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### Course: Microeconomics>Unit 5

Lesson 3: Utility maximization with indifference curves

# Optimal point on budget line

Using indifference curves to think about the point on the budget line that maximizes total utility. Created by Sal Khan.

## Want to join the conversation?

• What is Marginal Rate of Substitution?
(Sal Mensioned at )
(16 votes)
• the Marginal Rate of substitution measures how much you have to give up a certain commodity to get another commodity while still being on the same level of satisfaction.
(50 votes)
• I was a little confused by the way Sal drew one indifference curve, and then to find the optimal point, he drew a different indifference curve. Is there an optimal point with the original indifference curve? Do you have to actually create a new indifference curve to find the optimal point? I thought the indifference curve was a static thing based on preferences.
(21 votes)
• The indifference curve is a static thing based on preferences. However, there are an infinite number of indifference curves, each with a different value of utility.
What the indifference curve says is that every point along it gives the same value of utility. All other points, not along that indifference curve give different amounts of utility.
When Sal drew a second indifference curve, he was saying that the amount of utility that that first one gave wasn't right. In this case he wanted a curve with more utility. So he made one.
(15 votes)
• What is the point of Indifference Curves if you can just put them anywhere you want and have as many on the graph at once as you want? I don't see the point of them even existing at that point, because if you add another indifference curve to the right & above of a previous one, then it essentially just negates the old one, making it useless..Anyone else?
(6 votes)
• Hello Arjun, if you add another indifference curve to the right and above it does not negates the previous one, because they are not tangent to the budget line. There is only one indifference curve that is tangent to the consumers budget line and only at one point.

At the point where MRS = P1 / P2. The MRS derived from the indifference curve and I believe was not shown in the video but it should be equal to the Price of chocolate divided by the price of fruit, which is 1/2. You are essentially willing to give up one unit of chocolate for twice as many units of the fruit, this is MRS.

So, my point is there is only one indifference curve that is tangent at only one point to the budget line. You can draw other indifference curves above and below that, but they would not negate the one. Since it is at only one point where consumer reaches its equilibrium and derives the maximum utility (pleasure) from the bundle of goods given his budget constraints (depicted by the budget line).

All the other indifference curves depicted as an aid to the example of inferior options or unattainable options.

One thing to keep in mind with this budget line and indifference curve equilibrium is that we are trying to figure out what combination of goods would maximize our utility given our budget constraints.

The budget line shows us simply the quantity of the combination of the products attainable given our limited income. And the indifference curve shows us simply utils derived from this combination.

At the tangency point, we are at optimum.
(3 votes)
• Given this example of chocolate and fruit, what dictates the indifference curve? Is it the person's particular feeling / mood at the time of polling?

What dictates the indifference curve points on a wider example (say: a market)?
(5 votes)
• It's the preferences that dictate the utility funtion, thus the indifference curves. However, preferences are very difficult to measure and create a function from them. Still, they are very useful, as in many cases assuming a given type of utility function (like Cobb-Douglas, perfect substitutes, etc...) can well serve our purposes. Assuming for example in a model, that the consumer has Cobb-Douglas utility function might seem as a too great simplification, but they model usually explains what we experience in the real world, so economists believe it's worth using that utility function, even though we are not completely sure about the preferences of the consumer.
(3 votes)
• is the shape of the indiffent curve on the original budget lineidentical with the shape of the indifferent curve on the new budget line? I guess these two curves have different shape at each optimal point. and one more. what was his intention of drawing the first indifference curve wich intersects the original budget line at　(1, 18) and (8, 4)?He came up with the curve out of thin air?
(3 votes)
• Good questions. I'll answer your questions backward, as I think it will make more sense.

Yes, he created those curves out of thin air. The indifference curves he drew are hypothetical examples—to derive one would be beyond the scope of this video (and in fact, this site, as it currently deals with first year microeconomics).

His purpose of drawing the first IC—which intersects (1,18) and (8,4)—is to show that there are two bundles (those two mentioned) that provide a certain level of utility and are "possible" (i.e., they can be purchased within a particular budget). What this means, which he goes on to show later in the video, is that there is another indifference curve—a "higher" IC—that only touches the budget line at one point. The point where an IC just touches (i.e., is tangential) to the budget curve is the bundle that provides the highest utility within the constraints of a budget (starting at ).

Because the slope of the indifference curve is constantly changing at each point along it, it will "look different" depending on the point of the IC that intersects or touches the budget curve. The optimal point on the first budget line will likely have a different slope than the optimal point on the second (i.e., "new") budget line.
(3 votes)
• What is the difference between these two equations? 1. Px/Py = MUx/MUy and 2. MUx/Px = MUy/Py. I know that equation 1 is the budget line slope equal to the indifference curve slope which shows the utility maximization point relative to a budget constraint. But isn't equation 2 the same thing? I'm a bit confused. Thanks
(2 votes)
• Both formulae are the same thing; variables have simply been shifted around.
(4 votes)
• Can you have more than one indifference curve that is tangent to the budget line?
(1 vote)
• You can have more than one indifference curve that is tangent to the budget line, but it means that the indifference curves belong to different person having the same budget constraint.
(4 votes)
• Hi Sal,
Is the underlying assumption in this video that "consumption" of either fruits or chocolates are the only ways one could spend money? Or perhaps, is "consumption of any good" the only way to maximize one's utility? Is it possible that "saving money" could be another commodity like fruit or chocolate, and one could plot that in this budget graph and then, plot an indifference curve for that as well, so as to figure out one's optimal point in budget line? Thank you,
(2 votes)
• When we study the indifference curve,we do assume that there are only two goods in the economy. When we study the "savings" that comes under inter temporal choices where we study the consumption today and consumption in future that count as "savings" which is taken as the other commodity. Hope that solves the doubt!!
(2 votes)
• I was reviewing my microeconomic concepts and don't really want to open Varian. Question. We choose the point where the indifference curve is tangent to the budget constraint because at any point where the bc crosses the ic, there is another point which is affordable and at a higher ic? So in other words we can afford another bundle that gives us a higher utility
(2 votes)
• Exactly. Indifference curves are plotted for a particular value of 'total utility', and how different combinations of goods would add up to that value of total utility. If the Budget Line crosses the IC, it signifies that a higher value of 'total utility' is achievable, so we plot Indifference curves for those higher values, till we achieve the curve where the Budget line is tangent at exactly one point - giving the maximum value attainable of 'total utility'.
(1 vote)
• what happens when the inflation increases the price of apple by 20 percent and orange by 35 percent. Does the budget line shift parallel or rotate inward, outward or not at all for these two commodities and why
(2 votes)
• i suppose the budget line would shrink inwards. the budget line represents how much of each good you can get for your budget. if the price of the goods increases, the amount you can get decreases. therefore the x and y intercepts come closer to the origin (since you cant buy as much with your budget)
(1 vote)

## Video transcript

So let's just review what we've seen with budget lines. Let's say I'm making \$20 a month. So my income is \$20 per month. Let's say per month. The price of chocolate is \$1 per bar. And the price of fruit is \$2 per pound. And we've already done this before, but I'll just redraw a budget line. So this axis, let's say this is the quantity of chocolate. I could have picked it either way. And that is the quantity of fruit. If I spend all my money on chocolate, I could buy 20 bars of chocolate a month. So that is 20. This is 10 right over here. At these prices, if I spent all my money on fruit I could buy 10 pounds per month. So this is 10. So that's 10 pounds per month. That would be 20. And so I have a budget line that looks like this. And the equation of this budget line is going to be-- well, I could write it like this. My budget, 20, is going to be equal to the price of chocolate, which is 1, times the quantity of chocolate. So this is 1 times the quantity of chocolate, plus the price of fruit, which is 2 times the quantity of fruit. And if I want to write this explicitly in terms of my quantity of chocolate, since I put that on my vertical axis and that tends to be the more dependent axis, I can just subtract 2 times the quantity of fruit from both sides. And I can flip them. And I get my quantity of chocolate is equal to 20 minus 2 times my quantity of fruit. And I get this budget line right over there. We've also looked at the idea of an indifference curve. So for example, let's say I'm sitting at some point on my budget line where I have-- let's say I am consuming 18 bars of chocolate and 1 pound of fruit. 18-- and you can verify that make sense, it's going to be \$18 plus \$2, which is \$20. So let's say I'm at this point on my budget line. 18 bars of chocolate, so this is in bars, and 1 pound of fruit per month. So that is 1. And this is in pounds. And this is chocolate, and this is fruit right over here. Well, we know we have this idea of an indifference curve. There's different combinations of chocolate and fruit to which we are indifferent, to which we would get the same exact total utility. And so we can plot all of those points. I'll do it in white. It could look something like this. I'll do it as a dotted line, it makes it a little bit easier. So let me draw it like this. So let's say I'm indifferent between any of these points, any of those points right over there. Let me draw it a little bit better. So between any of these points right over there. So for example, I could have 18 bars of chocolate and 1 pound of fruit, or I could have-- let's say that is 4 bars of chocolate and roughly 8 pounds of fruit. I'm indifferent. I get the same exact total utility. Now, am I maximizing my total utility at either of those points? Well, we've already seen that anything to the top right of our indifference curve of this white curve right over here-- let me label this. This is our indifference curve. Everything to the top right of our indifference curve is preferable. We're going to get more total utility. So let me color that in. So everything to the top right of our indifference curve is going to be preferable. So all of these other points on our budget line, even a few points below or budget line, where we would actually save money, are preferable. So either of these points are not going to maximize our total utility. We can maximize or total utility at all of these other points in between, along our budget line. So to actually maximize our total utility what we want to do is find a point on our budget line that is just tangent, that exactly touches at exactly one point one of our indifference curves. We could have an infinite number of indifference curves. There could be another indifference curve that looks like that. There could be another indifferent curve that looks like that. All that says is that we are indifferent between any points on this curve. And so there is an indifference curve that touches exactly this budget line, or exactly touches the line at one point. And so I might have an indifference curve that looks like this. Let me do this in a vibrant color, in magenta. So I could have an indifference curve that looks like this. And because it's tangent, it touches at exactly one point. And also the slope of my indifference curve, which we've learned was the marginal rate of substitution, is the exact same as the slope of our budget line right over there, which we learned earlier was the relative price. So this right about here is the optimal allocation on our budget line. That right here is optimal. And how do we know it is optimal? Well, there is no other point on the budget line that is to the top right. In fact, every other point on our budget line is to the bottom left of this indifference curve. So every other point on our budget line is not preferable. So remember, everything below an indifference curve-- so all of this shaded area. Let me actually do it in another color. Because indifference curve, we are different. But everything below an indifference curve, so all of this area in green, is not preferable. And every other point on the budget line is not preferable to that point right over there. Because that's the only point-- or I guess you could say, every other point on our budget line is not preferable to the points on the indifference curve. So they're also not preferable to that point right over there which actually is on the indifference curve. Now, let's think about what happens. Let's think about what happens if the price of fruit were to go down. So the price of fruit were to go from \$2 to \$1 per pound. So if the price of fruit went from \$2 to \$1, then our actual budget line will look different. Our new budget line. I'll do it in blue, would look like this. If we spent all our money on chocolate, we could buy 20 bars. If we spent all of our money on fruit at the new price, we could buy 20 pounds of fruit. So our new budget line would look something like that. So that is our new budget line. So now what would be the optimal allocation of our dollars or the best combination that we would buy? Well, we would do the exact same exercise. We would, assuming that we had data on all of these indifference curves, we would find the indifference curve that is exactly tangent to our new budget line. So let's say that this point right over here is exactly tangent to another indifference curve. So just like that. So there's another indifference curve that looks like that. Let me draw it a little bit neater. So it looks something like that. And so based on how the price-- if we assume we have access to these many, many, many, many, many indifference curves, we can now see based on, all else equal, how a change in the price of fruit changed the quantity of fruit we demanded. Because now our optimal spent is this point on our new budget line which looks like it's about, well, give or take, about 10 pounds of fruit. So all of a sudden, when we were-- so let's think about just the fruit. Everything else we're holding equal. So just the fruit, let's do, when the price was \$2, the quantity demanded was 8 pounds. And now when the price is \$1, the quantity demanded is 10 pounds. And so what we're actually doing, and once again, we're kind of looking at the exact same ideas from different directions. Before we looked at it in terms of marginal utility per dollar and we thought about how you maximize it. And we were able to change the prices and then figure out and derive a demand curve from that. Here we're just looking at it from a slightly different lens, but they really are all of the same ideas. But by-- assuming if we had access to a bunch of indifference curves, we can see how a change in price changes our budget line. And how that would change the optimal quantity we would want of a given product. So for example, we could keep doing this and we could plot our new demand curve. So I could do a demand curve now for fruit. At least I have two points on that demand curve. So if this is the price of fruit and this is the quantity demanded of fruit, when the price is \$2, the quantity demanded is 8. And when the price is-- actually, let me do it a little bit different. When the price is \$2-- these aren't to scale-- the quantity demanded is 8. Actually let me do it here-- is 8. And these aren't to scale. But when the price is \$1, the quantity demanded is 10. So \$2, 8, the quantity demanded is 10. And so our demand curve, these are two points on it. But we could keep changing it up assuming we had access to a bunch of indifference curves. We could keep changing it up and eventually plot our demand curve, that might look something like that.