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## Microeconomics

### 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 ) •  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.
• 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. • 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.
• 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? • 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.
• 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)? • 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.
• 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 • Can you have more than one indifference curve that is tangent to the budget line?
(1 vote) • 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, • 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? • 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.  