 you tales from this curve. So you imagine if he could pick a point on one of the curves he'd rather be on on the 750 curve, right? Because he gets more satisfaction out of that. And the logic here is that people prefer to consume more. The idea is as you take more, you consume more, you're getting more utility. Okay, the more you consume, the more utility you get. Alright, that's some capitalist stuff right there. And then we love that. So higher indifference curves result in more consumption as well. Okay, so when we're on a higher indifference curve, we have more consumption and we have more utility as well. So we're gonna say that people want to be on higher indifference curves to get more utility. Next is the property that in different curves are downward sloping, just like we see as well as they bow inwards and bow inwards. Okay, so the idea here is that consumers are generally gonna like both goods, right? This is why we're doing this whole topic is because they like both things. So what's gonna be a good mix of the two products? So you can imagine if one quantity is decreased, right? They like both of the things, if they're gonna get less of one thing, that means they're gonna be sad about that, right? They're gonna lose some utility from having less of that. That means they're gonna need more of the other thing to balance out that utility. So the other must be increased to remain indifferent, Right? And that's that property of downward sloping when one goes down the other goes up, and that's how we get the indifference curve, Right? So the next one is the bowing inwards. So when one, when consumption of one good is low, we're willing to give up uh more of the other good, right? When we only have a little bit of one good, we want more of that because we're getting more satisfaction when we have few of something. You can imagine when you only have one slice of pizza, that's second slice of pizza is gonna bring a lot of satisfaction when you've got 10 slices of pizza, and 11 slice of pizza doesn't bring you as much satisfaction. All right, So that's the idea, and that's why it's gonna bow inwards here, because you're gonna want to give up more of the other good and we're gonna get those drastic slopes and when we're near the edge, right? Where we're near the low quantity on this side, we have a really drastic this way, and we're on the low quality quantity for the y axis. We have a really steep this way. Okay, so that's why we get this bowing inwards kind of look and the last property here is that indifference curves never I'm gonna do it in caps to never cross. Okay, they're never gonna cross with each other. That's gonna be just impossible, right? Because what does this imply if they're crossing each other? This implies that, remember these different utility indifference curves, uh signify different levels of utility. So, we would say that this one is 500 utility right here, and this one is 7 50 utility. These two curves. Well, what's happening at this point? At this point, it's like Schrodinger's utility, it's at both times 500 utility and 7 50 utility at the same moment. Right? And that can't happen, right? That would not make sense. There has to be one level of satisfaction that you get from this level of goods. So, an intersecting point means that the same level of consumption results in different levels of utility and that's just impossible. Okay, so they're never gonna cross. They're always gonna kinda go out and out, just like we saw. Alright, so those are the properties of indifference curves. Let's go ahead and move on to the next video

Which of the following is true about indifference curves?

• A. Indifference curves shift outward as income increases
• B. When a consumer has more of one good, they are less willing to exchange it for a unit of another good
• C. Indifference curves show all combinations of goods that result in the same level of utility
• D. Both (a) and (c)

At different points along an indifference curve,

• A. The marginal rate of substitution remains constant
• B. The marginal rate of substitution is zero
• C. A consumer prefers the consumption points that are further from the origin
• D. A consumer does not prefer one consumption level over another

If the marginal rate of substitution is equal to 2 at a point on an indifference curve, then the consumer would:

• A. Give up 1 units of the 'y-axis' good for 2 units of the 'x-axis' good
• B. Give up 2 units of the 'y-axis' good for 1 unit of the 'x-axis' good
• C. Pay an additional $2 for one unit of the 'y-axis' good
• D. Pay an additional $2 for one unit of the 'x-axis' good