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# Allocative efficiency and marginal benefit

## Video transcript

We've already spent a
lot of time thinking about these six different
scenarios, all of which sit on the production
possibilities frontier, which means that in any
of these scenarios, we have achieved
productive efficiency. And it's true not just
of these scenarios. It's true of any of the
points on this curve. So you have achieved,
any point on that curve, productive-- let
me give ourselves some real estate on
the right-- efficiency. Which means, another
way to think about it, is that as soon as you're
at any point on that curve, if you want any more
of one of these things you have to give up
some of the other. So for example, if
you're at point C, and if you want more rabbits,
if you want 1 more rabbit, you're going to have to
give up some berries. Or if you're at point C
and you want more berries, you're going to have to
give up some rabbits. And that's true of any point
on the production possibilities frontier. A point over here-- let me
do this in a different color. So let's say at this
point right over here, you have not achieved
productive efficiency here because you can get more
rabbits without having to give up any berries. And you could get to Scenario
B. Or you could get more berries and not have to
give up any rabbits, and you would get to Scenario D. So this right over
here is inefficient. Now, all of these,
that's all good. All of these five
or six scenarios, we've achieved
productive efficiency. But which of these do we pick? How do we decide to
allocate our time? So what I want to talk
about in this video is allocative efficiency. And it's somewhat subjective,
based on the preferences of, if we are the hunter gatherer,
based on our preferences. But at least it
gives us a framework for thinking, which of these
meets our preferences the best. And to do that, I will review a
little bit from the last video. In the last video, we talked
about the marginal cost of each incremental rabbit. Or we said the opportunity cost
of each incremental rabbit, and the opportunity cost of
one incremental unit, that really is just
the marginal cost. So let's just write these
different scenarios. So let's write the scenarios,
scenario for short, scene for short. And then let's think
about the marginal cost of 1 incremental rabbit. I'll just draw a rabbit here. And it's going to
be given in berries. All right. Let's start with
Scenario F. And this is all review from
the last video. Sitting in Scenario F, if we
want to get 1 extra rabbit, we are going to have
to give up 20 berries. In Scenario E, if we're
sitting in Scenario E, and we want even 1
more rabbit we now have to give up 40 berries. So the marginal cost at
that point of 1 more, I keep wanting to say squirrel,
1 more rabbit is 40 berries. Now let's go to Scenario D.
And I encourage you to pause and do this yourself. It'll help if you
kind of work it out. Scenario D, the cost of 1
extra rabbit is now 60 berries. You go to Scenario C. The
cost is now 80 berries. So in Scenario C the
cost is now 80 berries. Finally you got to
Scenario B and the cost of, sitting in Scenario B, of
getting 1 extra rabbit-- you're going to have to
give up 100 berries. And I won't even
go into Scenario A, because it will be impossible
for you to have any more rabbits and you have no
more berries to give up. So these are all the
possible scenarios and the marginal costs of them. And we can actually
plot them on a line. So let me do that
right over here. This will be useful. So let me draw one axis right
over here, one axis over here. And this is, let's call this
the different scenarios. So this-- let me do
in the same order. Let's call this
Scenario F, Scenario E. I'll just do it in
one color right now. Scenario E, Scenario D, Scenario
C and Scenario B. Actually, let me-- instead of
doing it that way, let me just talk
about it in terms of the number of
squirrels I have. So the number of
squirrels that I have. So in Scenario F, if you
remember, in Scenario F-- oh, not squirrels, rabbits. In Scenario F you
have 0 rabbits. Scenario F you have 0 rabbits. So let's say 0,
1, 2, 3, 4, and 5. And so this is the number
of rabbits, not squirrels, the number of rabbits
that you right now are able to catch,
on average, each day. And then in the vertical
axis, right now, I want to put the
marginal cost in berries. And let's see, it goes
from 20 up to 100. So let's say that this is
20, 40, 60, 80, and 100. So Scenario F, that's
when we had 0 rabbits. And the marginal cost of
trying to get another rabbit, you would have to
give up 20 berries. So that is Scenario
F right over there. Scenario E, that's one where
we had 1, where we already had 1 rabbit and we are
thinking about the marginal cost of getting another one. So that's scenario E,
is right over there. This is scenario D.
Marginal cost is 60. We already have 2
rabbits and we are thinking about getting a third. That's Scenario D. And then Scenario C, we
already have 3 rabbits, thinking about getting a fourth. That's Scenario C.
And then finally, we have Scenario B where we
already have 4 rabbits and we're thinking
about getting a fifth. And we would have to
give up 100 berries to get that fifth rabbit. So that's Scenario
B right over there. So what I've just done is
plotted the marginal cost along-- these are points on,
essentially, our marginal cost curve, our marginal
cost as a function of the number of
rabbits we have. So let me connect all the dots. And then this scenario
just happened to be a line. Doesn't always have to be a
line but in many introductory economics courses, it's
often a line for simplicity. So let me make this a
line right over here. This is our marginal
cost as a function of the number of
rabbits we have. And actually, I should
probably draw this axis, I should probably draw--
let me copy and paste this. So let me cut this. Let me cut that and then let
me paste it, because it really should sit on the 0
point right over there. And ignore that little
line right over there. So there you have marginal
cost as a function of berries. But we still don't know
which scenario to pick. And to think about that, I
want to introduce something called the marginal benefit. And I'll write it as
MB, the marginal benefit of an incremental rabbit. And once again, we're going
to write it in berries. And the way to think
about the marginal benefit is, if we are the
hunter-gatherer we're saying, if we're sitting in one of
these scenarios, how much would we paid to some hypothetical
convenience store in berries-- maybe that convenience
store only sells bunnies and they only accept
berries-- how much would we pay to them in berries
for an extra rabbit? And let's not even look at
this thing right over here. So if we're sitting in Scenario
F, we're sitting in Scenario F. And you remember Scenario
F is right over here. We have no rabbits. How much would we
be willing to pay? We have no rabbits and we
actually have a ton of berries. So in Scenario F right
here, we have no rabbits and we have 300 berries. If we have no rabbits
and a lot of berries, let's say, we'll say, we
have a lot of berries. We might be in the
mood for a rabbit. We would be willing to pay a
lot in berries for a rabbit. So let's say we would pay 100. We would pay 100 berries to
that hypothetical convenience store for a rabbit. Now let's say that we're in
Scenario E. We're in Scenario E, how much would we pay to that
hypothetical convenience store? Well, in Scenario E we
already have 1 rabbit and we have fewer berries. So we need a rabbit less and
we have fewer berries to give, so we're not willing to
give quite as many berries for another rabbit. So maybe we'll only
give 80 berries. Then you go to Scenario D. We already have 2 rabbits and
we have even fewer berries so we're willing to
give even fewer berries for another rabbit. This is what we would pay
to a convenience store, just based on thinking about
it, our current preferences. Then we can go all
the way to Scenario C. And it is subjective. It's not like a
measurable thing. It's just based on this
person's preferences, this hunter-gatherer's
preferences. Scenario C, well, they already
have more rabbits, even fewer berries. So they'll pay even less. And then finally
Scenario B. They have a good number of rabbits
and even fewer berries. They would be willing
to pay very little for an incremental rabbit. So let's plot the
marginal benefit as a function of the number of
rabbits that they already have. So if we go to Scenario
F, the marginal benefit, doing that little thought
experiment is 100. In Scenario E, the
marginal benefit, how much you would
hypothetically be willing to pay in
berries, is now 80 berries. In Scenario D it is 60 berries. In Scenario C it is 40 berries. So Scenario C is
right over here. So in Scenario C
it's 40 berries. And then in Scenario
B it is 20 berries. So in Scenario B it is 20
various, just like that. So now we're not just
plotting the marginal cost. We're plotting the marginal
cost and the marginal benefit in berries. And the marginal
benefit curve-- and it's really a line here, once
again, for simplicity-- looks like that. Now, given this-- so this is
the marginal benefit curve. Marginal benefit is a function
of the number of rabbits that we already have. And this is the marginal
cost as a function of the number of
rabbits we already have. And so when I say
E, this is actually Situation E. That's Situation
D. This is also Situation C and this is also-- this is the
marginal benefit at Situation B. So given this, what
would I rationally do? If these really
are my preferences, what would I rationally do? So if I'm sitting here in
Situation F, I have no rabbits. I already know that it
would cost me 20 rabbits to try to get an
incremental one. But I've already said that
I'd be willing to pay 100. Sorry, it would
cost me 20 berries to get an incremental rabbit. But I've already said
that I'm willing to pay 100 berries to get an
incremental rabbit. So I would want to
move along the curve. So I would definitely
want to get more rabbits. I said that I'm willing to
pay 100 berries for a rabbit and it would only cost me
20 berries for a rabbit. So I'm saying that I
want to get more rabbits. And another way to look at
this visually, marginal benefit is much higher than
marginal cost here. So I'm willing to go forth
and try to get more rabbits. That's even true in Scenario
E. The marginal benefit of an incremental rabbit
is worth much more to me than the marginal cost,
so I'm willing to try to get more rabbits. So in Scenario E I'm still
trying to get more rabbits. I still want to move along
the production possibilities frontier in this
general direction. Now what happens as
I get closer to D? So if I'm in this
scenario right over here, and this isn't one of
our labeled scenarios, but if I'm right
over there-- still, my marginal cost is lower
than my marginal benefit. So I'll still want to get
more rabbits, all the way until I'm Scenario D. In Scenario D I'm a
little bit neutral. I'm willing to pay 60
berries for a rabbit, but that's exactly
how much I'd have to give up to get
that extra rabbit. So let's just think about
Scenario D for a little bit. I'll just circle
it right over here. Because it looks
kind of interesting. Now, let's go--
now would we want to do anything
beyond Scenario D? So if I'm at this
point right over here, if I'm working
enough on average, to say get 2 and
1/2 rabbits a day, would I-- does this
make sense for me to try to get any more rabbits? Well, at that point
the benefit of getting an incremental rabbit
is smaller than the cost of getting a rabbit. At that point, if I try
to get another rabbit, I'm getting less benefit from
it than the cost associated with it. So I definitely don't
want to move past D. So I achieve
allocative efficiency where my marginal cost and
my marginal benefit is equal. So based on the way
that I've rigged the numbers in this
example right over here, you want to settle
on Scenario D. We have achieved allocated
efficiency over there. The marginal cost as a
function of our rabbits and the marginal benefit of our
function of rabbits is equal.