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## AP®︎/College Microeconomics

### Unit 1: Lesson 6

Marginal analysis and consumer choice- Marginal utility and total utility
- Visualizing marginal utility MU and total utility TU functions
- Total Utility and Marginal Utility
- Utility maximization: equalizing marginal utility per dollar
- Marginal utility free response example
- Marginal benefit AP free response question
- Utility Maximization

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# Marginal utility and total utility

AP.MICRO:

CBA‑2 (EU)

, CBA‑2.A (LO)

, CBA‑2.A.1 (EK)

, CBA‑2.A.2 (EK)

, CBA‑2.A.3 (EK)

, CBA‑2.A.4 (EK)

, CBA‑2.B (LO)

, CBA‑2.B.1 (EK)

, CBA‑2.B.3 (EK)

When allocating a budget, we can use the concepts of marginal utility and marginal benefit to help us decide where our money is best spent. In general, we should allocate our budget towards items that will provide us with the highest marginal utility or marginal benefit. This way, we will be maximizing the satisfaction or value we receive from our budget. Created by Sal Khan.

## Want to join the conversation?

- Is there any exception to the Law of Diminishing Marginal Utility ?

That is that as more units are consumed the utility obtained rises.(32 votes)- Yes: addictive substances. The more you consume, the more you will give up to get an additional dose.(87 votes)

- But how do economists actually calculate marginal utility? How can you assign a "figure" to the level of "satisfaction"? How can you know the MU from first chocolate bar to the second drops 20% and not 30% for instance? When you make a vague concept like satisfaction mathematical and represent it by figures, they should be accurate or tend to be accurate, because you're gonna rely on all their graphs and conclusions inferences derived from them. No?

(sorry for my English though)(23 votes)- The marginal utility is different for each person. It isnt a value that you can read in a table somewhere. If you are looking at a group of people that are allergic to fruits then their marginal utility will be different than yours for example. But you can conduct surveys and statistically say things like "The average english 18 year old boy has a utility function that looks like ...."(31 votes)

- alright, this sort of confused me around the10:36mark when Sal talks about spending the 3rd dollar. the fruit costs $2/lb, so you cannot purchase a pound of fruit for just $1 (the third dollar). you would need to spend dollars 3 and 4 to purchase that pound of fruit.

i know that he clarifies things a bit more when talking about the 4th and 5th dollars, where each can only purchase 1/2 a pound of fruit. but just for the sake of clarification, if you were to opt on purchasing fruit with the 3rd dollar, you would need to spend the 3rd AND 4th dollar to get the 60 marginal units of satisfaction or whatever it's called right?(14 votes)- It messed with me too. He saying you can buy 1 Lb for $1 and it will give you 60 MU. What got me was the numbering of the MU of fruit. The MU/$ scale for fruit should be redo to state 0.5LB=MU 60, 1Lb=MU60, 1.5LB= MU50, 2LB=MU50, 2.5LB=MU25, 3LB=MU25 Etc.. When stated like this you can compare the MU cost of 1 bar to 0.5Lb or dollar to dollar. Does this help?(11 votes)

- If anyone is wondering - the "utility points" are called "utils". This is the unit they are measured in that my economics professor teaches anyway. So for example on the last two dollars spent, you would get 120 utils.(16 votes)
- What is barter system? explane with example,(3 votes)
- A barter economy is a cashless economic system in which services and goods are traded at negotiated rates. For example if i want eggs but i can only produce milk i would barter (trade) my milk with eggs provided by someone who produces eggs.(5 votes)

- It is said that as we get more and more of anything, our marginal utility falls. Can this be applied to money as well?(1 vote)
- It applies perfectly well to money. The utility I gain going from $100 to $200 is a lot higher than the utility I gain going from $5000 to $5100 (per week, month, or whatever unit of time over which you are measuring).(6 votes)

- I read from a book that the utility is maximized when MUx/Px=MUy/Py. Why by using this equation can we find the combination with maximized utility with this equation?(3 votes)
- The equation is equivalent to: MUx / MUy = Px/Py, so the ratio of the marginal utilities is equal to the ratio of prices. Therefore, increasing your collection by a marginal unit of X (& decreasing by a marginal unit of Y) has the same utility and same cost as the initial collection. The same is true if X is decreased by a marginal unit, and Y is increased by a marginal unit (assuming that the commodities can be divided into small enough units, technically continuous). Thus the total utility derived cannot be increased by trading a marginal unit of X for Y, or Y for X, so the total utility derived from the collection is at a maximum.

A more intuitive way of thinking about it is to consider the individual's indifference map related to the two commodities. The total utility is maximised at the point on the budget line [possible collections of X and Y the consumer can buy with a given amount of money], where an indifference curve is tangential to the budget line [assuming that the indifference curve is convex to the origin and likewise that the law of diminishing marginal utility indeed holds for each of the commodities]. At this point, the gradient (derivative) of the indifference curve (MUy/MUx) equals the gradient of the budget line (Py / Px) so MUy/MUx = Py/Px.(3 votes)

- In the example of the video the first chocolate bar gave 100 marginal "satisfaction points" and the second bar gave 80 marginal "satisfaction points".

Say there were no fruits and I wanted to have 100 marginal "satisfaction points", would I just buy the next 2 bars at once?(2 votes)- Not really. Think about it this way - if you eat one chocolate bar, after a long time of having no chocolate, boy is that bar GOOD. That is the absolute best a bar can taste. That's the 100 points bar. But the bar you have immediately after it, it's good alright, mmm, but it doesn't quite taste the same as the first bar. And the tenth bar is making you feel positively queasy.

There's not much you can do to make the second bar as good as the first, so marginal satisfaction is always going to decrease with the second bar.(5 votes)

- Is it possible to compare the utilities of two different persons, given that the budget constraint for them is equal?(2 votes)
- I think you can compare the utilities in relation. Lets not use colors but real items. For example oranges and apples. I like apples more than oranges and so do you. But how many oranges would you "pay" to get one first apple? I might say: If I can have 1 apple I am willing to give you 3 oranges. But you might say "I only give you 2 oranges for one apple". So who like the first apple more?(2 votes)

- What is marginal benefit, and what is marginal cost?(2 votes)

## Video transcript

What I want to do in this
video is think about a concept that we've already thought
about multiple times in the context of
many, many videos. And this is the idea of
utility-- utility, which is really just a way of
saying how much benefit or satisfaction or
value do you get out of getting a good or service. But the angle that we're
going to take in this video is going to be
slightly different. In the past, when we were
measuring benefit or value, we either measured
in terms of dollars, where we said, hey, the benefit
of getting an incremental Honda Civic was $5,000. And we talk about
the incremental-- we're talking about, and we've
heard the word many times-- we were talking about
the marginal benefit. Or early on, when we
talked about the production possibilities
frontier and we talked about the marginal benefit
of another squirrel, we were talking about
it in terms of berries. We were talking
about it in terms of another good or service. What we're going
to do in this video is just think about
it in absolute terms. We're just going to think of
some arbitrary way of measuring utility and then just
assign values to. What's the value of
getting one chocolate bar? And then what's the value that
we give to the next chocolate bar and then the
chocolate bar after that? And we're going to do the
same things about fruit. And from that,
we're going to see if we can build up
some of the things that we already know
about demand curves and how things relate to price
and the price of other goods and things like that. And in particular, we're going
to focus on marginal utility. So obviously, you could
have total utility. If I have four
chocolate bars, you could say the total utility I'm
getting from all four of them. Or, you could think
about marginal utility, the utility I'm getting from
the next incremental chocolate bar or the next
incremental pound of fruit. And before I move on,
there's one thing-- and this was a point
of confusion for me when I first learned
this-- is OK, I'm using the word
marginal utility now. In the past, I've used
the word marginal benefit. They sound very similar. In fact, I even used
the word benefit when I defined the word utility. How are these two
things different? And the simple answer is,
conceptually, they aren't. Conceptually, they are
the exact same thing. The difference is
how the words tend to be used in the context of
a traditional microeconomics class. So when people
talk about utility, they tend to measure it
in terms of some type of absolute measure that
they just came up with. You can view them
as utility unit, some type of satisfaction units. While when they talk
about marginal benefit, they tend to measure
it either in dollars or in terms of some other goods. But I've seen either
term used either way. So they really do mean
the exact same thing. But in this video, we're
going to use the term utility, and we're going to come
up with a measuring scale, and it's a somewhat
arbitrary one. And we're going to
use that to come up with some conclusions about
the basket of goods someone might purchase depending
on different prices. So as you could imagine, I
pre-wrote these two things. We're going to talk
about chocolate bars, and we are going to
talk about fruit. So right here in these
little tables here, I've shown the marginal
utility of each incremental. In the case of chocolate
bars, each incremental bar, and in the case of fruit, each
incremental pound of fruit. So this is saying that first
chocolate bar-- obviously, if I have no chocolate
bars I'm getting no utility from
chocolate bars-- and this is saying that that
first chocolate bar has a marginal utility. So the utility of that next
incremental one is 100. I'm not saying $100. I'm not saying it's equivalent
to 100 pounds of fruit. I'm not saying it's
equivalent to 100 berries. I'm just arbitrarily
saying it is 100. And what matters
is not that this is 100 or 1,000 or a million. What matters is how this
compares to other things. So for example, if I--
let's say this is 100, and if I know that I like
fruit-- a pound of fruit-- 20% more than that
first-- Or if I like an incremental-- my first
pound of fruit-- 20% more, then I would have to say
that the marginal utility of my first pound
of fruit is 120. And this is what we
said right over here. And if, another way
to think about it is, if the marginal utility
of the second chocolate bar I get-- because
I've already enjoyed a little bit of chocolate bar,
and I'm a little chocolated out-- is 20% less than
that, then if this is 100, then this would have to be 80. I could have set this
to be 1,000 and this to be 800 and this to be 1,200. I could have set this
to be 10 and this to be 8 and this to be 12. What matters is, is
that they really just have the same ratios
between them that really do reflect my actual preferences. So let's just think
about this a little bit. My first chocolate bar,
I'm pretty excited. I just call it 100. The next chocolate bar, I'm
a little bit less excited about it. I've already had some chocolate. My craving has been
satiated to some degree, but I still like chocolate. So I'll call that an 80. We could call it 80
satisfaction units, whatever you want to call it. Then the next chocolate
bar after this-- now I'm starting to get pretty stuffed,
and I'm really chocolated out. And so I'm not getting
as much benefit from it. And then finally if you give
me another chocolate bar, it's even less. And if we were to list
a fifth chocolate bar, I might not want it at all. My marginal utility
might go to 0 maybe for that fifth chocolate bar. Maybe that sixth chocolate bar,
I have to somehow get rid of it somehow, because I'm so
tired of chocolate bars. Maybe it'll have a
negative marginal utility. And we could think about
the same thing with fruit. The first pound of fruit, I'm
pretty excited about fruit. I have a fruit craving. I like that first pound
of fruit even more than that first chocolate bar. I like it 20% more. So I get to 120, you could
call it utility points or whatever arbitrary
unit you want to call it. Then my next pound
of fruit, once again I'm having diminishing
utility, diminishing benefit as I get more and more
incremental pounds of fruit. Now, it's very
important to realize this is marginal utility,
not total utility. This is a utility I'm getting
from each incremental pound. It's positive, so
I'm still enjoying that next incremental pound. I'm just enjoying it a little
bit less than the pound before. And to realize what
total utility is, if I were to have
two pounds of fruit, I would have 120 of utility
from that first pound. And then I would have 100
from the second pound. And so you would say I had
a total utility of 220, you could call them utility
units, from both pounds. Now with just the information
that I've given here, there's a few things
you could say. You could say, well look,
my first pound of fruit I enjoy more, 20% more than
my first chocolate bar. You could also say that
my second pound of fruit, I enjoy it or I could derive
about the same amount of value as my first chocolate bar. You could say that my
second chocolate bar I enjoy less than my
first chocolate bar. You could even say 20% less
if these numbers are good. But this still
doesn't give you a lot of information about
how you would actually spend your money. You might say, well,
obviously wouldn't you want to just buy fruit
over chocolate bars, or at least that first pound of
fruit over that first chocolate bar? Well, you might, but it depends
on how much that fruit actually costs. Just looking at this
alone, we can just make relative judgments
about how much we prefer each incremental
bar or each incremental pound or them relative to each other. But it really
doesn't tell us how we would spend our actual money. So let's think about things. Let's put some prices
on some of these goods and think about how
we would actually allocate our dollar given
these marginal utility numbers right over here. So let's say that the
chocolate bars are $1 per bar. And let's say that the
fruit is $2 per pound. So this is going
to be per pound. This is going to be per bar. And what we're
going to think about is we're going to think
about marginal utility for that incremental
chocolate bar per price of that incremental
chocolate bar. And here the price is going
to be at $1 per pound. So here, for that first bar,
I'm going to be spending $1, and I'm getting 100
marginal utility points, whatever
you want to call it. So I'm getting 100 marginal
utility points for that dollar. So I'm getting 100 marginal
utility points per dollar. Here, same logic. I'm getting 80 marginal
utility points per dollar. This is pretty simple math. Here I'm getting 60 marginal
utility points for the dollar. Here I'm getting 40. So that doesn't seem
too interesting. It might be a little bit
more interesting here. What is the marginal utility
per incremental fruit that I'm getting per dollar,
per price, or actually per price of the incremental fruit here? Well here, that first
pound of fruit I'm getting 120 marginal utility
points we could call them. But I paid $2 for it. So 120-- let me
write it over here. So for that first
incremental fruit, the marginal utility for
that first fruit is 120. And the price of that first
pound of fruit is equal to 2. So I'm getting 60 marginal
utility points per dollar. I'm getting 60. Here, 100 marginal utility
points, but I'm spending $2. So that's 50 points per dollar. This is 25 points per dollar. This is 10 points per dollar. Now this makes things a
little bit more interesting. If I had $5 to spend, how
would I want to spend my $5? What you really just
want to think about, where are you getting the most
satisfaction for each dollar? Where are you getting the
most bang for your buck? So where am I going to
spend my first dollar? So dollar one. So let's think about
it a little bit. My first dollar,
where am I going to get the most
satisfaction per dollar? Well, I get the
most satisfaction per dollar right over here. I get 100 satisfaction
units for a dollar. Even though I like
a pound of fruit, I'm getting less
satisfaction per dollar. So I'm getting less
bang for my buck. So my first dollar is going
to go right over there. I'm going to buy one candy bar. Then where am I going to
spend my second dollar? So once again, I just want
to look at all of my options, and we're going
to assume that I'm going to spend my $5 on
either of these two just to limit our universe. Once again, I'm going to
maximize my bang for buck. I get 80 satisfaction points
or marginal utility points over here per dollar. I only get 60 over here. So I'm going to buy even
a second chocolate bar. Let's keep going. Where am I going to
spend my third dollar? Now, it gets a little
bit interesting. I could spend my third dollar
right over here and get 60 points per dollar,
or I could spend it over here and get 60
points per dollar. I'd actually get
the same amount. There are both 60
points per dollar. So I'm kind of neutral. I'm going to get the
same bang for my buck whether I get
another chocolate bar or whether I get another fruit. So just for
simplicity, let's say I get another chocolate bar. I could have got the fruit too. It's really a toss up. I could flip a
coin, and I choose to get another chocolate bar. So I first spent my first
$3 on three chocolate bars. Now where am I going to
spend my fourth dollar? Well, my fourth dollar, now
my best bang for my buck isn't to get another
chocolate bar. I'm only going to get
40 units per buck there. Now it is to spend it on fruit. So now the next dollar I could
spend on half a pound of fruit, and I would get this. So my fourth dollar
I could spend on this for half
a pound of fruit because it's $2 per pound. And then I could spend my
fifth dollar there too. So this is my fourth and my
fifth dollar because it's $2. You could think of it
that we're spending $2 for one pound of fruit. And we're getting 60
utility points per dollar. So we're getting the best bang
for our buck right over there. But what was useful
about this is it allowed us without
thinking about money to say how much do we like
these things irrespective of their actual price and
then give it a certain price. It allowed us to think
rationally about, well, how would we actually
spend our money. In this case, when
chocolate bars are $1 and fruit is $2 per
pound, we decided to buy three chocolate bars
and only one pound of fruit.