Marginal revenue below average total cost

WEBVTT
Kind: captions
Language: en

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In the last video,
we finished up

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asking ourselves, how
much do we produce

00:00:04.580 --> 00:00:11.330
if the market price is at $0.45?

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And just going with the
logic that we introduced

00:00:13.330 --> 00:00:15.840
in the last video, you want
to produce as much as possible

00:00:15.840 --> 00:00:18.690
to spread out the fixed cost.

00:00:18.690 --> 00:00:21.340
But you don't want to produce so
much that the marginal cost is

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higher than your
marginal revenue.

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And your marginal revenue
is your market price.

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Every unit, every
incremental unit,

00:00:27.510 --> 00:00:29.390
you're going to get $0.45.

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So you want to look
at the quantity

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where your marginal
revenue, the $0.45,

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is equal to your marginal cost.

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So we could look
at it over here.

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So if we look at our
marginal revenue,

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let's say $0.45 is
right over there.

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You want to look where the $0.45
is equal to your marginal cost.

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And it looks like it
is right over there.

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Now we could even
see it on our table.

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When does our marginal
cost equal $0.45?

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It equals that when we produce
8,000 gallons of our juice.

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Now the reason why this
is somewhat interesting

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is at that point the
amount of revenue

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that we're getting per
unit, our marginal revenue,

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is less than our
total cost per unit.

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We're selling each
unit at $0.45,

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but our total cost for
each of those units

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is $0.48 on average.

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So this right over
here is our total cost.

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So you might say, look, I'm
making a loss on every unit.

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The total amount of
revenue I'm getting

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is a smaller
rectangle over here.

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It's the quantity times the
marginal revenue per unit.

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So this is the amount of
revenue that I'm getting.

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Let me color it in carefully.

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That is the amount of
revenue that I'm getting.

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While my costs are
this larger rectangle.

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My quantity times my
average total cost per unit.

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And so what I end
up with is if you

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take that revenue and you
subtract out that quantity,

00:01:58.780 --> 00:02:03.490
you end up with a loss
of exactly this much.

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You are operating, in
this situation, at a loss.

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You're operating at a loss when
you are producing 8,000 units

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and you're getting
$0.45 per unit.

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So does it make sense
for you to do this?

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And we can even
figure out the loss.

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You are producing 8,000 units.

00:02:20.740 --> 00:02:23.080
You're selling them
for $0.45 a unit.

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And it costs you $0.48 per unit
to produce them on average when

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you put all the costs
in, $0.48 cents per unit.

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So you are losing $0.03
per unit, I guess gallon.

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We're talking about
orange juice here.

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And it's times
8,000 gallons, means

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that we are losing
we are losing $240.

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8,000 times $0.06
is 24,000 cents,

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which is the same thing as $240.

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So does it make sense
for us to do this?

00:02:56.452 --> 00:02:58.910
Well, one way to think about
it, let's say we didn't do it.

00:02:58.910 --> 00:03:00.480
Let's say we're
like, hey, I'm not

00:03:00.480 --> 00:03:01.770
going to produce any gallons.

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Well then what's
going to be our loss?

00:03:03.740 --> 00:03:05.870
Well, we're assuming that
this is our fixed cost.

00:03:05.870 --> 00:03:07.750
We've already
committed ourselves

00:03:07.750 --> 00:03:09.530
to this expenditure
right over here.

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Whether we produce no
drops of orange juice,

00:03:13.440 --> 00:03:16.510
we are still going to be
spending $1,000/ So if we

00:03:16.510 --> 00:03:20.610
produce nothing, we are
guaranteeing ourselves a weekly

00:03:20.610 --> 00:03:22.880
loss of $1,000.

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And so this is at
least better than that.

00:03:25.170 --> 00:03:27.340
So by starting to
produce some units,

00:03:27.340 --> 00:03:29.830
we are at least able to
offset some of that loss.

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And we're spreading
out that fixed costs

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over more and more
and more gallons.

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And you might say,
hey, well why don't I

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just keep producing
more and more units?

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Why don't I go here and maybe
I produce 9,000 units where

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the marginal cost
all of a sudden

00:03:42.980 --> 00:03:45.200
is higher than our
marginal revenue?

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And the reason why that
won't make any sense to do

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is because if you produce
that many units, then

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all of a sudden each of
those incremental units

00:03:52.910 --> 00:03:55.530
that you're producing
beyond the 8,000,

00:03:55.530 --> 00:03:57.150
you're losing money on those.

00:03:57.150 --> 00:04:00.060
That 8,000 in first
unit, the marginal cost

00:04:00.060 --> 00:04:02.120
is going to be higher
than the marginal revenue

00:04:02.120 --> 00:04:03.680
that you're bringing
in on that unit.

00:04:03.680 --> 00:04:05.210
So you're going to
be losing money.

00:04:05.210 --> 00:04:09.320
You're going to start having
a lower profit than even

00:04:09.320 --> 00:04:11.670
the negative $240 loss.

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It'll start going at a negative
240 something, negative 250,

00:04:14.640 --> 00:04:16.209
and so forth and so one.

00:04:16.209 --> 00:04:19.800
So you still don't want to
produce beyond that point.

00:04:19.800 --> 00:04:22.800
And we'll touch more deeply
on it in future videos,

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but this is essentially
what differentiates

00:04:25.180 --> 00:04:29.050
the short-term supply curve
from the long-run supply curve.

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In the short-term,
we're going to assume

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that we have these fixed costs.

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And so it's just
going to make sense

00:04:34.470 --> 00:04:37.020
to produce equivalent
to our marginal cost.

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But over the long-run, maybe
our fixed items, our capital,

00:04:41.860 --> 00:04:46.130
our machinery wears off or maybe
the contract for my employees

00:04:46.130 --> 00:04:48.230
wear off, and then we
have a different cost

00:04:48.230 --> 00:04:50.060
structure over the long-term.

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But we'll think about
that in another video.

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But the simple answer
is, assuming these really

00:04:55.330 --> 00:04:57.660
are your fixed
costs, you still want

00:04:57.660 --> 00:05:00.130
to produce as many
units as possible

00:05:00.130 --> 00:05:05.850
so that your marginal cost is
equal to your marginal revenue,

00:05:05.850 --> 00:05:07.510
which in this case
is the market price.

00:05:07.510 --> 00:05:09.400
We are price takers.

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So it actually is a rational
thing to produce 8,000 units

00:05:12.970 --> 00:05:17.550
and take a loss on that and
take a $240 per week loss

00:05:17.550 --> 00:05:21.250
as opposed to just
producing nothing and taking

00:05:21.250 --> 00:05:23.420
$1,000 per week loss.

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Now it might not be rational
once these things have

00:05:25.730 --> 00:05:29.570
been worn out-- your robots
and the employees' contracts.

00:05:29.570 --> 00:05:32.840
It might not be rational to
continue them past their term.

00:05:32.840 --> 00:05:36.770
And we'll think about that
more because obviously, we

00:05:36.770 --> 00:05:38.140
are running at a loss.

00:05:38.140 --> 00:05:40.437
This is not necessarily
a good business to be in,

00:05:40.437 --> 00:05:42.270
but now that we've
gotten into the business,

00:05:42.270 --> 00:05:43.900
we might as well
stay in it in order

00:05:43.900 --> 00:05:47.750
to recoup some of our costs here
or at least spread them out,

00:05:47.750 --> 00:05:52.720
or at least not have
$1,000 per week loss.

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Anyway, see you
in the next video.


Marginal revenue and marginal cost

WEBVTT
Kind: captions
Language: en

00:00:00.732 --> 00:00:02.072
Let's continue with our

00:00:02.072 --> 00:00:04.546
orange juice producing example

00:00:04.546 --> 00:00:06.238
In this situation I want to think about

00:00:06.238 --> 00:00:09.432
what a rational quantity of orange juice might be

00:00:09.432 --> 00:00:11.541
what would be a rational quantity

00:00:11.541 --> 00:00:12.994
of orange juice to produce

00:00:12.994 --> 00:00:14.725
given a market price

00:00:14.725 --> 00:00:15.705
So let's say that

00:00:15.705 --> 00:00:20.115
the market price right now is

00:00:20.115 --> 00:00:21.973
50 cents a gallon

00:00:21.973 --> 00:00:23.253
and I'm going to assume that

00:00:23.253 --> 00:00:24.887
there are many producers here

00:00:24.887 --> 00:00:26.756
so we're going to have to be price takers

00:00:26.756 --> 00:00:27.817
and obviously we want to charge

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as much as we can per gallon

00:00:29.345 --> 00:00:31.824
but if we charge even a penny

00:00:31.824 --> 00:00:33.318
over 50 cents a gallon

00:00:33.318 --> 00:00:34.389
then people are going to buy

00:00:34.389 --> 00:00:35.254
all of their orange juice

00:00:35.254 --> 00:00:36.160
from other people

00:00:36.160 --> 00:00:38.965
so this is the price that we can charge

00:00:38.965 --> 00:00:40.614
50 cents per gallon

00:00:40.614 --> 00:00:41.682
So, if we think about it

00:00:41.682 --> 00:00:43.896
in terms of marginal revenue

00:00:43.896 --> 00:00:45.827
per incremental gallon

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well that first incremental gallon

00:00:47.383 --> 00:00:48.908
we're going to get 50 cents

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the next incremental gallon

00:00:50.000 --> 00:00:51.652
we're going to get 50 cents for that one

00:00:51.652 --> 00:00:52.584
and the next one

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we're going to get 50 cents as well.

00:00:53.470 --> 00:00:54.535
for the first thousand gallons

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we're going to get 50 cents

00:00:55.458 --> 00:00:56.807
for each of those gallons

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for the first 10 thousand gallons

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we'll get 50 cents per gallon

00:01:00.058 --> 00:01:01.554
So, our marginal revenue curve

00:01:01.554 --> 00:01:04.391
will look something like this

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Our marginal revenue is a flat curve

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right at 50 cents a gallon

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so that is our marginal revenue

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at 50 cents

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at a market price of 50 cents per gallon

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now in this situation

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what's a reasonable quantity

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that we would want to produce?

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Now there's two dynamics here

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we want to produce as much as possible

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so that we can spread our fixed cost

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over those gallons

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that's one way of thinking about it

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or, another way of thinking about it is

00:01:41.501 --> 00:01:43.216
we have a certain amount of fixed cost

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we are spending $1000 no matter what

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so why don't we try to get

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as much revenue as possible

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to try to make up for those fixed costs

00:01:52.055 --> 00:01:53.036
or if we think about it

00:01:53.036 --> 00:01:54.655
in terms of average fixed cost

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the more quantity that we produce

00:01:57.017 --> 00:01:59.516
the component of the cost for that

00:01:59.516 --> 00:02:00.769
from the fixed cost

00:02:00.769 --> 00:02:02.652
goes down and down and down

00:02:02.652 --> 00:02:04.322
so we want to have as much as possible

00:02:04.322 --> 00:02:05.913
to spread our fixed costs

00:02:05.913 --> 00:02:08.761
now the one thing that we do need to think about is

00:02:08.761 --> 00:02:11.726
especially once we kind of get beyond the little dip

00:02:11.726 --> 00:02:13.286
in the marginal cost curve

00:02:13.286 --> 00:02:15.123
and as we produce more and more units

00:02:15.123 --> 00:02:18.551
the marginal cost is going up higher and higher and higher

00:02:18.551 --> 00:02:20.117
we don't want to produce so much

00:02:20.117 --> 00:02:22.885
that the cost of producing that incremental unit

00:02:22.885 --> 00:02:25.296
the marginal cost of that incremental unit

00:02:25.296 --> 00:02:28.908
is more than the marginal cost of that actual

00:02:28.908 --> 00:02:31.074
or the marginal cost of that incremental unit

00:02:31.074 --> 00:02:33.004
is not higher than the marginal revenue

00:02:33.004 --> 00:02:35.802
that we're getting on that incremental unit

00:02:35.802 --> 00:02:45.685
so, until marginal revenue is equal to marginal cost

00:02:45.685 --> 00:02:47.263
or another way to think about it

00:02:47.263 --> 00:02:51.846
you don't want marginal cost

00:02:51.846 --> 00:02:53.726
and this is after we go to this little dip here

00:02:53.726 --> 00:02:55.605
we're trying to do as much as possible

00:02:55.605 --> 00:02:57.636
marginal cost is going higher and higher and higher

00:02:57.636 --> 00:02:59.641
we don't want to produce this much right over here

00:02:59.641 --> 00:03:03.659
because here the cost for that extra gallon is higher

00:03:03.659 --> 00:03:06.210
than what we're going to get for that extra gallon

00:03:06.210 --> 00:03:07.950
looks like that cost for that extra gallon

00:03:07.950 --> 00:03:09.430
might be 53 cents

00:03:09.430 --> 00:03:10.664
while we're only gonna get 50 cents

00:03:10.664 --> 00:03:11.733
for that extra gallon

00:03:11.733 --> 00:03:13.800
so every extra gallon we produce over here

00:03:13.800 --> 00:03:15.240
we're going to be losing money

00:03:15.240 --> 00:03:18.457
so you don't want marginal cost

00:03:18.457 --> 00:03:23.339
to be greater than marginal revenue

00:03:23.339 --> 00:03:25.282
so when you look at the curves like this

00:03:25.282 --> 00:03:26.284
and make sense to just say

00:03:26.284 --> 00:03:30.063
when does marginal revenue equal marginal cost?

00:03:30.063 --> 00:03:32.183
and that's this point right over here

00:03:32.183 --> 00:03:35.046
and that is the rational amount to produce

00:03:35.046 --> 00:03:37.881
so that is 9000 units

00:03:37.881 --> 00:03:39.832
so we're going to be at this line over here

00:03:39.832 --> 00:03:43.365
we're gonna produce 9000 gallons of juice

00:03:43.365 --> 00:03:45.059
our revenue that we're going to get

00:03:45.059 --> 00:03:47.862
is going to be the rectangle of the area

00:03:47.862 --> 00:03:52.383
that is high as the price we're getting per unit

00:03:52.383 --> 00:03:54.615
times the number of units

00:03:54.615 --> 00:03:57.203
so this is gonna be the total revenue we get

00:03:57.203 --> 00:03:58.547
if we were to shade this in

00:03:58.547 --> 00:03:59.595
I'm not gonna shade this in

00:03:59.595 --> 00:04:01.808
because it's going to make my whole diagram messy

00:04:01.808 --> 00:04:03.712
and what's our total cost?

00:04:03.712 --> 00:04:06.815
well, we have our average total cost right here

00:04:06.815 --> 00:04:09.791
this is our average total cost at 48 cents

00:04:09.791 --> 00:04:12.356
that's the little green triangle here

00:04:12.356 --> 00:04:14.733
so it's 48 cents per unit

00:04:14.733 --> 00:04:16.771
times the total number of units

00:04:16.771 --> 00:04:21.168
our cost, the area in this rectangle

00:04:21.168 --> 00:04:22.349
so if I were to shade this in

00:04:22.349 --> 00:04:24.406
this little slightly smaller rectangle

00:04:24.406 --> 00:04:27.073
and so our profits are the difference between the two

00:04:27.073 --> 00:04:30.799
our total revenue is the area under the rectangle

00:04:30.799 --> 00:04:34.690
that has this marginal revenue line as its upper bound

00:04:34.690 --> 00:04:36.253
and our cost is the rectangle

00:04:36.253 --> 00:04:38.059
that has our average total cost

00:04:38.059 --> 00:04:39.586
this line right over here

00:04:39.586 --> 00:04:40.820
as its upper bound

00:04:40.820 --> 00:04:44.389
so our profits in this circumstance

00:04:44.389 --> 00:04:47.090
are going to be the area right over here

00:04:47.090 --> 00:04:51.159
the height is the difference between our marginal cost

00:04:51.159 --> 00:04:52.788
which is the same as our marginal revenue

00:04:52.788 --> 00:04:53.838
and our total cost

00:04:53.838 --> 00:04:56.149
so the heigh is going to be

00:04:56.149 --> 00:04:58.043
this two cents right over here

00:04:58.043 --> 00:05:00.023
we're taking the difference of 50 and 48

00:05:00.023 --> 00:05:01.608
so it's gonna be 2 cents

00:05:01.608 --> 00:05:03.238
and then, the quantity produced

00:05:03.238 --> 00:05:05.977
is going to be 9000 units

00:05:05.977 --> 00:05:07.630
so 9000

00:05:07.630 --> 00:05:09.674
we're making 2 cents per unit

00:05:09.674 --> 00:05:11.857
remember, our average cost

00:05:11.857 --> 00:05:14.401
our average total cost is 48 cents per unit

00:05:14.401 --> 00:05:15.882
we're selling that 50 cents per unit

00:05:15.882 --> 00:05:17.267
so we're making 2 cents per unit

00:05:17.267 --> 00:05:18.313
that's not 20

00:05:18.313 --> 00:05:20.318
we're making 2 cents per unit

00:05:20.318 --> 00:05:26.560
2 cents times 9000 units gives us

00:05:26.560 --> 00:05:32.993
that's 18000 cents, or 180 dollars of profit

00:05:32.993 --> 00:05:35.049
now what I want you to think about

00:05:35.049 --> 00:05:36.802
and we'll answer this in the next video

00:05:36.802 --> 00:05:41.956
is does it make sense to sell units at all

00:05:41.956 --> 00:05:44.146
and if so, how many units should we sell

00:05:44.146 --> 00:05:45.837
if, and here is the question

00:05:45.837 --> 00:05:50.326
if the market price is lower

00:05:50.326 --> 00:05:52.792
than your average total cost

00:05:52.792 --> 00:05:54.053
so does it make sense

00:05:54.053 --> 00:05:57.473
and how many units does it make sense to produce

00:05:57.473 --> 00:06:05.519
let's say if the market price were 45 cents per unit

00:06:05.519 --> 99:59:59.999
does it make sense for us to produce


Marginal cost and average total cost

WEBVTT
Kind: captions
Language: en

00:00:00.398 --> 00:00:01.677
Voiceover: What I want to do in this video

00:00:01.677 --> 00:00:03.782
is think about a fairly
traditional business.

00:00:03.782 --> 00:00:06.316
I am going into the orange juice business.

00:00:06.316 --> 00:00:07.276
Right over here,

00:00:07.276 --> 00:00:09.536
I've written the gallons of orange juice

00:00:09.536 --> 00:00:11.776
I am going to produce each week,

00:00:11.776 --> 00:00:14.276
so all of this is going
to be in a per week basis.

00:00:14.276 --> 00:00:15.413
This is my fixed cost,

00:00:15.413 --> 00:00:17.743
so I'm assuming this is
going to cost me $1,000,

00:00:17.743 --> 00:00:19.006
and let's say that that's the rent

00:00:19.006 --> 00:00:21.693
for this super robotic orange juicer

00:00:21.693 --> 00:00:23.442
that I bought that can really,

00:00:23.442 --> 00:00:25.873
and through that for
the sake of simplicity,

00:00:25.873 --> 00:00:26.971
we're assuming that we can put

00:00:26.971 --> 00:00:28.366
as much orange juice as we want,

00:00:28.366 --> 00:00:29.681
or at least any of the amounts

00:00:29.681 --> 00:00:31.469
that I've listed right over here,

00:00:31.469 --> 00:00:33.395
and it also takes into the cost

00:00:33.395 --> 00:00:35.413
of maybe some employees

00:00:35.413 --> 00:00:36.609
who are spending some of their time

00:00:36.609 --> 00:00:39.393
operating this super orange juice mixer.

00:00:39.393 --> 00:00:41.379
I'm assuming all of those are fixed cost,

00:00:41.379 --> 00:00:43.944
and I can't get out of
them or buy them overnight,

00:00:43.944 --> 00:00:44.940
that I've decided,

00:00:44.940 --> 00:00:46.752
I've plunked down the
cost for the machine,

00:00:46.752 --> 00:00:48.858
and I've given these employees,

00:00:48.858 --> 00:00:50.001
let's say I've given them already

00:00:50.001 --> 00:00:51.399
a one-year contract.

00:00:51.399 --> 00:00:52.457
These are going to be fixed,

00:00:52.457 --> 00:00:54.085
at least for the next year.

00:00:54.085 --> 00:00:55.404
Now, my variable costs, here,

00:00:55.404 --> 00:00:56.655
these are going to be given

00:00:56.655 --> 00:00:58.826
the amount of juice I want to produce.

00:00:58.826 --> 00:01:00.801
This is going to be the
cost of the oranges,

00:01:00.801 --> 00:01:02.454
and I guess we can also say the cost of

00:01:02.454 --> 00:01:04.198
transporting the oranges,

00:01:04.198 --> 00:01:05.467
and so we see here,

00:01:05.467 --> 00:01:06.814
obviously if we produce no oranges,

00:01:06.814 --> 00:01:08.596
we have no variable cost.

00:01:08.596 --> 00:01:10.614
If we produce 1,000 oranges,

00:01:10.614 --> 00:01:12.190
then our cost of the oranges

00:01:12.190 --> 00:01:14.991
and transporting them is $500.

00:01:14.991 --> 00:01:17.221
If we produce 2,000, it's 850,

00:01:17.221 --> 00:01:18.663
and something interesting happened.

00:01:18.663 --> 00:01:21.847
Our incremental variable
cost right over here

00:01:21.847 --> 00:01:24.183
was only $350.

00:01:24.553 --> 00:01:26.408
The first 1,000 oranges was 500,

00:01:26.408 --> 00:01:27.660
and then the next 1,000,

00:01:27.660 --> 00:01:29.651
it was only 350.

00:01:29.651 --> 00:01:30.866
So what's happening here is

00:01:30.866 --> 00:01:32.396
I've probably got some economies ...

00:01:32.396 --> 00:01:34.891
I've probably got some
negotiating power now

00:01:34.891 --> 00:01:36.864
with some of these suppliers.

00:01:37.202 --> 00:01:39.864
I'm like, "Look, I'm buying
a lot more oranges now.

00:01:39.864 --> 00:01:41.650
"Let me negotiate the price down,"

00:01:41.650 --> 00:01:43.157
and also maybe with some of the people

00:01:43.157 --> 00:01:44.596
who are doing my shipping,

00:01:44.596 --> 00:01:45.489
my transportation.

00:01:45.489 --> 00:01:46.874
"Look, I'm shipping a lot.

00:01:46.874 --> 00:01:49.356
"Now, why don't you
give me a better deal?"

00:01:49.356 --> 00:01:51.262
We see the deal got even better.

00:01:51.262 --> 00:01:54.543
The incremental from
this to this is only 250.

00:01:54.543 --> 00:01:56.998
Then it starts getting
more expensive again.

00:01:56.998 --> 00:01:58.340
What's probably happening is,

00:01:58.340 --> 00:02:00.645
as I start buying more and more oranges

00:02:00.645 --> 00:02:01.764
from the local distributors,

00:02:01.764 --> 00:02:03.193
I get a better, better deal.

00:02:03.193 --> 00:02:05.293
They view me as a bigger
and bigger customer,

00:02:05.293 --> 00:02:07.192
but once I tap them out,

00:02:07.192 --> 00:02:08.858
then I have to go
further and further away.

00:02:08.858 --> 00:02:10.945
Maybe it's costing more to transport them,

00:02:10.945 --> 00:02:12.551
or maybe these other suppliers

00:02:12.551 --> 00:02:13.688
don't take me as seriously

00:02:13.688 --> 00:02:16.032
or I go to slightly
more expensive suppliers

00:02:16.032 --> 00:02:18.858
because I've tapped out
all of the cheap ones,

00:02:18.858 --> 00:02:21.064
and so my incremental variable costs

00:02:21.064 --> 00:02:23.287
for the next 1,000, and
we'll think about that later,

00:02:23.287 --> 00:02:25.293
keeps going up and up and up.

00:02:25.293 --> 00:02:26.537
The total costs, obviously,

00:02:26.537 --> 00:02:28.465
are just the sum of my fixed costs

00:02:28.465 --> 00:02:29.661
and my variable costs.

00:02:29.661 --> 00:02:30.859
So, if I want to produce

00:02:30.859 --> 00:02:33.385
9,000 gallons of orange juice,

00:02:33.385 --> 00:02:36.851
it's going to cost me $4,360.

00:02:36.851 --> 00:02:38.501
Let's calculate using,

00:02:38.501 --> 00:02:40.235
and I'm just using Excel, here.

00:02:40.650 --> 00:02:43.594
Let's calculate the average fixed cost,

00:02:43.594 --> 00:02:45.705
so we don't want to divide by zero.

00:02:45.705 --> 00:02:47.115
Remember, the average cost,

00:02:47.668 --> 00:02:49.199
the average fixed and the average variable

00:02:49.199 --> 00:02:50.566
and the average total cost,

00:02:50.566 --> 00:02:53.266
these are each of those costs divided by

00:02:53.266 --> 00:02:55.956
the total amount of
juice that I'm producing.

00:02:55.956 --> 00:02:58.854
You can kind of view them
as the cost per gallon.

00:02:58.854 --> 00:03:00.017
So that we're thinking of

00:03:00.017 --> 00:03:01.911
the average fixed cost per gallon,

00:03:01.911 --> 00:03:02.745
so what we're going to do,

00:03:02.745 --> 00:03:04.599
so I'm writing equal to let Excel know

00:03:04.599 --> 00:03:06.270
that I'm doing a formula now,

00:03:06.270 --> 00:03:08.845
this is going to be equal to my fixed cost

00:03:08.845 --> 00:03:12.793
divided by, so divided by,

00:03:12.793 --> 00:03:15.579
divided by my gallons,

00:03:15.579 --> 00:03:17.752
and you can see that's G8 divided by F8,

00:03:17.752 --> 00:03:19.665
and actually, I guess you
can't see my Gs and Fs,

00:03:19.665 --> 00:03:21.104
but this is the 8th row.

00:03:21.104 --> 00:03:23.323
That's that right over there,

00:03:23.323 --> 00:03:24.966
so that is $1.

00:03:25.396 --> 00:03:27.223
If I want my average variable costs,

00:03:27.223 --> 00:03:30.097
that's going to be my variable costs

00:03:30.097 --> 00:03:31.478
divided by,

00:03:31.478 --> 00:03:35.105
divided by my total number of gallons,

00:03:35.105 --> 00:03:36.334
so that's 50 cents,

00:03:36.334 --> 00:03:39.068
so that's the first 1,000 gallons

00:03:39.068 --> 00:03:40.360
to produce the orange juice,

00:03:40.360 --> 00:03:42.088
the orange juice for ...

00:03:42.088 --> 00:03:43.045
to produce a gallon,

00:03:43.045 --> 00:03:45.544
it costs me about 50
cents worth of oranges.

00:03:45.544 --> 00:03:47.886
That includes the transportation cost.

00:03:47.886 --> 00:03:50.829
Then the total is just the
sum of these two things.

00:03:50.829 --> 00:03:52.230
Or, we could have done it another way.

00:03:52.230 --> 00:03:53.825
We could have taken this right ...

00:03:53.825 --> 00:03:56.552
We could have said that
this is just equal to,

00:03:57.090 --> 00:03:59.422
this is just equal to our total cost,

00:03:59.422 --> 00:04:04.332
our total cost divided by
the total number of gallons.

00:04:04.332 --> 00:04:05.334
Either way, you'll get the same thing,

00:04:05.334 --> 00:04:07.533
and maybe I'll do a video mathematically

00:04:07.533 --> 00:04:08.129
on why that is,

00:04:08.129 --> 00:04:10.506
or maybe you should explore that yourself.

00:04:10.506 --> 00:04:12.642
Now, the marginal cost.

00:04:12.642 --> 00:04:16.311
This is equal to our change in cost,

00:04:16.311 --> 00:04:17.771
our change in total cost

00:04:17.771 --> 00:04:21.182
divided by our change in gallons of juice.

00:04:21.182 --> 00:04:23.220
Our change in total costs

00:04:23.220 --> 00:04:27.291
is going to be 1,500 minus 1,000.

00:04:27.291 --> 00:04:29.403
That's our change in total cost

00:04:29.403 --> 00:04:32.026
divided by our change in gallons,

00:04:32.026 --> 00:04:35.753
divided by 1,000 minus 0,

00:04:35.753 --> 00:04:37.491
our change in gallons,

00:04:37.491 --> 00:04:39.336
and that give us 50 cents.

00:04:39.336 --> 00:04:41.466
Now, this is the fun
thing about spreadsheets,

00:04:41.466 --> 00:04:43.662
one of the many fun
things of spreadsheets,

00:04:43.662 --> 00:04:45.605
is now I can select all of these

00:04:45.605 --> 00:04:48.659
and fill in all of the things below it.

00:04:48.659 --> 00:04:52.298
They will use the same
relative calculations.

00:04:52.298 --> 00:04:53.196
Let me just ...

00:04:53.196 --> 00:04:55.110
I'm going to fill without formatting.

00:04:55.110 --> 00:04:55.857
Now, what was neat here,

00:04:55.857 --> 00:04:57.544
and I already set up
this chart ahead of time,

00:04:57.544 --> 00:05:00.541
is to plot these things right over here,

00:05:00.541 --> 00:05:02.138
and so we see what's going on.

00:05:02.138 --> 00:05:04.065
This is a plot that we
looked at in the last video,

00:05:04.065 --> 00:05:06.797
when we thought about software developers.

00:05:06.797 --> 00:05:08.480
This was our fixed cost,

00:05:08.480 --> 00:05:09.824
our variable costs go up

00:05:09.824 --> 00:05:11.188
as we produce more and more.

00:05:11.188 --> 00:05:13.358
Our total cost is just a sum of the two,

00:05:13.358 --> 00:05:15.005
so you just take your variable costs,

00:05:15.005 --> 00:05:17.640
and you add the $1,000
from the fixed costs,

00:05:17.640 --> 00:05:20.123
and you get this curve right over here.

00:05:20.123 --> 00:05:20.891
What we've done here

00:05:20.891 --> 00:05:22.345
is we've plotted all of this stuff.

00:05:22.345 --> 00:05:23.806
The average fixed costs,

00:05:23.806 --> 00:05:25.092
or actually the marginal costs,

00:05:25.092 --> 00:05:26.084
the average variable costs

00:05:26.084 --> 00:05:27.250
and the average total costs.

00:05:27.250 --> 00:05:28.996
I haven't plotted the
average fixed cost here,

00:05:28.996 --> 00:05:30.801
but it's really just
the difference between

00:05:30.801 --> 00:05:33.603
the total and the variable costs.

00:05:33.603 --> 00:05:36.095
Now, let's think about what's happening.

00:05:36.095 --> 00:05:37.688
First, let's look at the average,

00:05:37.688 --> 00:05:38.888
the marginal.

00:05:38.888 --> 00:05:40.435
Actually, let's look at
the marginal costs first,

00:05:40.435 --> 00:05:41.341
because this is interesting,

00:05:41.341 --> 00:05:44.487
and this kind of goes in with
this narrative of at first,

00:05:44.487 --> 00:05:46.542
those first oranges that we bought

00:05:46.542 --> 00:05:47.289
were expensive.

00:05:47.289 --> 00:05:48.924
We weren't a major producer,

00:05:48.924 --> 00:05:49.793
but incrementally,

00:05:49.793 --> 00:05:53.009
incrementally, as we
produce those next oranges,

00:05:53.009 --> 00:05:55.298
so as we go from 1,000 oranges,

00:05:55.298 --> 00:05:58.568
as we go from the oranges
needed for 1,000 gallons

00:05:58.568 --> 00:06:00.896
to the oranges needed for 2,000 gallons,

00:06:00.896 --> 00:06:03.222
all of a sudden, our
marginal cost went down.

00:06:03.222 --> 00:06:04.706
We're now a bigger buyer.

00:06:04.706 --> 00:06:06.756
We can now, those incremental oranges

00:06:06.756 --> 00:06:08.160
are now cheaper to us.

00:06:08.160 --> 00:06:09.420
As we get even more,

00:06:09.420 --> 00:06:11.365
as we go to 3,000
gallons worth of oranges,

00:06:11.365 --> 00:06:14.523
those incremental oranges
get even cheaper for us.

00:06:14.523 --> 00:06:15.991
Then we have to go and buy oranges

00:06:15.991 --> 00:06:17.236
from the outside,

00:06:17.236 --> 00:06:19.868
so those incremental
oranges get more and more

00:06:19.868 --> 00:06:22.074
and more and more expensive.

00:06:22.074 --> 00:06:24.067
That's most clear in
this marginal cost curve,

00:06:24.067 --> 00:06:25.835
and it's somewhat clear in the average,

00:06:25.835 --> 00:06:28.081
the average variable cost.

00:06:28.081 --> 00:06:29.604
In the average variable cost,

00:06:29.604 --> 00:06:31.366
it gets muffled to a certain degree,

00:06:31.366 --> 00:06:33.165
because remember the average variable cost

00:06:33.165 --> 00:06:34.191
at any one of these points,

00:06:34.191 --> 00:06:36.674
and we calculated it
already several times.

00:06:36.674 --> 00:06:38.504
The average variable cost
at any of these points

00:06:38.504 --> 00:06:39.773
is equal to,

00:06:40.496 --> 00:06:43.045
is equal to your variable costs divided by

00:06:43.045 --> 00:06:44.460
the gallons of juice.

00:06:44.460 --> 00:06:45.806
So another way to think about it,

00:06:45.806 --> 00:06:47.187
referring to the last video,

00:06:47.494 --> 00:06:48.898
if you're taking any one of these points,

00:06:48.898 --> 00:06:50.736
your average variable cost

00:06:50.736 --> 00:06:53.601
is the slope between that
point and the origin,

00:06:53.601 --> 00:06:55.715
while the marginal cost is the slope

00:06:55.715 --> 00:06:58.137
between that point and the previous point,

00:06:58.137 --> 00:06:59.889
so the marginal cost is really showing

00:06:59.889 --> 00:07:02.231
how much are those next
incremental oranges

00:07:02.231 --> 00:07:02.873
costing you,

00:07:02.873 --> 00:07:05.001
not just how much are all of the oranges

00:07:05.001 --> 00:07:06.744
on average costing you.

00:07:06.744 --> 00:07:09.027
That's why the marginal
cost curve captures,

00:07:09.027 --> 00:07:10.401
captures how much those

00:07:10.401 --> 00:07:13.732
that very next set of 1,000
gallons worth of oranges,

00:07:13.732 --> 00:07:15.854
how much that is costing you.

00:07:15.854 --> 00:07:17.888
Obviously, your average total cost,

00:07:17.888 --> 00:07:19.555
at first you have your fixed cost,

00:07:19.555 --> 00:07:21.343
aren't being spread out too much,

00:07:21.343 --> 00:07:23.883
but then as you get more and more

00:07:23.883 --> 00:07:25.341
gallons of orange juice produced,

00:07:25.341 --> 00:07:27.110
your fixed cost gets spread out

00:07:27.110 --> 00:07:28.343
more and more and more,

00:07:28.343 --> 00:07:30.008
and so you actually have this gap,

00:07:30.008 --> 00:07:32.262
this gap between the green curve

00:07:32.262 --> 00:07:33.243
and the orange curve,

00:07:33.243 --> 00:07:34.599
which is really just
your average fixed cost.

00:07:34.599 --> 00:07:38.760
That becomes lower and lower and lower.


Visualizing average costs and marginal costs as slope

WEBVTT
Kind: captions
Language: en

00:00:00.493 --> 00:00:01.681
Voiceover: What I want to do in this video

00:00:01.681 --> 00:00:03.903
is look at the data from the last video

00:00:03.903 --> 00:00:05.160
and make sure we understand it

00:00:05.160 --> 00:00:07.458
in maybe a more visual way.

00:00:07.458 --> 00:00:10.746
What I've done is, in
this graph over here,

00:00:10.746 --> 00:00:13.182
I used the lines of code per month,

00:00:13.182 --> 00:00:14.658
so this right over here.

00:00:14.658 --> 00:00:18.743
I used this, or this was what I used

00:00:18.743 --> 00:00:21.185
on my horizontal axis,

00:00:21.185 --> 00:00:21.684
so I kind of,

00:00:21.684 --> 00:00:24.075
if you view it in terms of independent

00:00:24.075 --> 00:00:25.074
and dependent variables,

00:00:25.074 --> 00:00:27.918
I kind of made this the
independent variable now.

00:00:27.918 --> 00:00:30.081
Given a certain number of lines of code

00:00:30.081 --> 00:00:31.517
you want to produce per month,

00:00:31.517 --> 00:00:34.060
what is the fixed cost, the variable cost,

00:00:34.060 --> 00:00:35.555
and the total cost,

00:00:35.555 --> 00:00:38.258
so this is on this axis right over here.

00:00:38.258 --> 00:00:40.253
This is lines of code,

00:00:40.253 --> 00:00:42.713
lines of code per month

00:00:42.713 --> 00:00:43.918
per month,

00:00:43.918 --> 00:00:44.649
right over there,

00:00:44.649 --> 00:00:47.320
and then you see it
goes up to about 12,000,

00:00:47.320 --> 00:00:50.741
and we see that covers
the entire range of data

00:00:50.741 --> 00:00:53.459
that we would have to worry
about right over here.

00:00:53.459 --> 00:00:54.610
On the vertical axis,

00:00:54.610 --> 00:00:56.106
as I just alluded to,

00:00:56.106 --> 00:00:58.258
we are plotting the cost,

00:00:58.258 --> 00:00:59.517
so we're going to plot the fixed cost,

00:00:59.517 --> 00:01:02.186
the variable cost, and the total cost.

00:01:02.186 --> 00:01:04.760
We see that there in our little legend.

00:01:04.760 --> 00:01:05.575
The fixed cost,

00:01:05.575 --> 00:01:08.141
no matter how many lines
of code we've produced,

00:01:08.141 --> 00:01:09.381
this is a little bit different

00:01:09.381 --> 00:01:11.129
than the way we thought
about it in the last video.

00:01:11.129 --> 00:01:12.415
In the last video, we said,

00:01:12.415 --> 00:01:14.256
"How many programmers do we have,

00:01:14.256 --> 00:01:15.666
"and what is going to be our fixed cost,

00:01:15.666 --> 00:01:17.328
"our variable cost, our total cost?"

00:01:17.328 --> 00:01:18.260
Now we're thinking about it

00:01:18.260 --> 00:01:20.003
in terms of lines of code per month,

00:01:20.003 --> 00:01:21.581
but no matter how many lines of code

00:01:21.581 --> 00:01:23.914
per month we produce within reason,

00:01:23.914 --> 00:01:26.117
our fixed costs are the same,

00:01:26.117 --> 00:01:29.010
$15,000 per month for the office space,

00:01:29.010 --> 00:01:31.369
the food in the office, the water cooler,

00:01:31.369 --> 00:01:33.860
the project manager, things like that.

00:01:33.860 --> 00:01:35.009
We see it right over here.

00:01:35.009 --> 00:01:38.632
This pale green line,
that is our fixed cost.

00:01:38.632 --> 00:01:39.816
That is our fixed cost.

00:01:39.816 --> 00:01:42.084
No matter how many lines
of code we produce,

00:01:42.084 --> 00:01:46.060
we are using exactly $15,000 per month.

00:01:46.060 --> 00:01:49.100
This is $15,000 right over there.

00:01:49.100 --> 00:01:50.896
Then you have your variable costs

00:01:50.896 --> 00:01:52.868
in this orange color,

00:01:52.868 --> 00:01:55.751
so the variable costs in the orange color,

00:01:55.751 --> 00:01:58.455
and we can see how the points are plotted.

00:01:58.455 --> 00:02:01.182
When you have no lines of code per month,

00:02:01.182 --> 00:02:03.006
your variable costs are 0.

00:02:03.006 --> 00:02:04.923
That's this point right over there.

00:02:04.923 --> 00:02:06.912
When you have 4,000 lines of code,

00:02:06.912 --> 00:02:09.327
your variable costs are 10,000.

00:02:09.327 --> 00:02:11.602
That's that point right over there.

00:02:11.602 --> 00:02:12.838
When you have,

00:02:12.838 --> 00:02:14.711
let me pick up a random point over here,

00:02:14.711 --> 00:02:18.559
when you have 11,400
lines of code per month,

00:02:18.559 --> 00:02:20.582
your variable costs are 70,000.

00:02:20.582 --> 00:02:23.164
11,400, let's see.

00:02:23.164 --> 00:02:26.381
This is about 11,000, 11,400,

00:02:26.381 --> 00:02:30.673
and your costs are $70,000.

00:02:30.673 --> 00:02:32.722
That's that point right over there.

00:02:32.722 --> 00:02:34.435
Then, finally, your total costs,

00:02:34.435 --> 00:02:36.878
or the sum of the fixed
plus the variable costs,

00:02:36.878 --> 00:02:39.712
and we've plotted this in this blue color,

00:02:39.712 --> 00:02:41.856
so the total costs,

00:02:41.856 --> 00:02:43.855
which is in blue right over here,

00:02:43.855 --> 00:02:46.863
it's really just the sum of
this green horizontal line

00:02:46.863 --> 00:02:48.251
and this orange line.

00:02:48.251 --> 00:02:49.203
Another way of thinking about it,

00:02:49.203 --> 00:02:50.666
take this orange line at any given point.

00:02:50.666 --> 00:02:52.581
That's the variable cost.

00:02:52.581 --> 00:02:53.717
Add the fixed cost,

00:02:53.717 --> 00:02:54.675
which is 15,000.

00:02:54.675 --> 00:02:56.854
It shifts you up to that blue line.

00:02:56.854 --> 00:02:58.850
So at any point, that
blue line is exactly,

00:02:58.850 --> 00:03:02.120
is exactly $15,000 higher.

00:03:02.120 --> 00:03:05.458
$15,000 higher than the orange line.

00:03:05.458 --> 00:03:07.343
You see it even over here,

00:03:07.343 --> 00:03:09.596
where it kind of bends back on itself.

00:03:09.596 --> 00:03:10.919
Then you're probably saying,

00:03:10.919 --> 00:03:14.116
"Well, why is it bending
back on itself like that?"

00:03:14.116 --> 00:03:16.076
And this goes straight
to what we talked about

00:03:16.076 --> 00:03:17.447
in the last video.

00:03:17.447 --> 00:03:19.883
That as we add more and more programmers,

00:03:19.883 --> 00:03:22.210
the average productivity
per programmer goes down

00:03:22.210 --> 00:03:23.826
because they have to
start meeting each other

00:03:23.826 --> 00:03:25.184
and coordinate with each other,

00:03:25.184 --> 00:03:26.601
and maybe they undo each other's work,

00:03:26.601 --> 00:03:28.451
and then there's some point at which,

00:03:28.451 --> 00:03:30.260
even when you add more resources,

00:03:30.260 --> 00:03:32.052
it actually decreases productivity.

00:03:32.052 --> 00:03:34.189
So we're adding more and more resources,

00:03:34.189 --> 00:03:35.511
and I don't have them plotted here,

00:03:35.511 --> 00:03:37.890
but we keep adding more
and more developers,

00:03:37.890 --> 00:03:38.725
and we get to this point

00:03:38.725 --> 00:03:40.514
where we're able to generate

00:03:40.514 --> 00:03:42.605
11,400 lines of code per month,

00:03:42.605 --> 00:03:43.916
but then all of a sudden,

00:03:43.916 --> 00:03:45.207
as we add more developers,

00:03:45.207 --> 00:03:47.100
it still adds cost,

00:03:47.100 --> 00:03:48.335
because obviously they're
going to cost something.

00:03:48.335 --> 00:03:49.262
We have to pay their salaries

00:03:49.262 --> 00:03:50.725
and their insurance and all of that,

00:03:50.725 --> 00:03:51.926
but then our total productivity

00:03:51.926 --> 00:03:53.766
starts going down again.

00:03:53.766 --> 00:03:54.855
That's what we're seeing here

00:03:54.855 --> 00:03:58.262
when both the variable cost curve

00:03:58.262 --> 00:04:03.331
and our total cost curve
start curving back on itself.

00:04:03.331 --> 00:04:04.559
Now, with this plotted,

00:04:04.559 --> 00:04:06.124
what I want to think about visually,

00:04:06.124 --> 00:04:07.396
and especially in terms of slope,

00:04:07.396 --> 00:04:08.441
I encourage you to,

00:04:08.441 --> 00:04:12.166
if the term slope seems a
little bit foreign to you,

00:04:12.166 --> 00:04:15.106
there's tons of videos
on the idea of slope

00:04:15.106 --> 00:04:16.876
in the algebra playlist,

00:04:16.876 --> 00:04:20.367
but the slope is really
just how inclined a line is.

00:04:20.367 --> 00:04:23.789
For example, this line has a higher slope

00:04:23.789 --> 00:04:26.248
than this line right over there.

00:04:26.248 --> 00:04:27.423
That the way we measure it

00:04:27.423 --> 00:04:29.860
is our change in our vertical axis,

00:04:29.860 --> 00:04:31.854
so our change in our vertical axis,

00:04:31.854 --> 00:04:33.729
often given by a change in y,

00:04:33.729 --> 00:04:36.070
the triangles, that's the delta,

00:04:36.070 --> 00:04:38.209
Greek letter Δ, means change in Y

00:04:38.209 --> 00:04:40.548
divided by our change in,

00:04:40.548 --> 00:04:43.492
divided by our change
in our horizontal axis,

00:04:43.492 --> 00:04:45.344
that is change in X.

00:04:45.344 --> 00:04:50.862
So, slope is equal to Δy over Δx,

00:04:50.862 --> 00:04:52.971
and when you measure it this way,

00:04:52.971 --> 00:04:53.813
this line over here,

00:04:53.813 --> 00:04:56.258
it looks like it has about
the same change in x,

00:04:56.258 --> 00:04:58.857
but has a much lower change in y,

00:04:58.857 --> 00:05:01.517
lower change in y.

00:05:01.517 --> 00:05:03.010
So when you take this lower change in y

00:05:03.010 --> 00:05:04.718
divided by the same change in x,

00:05:04.718 --> 00:05:07.402
you're going to get a lower slope.

00:05:07.402 --> 00:05:09.812
If you had a line that
looked something like,

00:05:09.812 --> 00:05:10.823
if you had a line that looked

00:05:10.823 --> 00:05:12.331
something like this,

00:05:12.331 --> 00:05:15.228
then you have a much higher change in y,

00:05:15.228 --> 00:05:17.528
so your numerator is higher,

00:05:17.528 --> 00:05:18.730
a higher change in y,

00:05:18.730 --> 00:05:20.779
and you have a lower change in x.

00:05:20.779 --> 00:05:22.056
Your denominator's lower.

00:05:22.056 --> 00:05:24.494
That'll increase the
value of the quantity,

00:05:24.494 --> 00:05:25.588
so your change in x.

00:05:25.588 --> 00:05:27.962
This right over here is
going to be a high slope,

00:05:27.962 --> 00:05:29.066
a high slope.

00:05:29.066 --> 00:05:31.186
With that little primer out of the way

00:05:31.186 --> 00:05:32.331
on what a slope is,

00:05:32.331 --> 00:05:34.109
what I want to do is think about

00:05:34.370 --> 00:05:35.895
these average fixed costs,

00:05:35.895 --> 00:05:36.890
average variable costs,

00:05:36.890 --> 00:05:38.040
average total costs,

00:05:38.040 --> 00:05:39.004
and marginal costs

00:05:39.004 --> 00:05:42.239
in terms of slopes of these lines

00:05:42.239 --> 00:05:43.368
right over here.

00:05:43.368 --> 00:05:45.041
When you're looking at average,

00:05:45.041 --> 00:05:47.419
if we look at this point right over here,

00:05:47.419 --> 00:05:50.535
average fixed cost, $3.75.

00:05:50.535 --> 00:05:51.859
What that means is

00:05:51.859 --> 00:05:54.458
when we're producing 4,000 lines of code,

00:05:54.458 --> 00:05:55.671
4,000 lines of code,

00:05:55.671 --> 00:05:58.352
our average fixed cost is $3.75,

00:05:58.352 --> 00:05:59.569
so I'm on the green line, actually.

00:05:59.569 --> 00:06:01.111
Let me use a green color right here.

00:06:01.111 --> 00:06:03.564
I'm on this green line right over here.

00:06:03.564 --> 00:06:04.773
To find that average,

00:06:04.773 --> 00:06:05.653
so that's our,

00:06:05.653 --> 00:06:06.528
that is our,

00:06:06.528 --> 00:06:08.763
that is our fixed cost.

00:06:08.763 --> 00:06:10.520
To find our average fixed cost,

00:06:10.520 --> 00:06:12.551
we want to divide our fixed cost,

00:06:12.551 --> 00:06:15.133
which is that height right over there.

00:06:15.133 --> 00:06:17.977
You want to divide it by
the total lines of code,

00:06:17.977 --> 00:06:20.058
and that gives us our fixed cost,

00:06:20.058 --> 00:06:22.378
our average fixed cost per line of code.

00:06:22.378 --> 00:06:25.148
We're taking a change in the vertical axis

00:06:25.148 --> 00:06:28.268
divided by our change in a
horizontal axis right there,

00:06:28.268 --> 00:06:31.376
so it's essentially giving
the slope of this line,

00:06:31.376 --> 00:06:32.739
just like that.

00:06:32.739 --> 00:06:34.280
It's giving the slope of that line,

00:06:34.280 --> 00:06:36.465
and that's this point right over here.

00:06:36.465 --> 00:06:38.749
When you go to this point right over here,

00:06:38.749 --> 00:06:40.033
you're saying, "Okay.

00:06:40.033 --> 00:06:42.081
"I'm producing 7,000 lines of code,

00:06:42.081 --> 00:06:47.129
"and it still costs me $15,000."

00:06:47.129 --> 00:06:48.536
That's $15,000.

00:06:48.536 --> 00:06:53.076
I divide my total change in fixed costs,

00:06:53.076 --> 00:06:55.132
divided by my

00:06:55.132 --> 00:06:57.081
or my total fixed cost

00:06:57.081 --> 00:07:00.477
divided by my total lines of code,

00:07:00.477 --> 00:07:02.245
divided by my total lines of code.

00:07:02.245 --> 00:07:03.845
I'm essentially getting the slope of,

00:07:04.552 --> 00:07:05.611
I know it's getting hard to see,

00:07:05.611 --> 00:07:06.591
the way I'm doing it.

00:07:06.591 --> 00:07:07.946
I'm essentially giving you the slope of,

00:07:07.946 --> 00:07:09.363
let me draw a little bit neater,

00:07:09.778 --> 00:07:10.982
this line right over here.

00:07:10.982 --> 00:07:13.217
You could see this line has a lower slope

00:07:13.217 --> 00:07:14.355
than the previous one,

00:07:14.355 --> 00:07:15.914
and that makes sense

00:07:15.914 --> 00:07:18.133
because the average fixed
cost per line of code

00:07:18.133 --> 00:07:19.419
should be going down.

00:07:19.419 --> 00:07:20.786
We have the same fixed cost

00:07:20.786 --> 00:07:22.331
and we're dividing it amongst more

00:07:22.331 --> 00:07:23.618
and more and more code.

00:07:23.618 --> 00:07:24.979
You can see if you go out here,

00:07:24.979 --> 00:07:26.535
and you do the slope from this point

00:07:26.535 --> 00:07:27.580
all the way over here,

00:07:27.580 --> 00:07:28.561
it's going to have even a little,

00:07:28.561 --> 00:07:30.121
even a lower slope,

00:07:30.659 --> 00:07:31.776
so let me clear this out of the way,

00:07:31.776 --> 00:07:32.884
so hopefully that makes sense.

00:07:32.884 --> 00:07:34.590
The fixed cost, at least for me,

00:07:34.590 --> 00:07:36.220
is maybe the easiest to understand.

00:07:36.220 --> 00:07:37.501
You're taking the same quantity,

00:07:37.501 --> 00:07:39.033
dividing it by more and more code,

00:07:39.033 --> 00:07:40.334
or by more and more developers.

00:07:40.887 --> 00:07:43.090
Now, the variable cost,
average variable cost,

00:07:43.090 --> 00:07:44.467
at any given point over here,

00:07:45.143 --> 00:07:46.277
we're taking the variable cost,

00:07:46.277 --> 00:07:48.583
and we're dividing it by
the total amount of code.

00:07:48.859 --> 00:07:50.045
So variable costs,

00:07:51.552 --> 00:07:54.176
over there it is $10,000,

00:07:54.176 --> 00:07:56.581
and we're dividing it
by 4,000 lines of code,

00:07:56.581 --> 00:07:59.345
so it is the slope of
this line right over here.

00:07:59.868 --> 00:08:01.789
When you go to 7,000 lines of code,

00:08:01.789 --> 00:08:05.859
you say, "Well, my total
variable cost is $20,000,

00:08:05.859 --> 00:08:09.243
"and I'm going to divide
it by 7,000 lines of code."

00:08:09.243 --> 00:08:14.055
So it is the slope of this
entire line right over here.

00:08:14.238 --> 00:08:16.120
I'm having trouble drawing these lines.

00:08:16.120 --> 00:08:20.788
It is the slope of this
line right over here.

00:08:20.788 --> 00:08:21.544
This is a curve,

00:08:21.544 --> 00:08:23.771
so the slope is different
here than it is over there.

00:08:24.109 --> 00:08:24.824
This line,

00:08:24.824 --> 00:08:27.423
when we're measuring the
average variable costs,

00:08:27.423 --> 00:08:27.917
we're measuring,

00:08:27.917 --> 00:08:30.110
you can imagine the average slope across

00:08:30.110 --> 00:08:32.344
from the beginning all
the way to this point

00:08:32.344 --> 00:08:33.381
right over here.

00:08:34.119 --> 00:08:35.678
Now, when you're doing
the average total cost,

00:08:35.678 --> 00:08:36.749
you're doing the same thing.

00:08:36.749 --> 00:08:38.202
The average total cost at that point

00:08:38.694 --> 00:08:40.141
is our total, total cost,

00:08:40.464 --> 00:08:42.733
so it's that, divided by,

00:08:43.163 --> 00:08:47.005
divided by the total code,

00:08:47.389 --> 00:08:48.832
so the total code.

00:08:48.832 --> 00:08:52.596
So it is the slope of this
line right over there.

00:08:52.596 --> 00:08:55.936
We see that, that slope,
when you start over here,

00:08:55.936 --> 00:08:58.840
when you start from this
point to that point,

00:08:58.840 --> 00:08:59.776
the slope goes down,

00:08:59.776 --> 00:09:02.041
but then we see the slope start going,

00:09:02.041 --> 00:09:03.538
it starts to go up again

00:09:03.538 --> 00:09:06.332
because we saw that the variables cost

00:09:06.332 --> 00:09:07.589
start increasing

00:09:07.589 --> 00:09:09.090
because we get less and less efficiency

00:09:09.090 --> 00:09:10.514
as we add more and more developers

00:09:10.514 --> 00:09:12.958
and attempt, at least, to write more code.

00:09:12.958 --> 00:09:15.023
Now, the marginal cost
is an interesting one.

00:09:15.023 --> 00:09:16.631
All of these other ones,

00:09:16.631 --> 00:09:17.710
we're taking our total cost,

00:09:17.710 --> 00:09:18.779
our total variable cost,

00:09:18.779 --> 00:09:19.945
our total total cost,

00:09:19.945 --> 00:09:20.912
our total fixed cost,

00:09:20.912 --> 00:09:22.985
and dividing by the total amount of code,

00:09:22.985 --> 00:09:24.785
so we're essentially
finding the slope of a line

00:09:24.785 --> 00:09:27.846
between these points and our origin.

00:09:28.076 --> 00:09:29.578
When you're doing the marginal cost,

00:09:29.578 --> 00:09:30.841
you're doing something different.

00:09:30.841 --> 00:09:32.022
Let me clear all of this out

00:09:32.022 --> 00:09:33.427
so that we can clear things up.

00:09:33.965 --> 00:09:36.646
Your marginal cost is you're measuring

00:09:36.646 --> 00:09:39.823
your change in total cost divided by,

00:09:39.823 --> 00:09:41.183
not your total total cost,

00:09:41.183 --> 00:09:43.018
you're doing your change in total cost

00:09:43.018 --> 00:09:47.341
divided by your change
in the lines of code.

00:09:47.817 --> 00:09:49.647
So, for example, that right over,

00:09:49.647 --> 00:09:51.160
let me do that in a more vibrant color.

00:09:51.544 --> 00:09:52.852
That marginal cost,

00:09:53.390 --> 00:09:55.418
that's at this point right over here,

00:09:55.418 --> 00:09:56.650
so let's say we're going to,

00:09:56.650 --> 00:09:58.986
we can do it with the variable cost curve

00:09:58.986 --> 00:10:00.633
or we could do it with
the total cost curve.

00:10:00.633 --> 00:10:01.644
i'll do it with the total cost curve,

00:10:01.644 --> 00:10:03.546
so it's this point right over here.

00:10:03.546 --> 00:10:04.962
What we're doing is,

00:10:05.454 --> 00:10:08.107
we're taking the change in total cost

00:10:08.107 --> 00:10:09.675
between the previous point.

00:10:09.675 --> 00:10:11.128
The previous point was there,

00:10:11.128 --> 00:10:12.684
so our change in total cost

00:10:12.684 --> 00:10:14.596
is just this part right over here,

00:10:14.596 --> 00:10:17.206
so this is our change in total cost,

00:10:17.206 --> 00:10:19.209
and we're dividing it by our change

00:10:19.209 --> 00:10:21.138
in the amount of code we produce.

00:10:21.707 --> 00:10:23.911
So we're dividing it by the change in,

00:10:23.911 --> 00:10:26.668
change in lines of code.

00:10:26.668 --> 00:10:29.209
So essentially, it's giving
us the slope of the line

00:10:29.578 --> 00:10:32.244
between the previous point
and the current point

00:10:32.244 --> 00:10:34.913
on the total cost curve.

00:10:34.913 --> 00:10:35.788
We could do it,

00:10:35.788 --> 00:10:36.965
so if we go right over here.

00:10:36.965 --> 00:10:38.832
Let me go to another arbitrary point

00:10:39.247 --> 00:10:40.678
that doesn't start from the beginning.

00:10:41.185 --> 00:10:43.777
Let's say we're looking
at this marginal cost.

00:10:44.069 --> 00:10:45.815
This was when we're talking about

00:10:45.815 --> 00:10:47.985
10,600 lines of code,

00:10:47.985 --> 00:10:51.131
and our total cost was $65,000.

00:10:51.561 --> 00:10:53.475
So our total cost is $65,000,

00:10:53.475 --> 00:10:55.372
10,600 lines of code.

00:10:55.372 --> 00:10:56.955
That's that point right over there.

00:10:57.508 --> 00:10:58.628
What this is measuring,

00:10:59.074 --> 00:11:01.189
it's our change in total cost

00:11:01.189 --> 00:11:03.049
since the last increment,

00:11:03.495 --> 00:11:04.546
so since the last increment,

00:11:04.546 --> 00:11:05.684
since the last point.

00:11:06.037 --> 00:11:07.869
It's our change in total cost.

00:11:08.238 --> 00:11:10.863
it's our change in total cost

00:11:10.863 --> 00:11:13.489
divided by the change in lines of code

00:11:13.489 --> 00:11:14.884
since the last point,

00:11:15.453 --> 00:11:18.070
so the change of lines
of code is just that,

00:11:18.070 --> 00:11:20.230
change in lines of code.

00:11:20.706 --> 00:11:23.291
Our marginal cost is this quantity

00:11:23.291 --> 00:11:24.048
divided by this quantity.

00:11:24.048 --> 00:11:27.080
It's the slope between these
two consecutive points.

00:11:27.080 --> 00:11:29.282
What the marginal cost is giving us,

00:11:29.282 --> 00:11:31.262
so I just want to make sure
we get everything clear,

00:11:31.262 --> 00:11:33.133
these average fixed, average variable,

00:11:33.133 --> 00:11:34.287
average total cost,

00:11:34.287 --> 00:11:35.698
that gives us a slope of the line

00:11:35.698 --> 00:11:37.701
between any of the points and the origin.

00:11:37.701 --> 00:11:39.727
The marginal cost is essentially giving us

00:11:39.727 --> 00:11:41.334
the slope of the curve

00:11:41.334 --> 00:11:43.989
between any two consecutive points

00:11:43.989 --> 00:11:45.481
on the total cost curve,

00:11:45.481 --> 00:11:46.771
or you could also view,

00:11:46.771 --> 00:11:48.414
because it's really just a shifted version

00:11:48.414 --> 00:11:49.623
of the variable cost curve,

00:11:49.623 --> 00:11:51.334
or you could do this as the same

00:11:51.334 --> 00:11:52.519
as the slope of the line

00:11:52.519 --> 00:11:55.638
between any two points on
the variable cost curve.

00:11:55.638 --> 00:11:58.048
This is an approximation

00:11:58.663 --> 00:11:59.833
you could do this as the average,

00:11:59.833 --> 00:12:01.281
and that's why I wrote average over here.

00:12:01.281 --> 00:12:03.086
This is the average slope of the curve

00:12:03.086 --> 00:12:05.333
between these two points.


Fixed, Variable, and Marginal Cost.

WEBVTT
Kind: captions
Language: en

00:00:00.600 --> 00:00:02.850
We here at the Khan
Academy are working

00:00:02.850 --> 00:00:05.380
on some type of a
software project.

00:00:05.380 --> 00:00:07.080
And we need to
think about what's

00:00:07.080 --> 00:00:09.660
the optimal number of
programmers we should hire,

00:00:09.660 --> 00:00:12.120
at least think about
how much productivity

00:00:12.120 --> 00:00:13.960
we're getting per
programmer when we're

00:00:13.960 --> 00:00:16.549
working on this
software project.

00:00:16.549 --> 00:00:18.840
And so what I've done over
here-- this is a spreadsheet

00:00:18.840 --> 00:00:19.880
so I'm not going to
be able to write.

00:00:19.880 --> 00:00:20.963
I'll only be able to type.

00:00:20.963 --> 00:00:23.410
This is Microsoft
Excel right over here.

00:00:23.410 --> 00:00:25.530
In this column, I have
the different numbers

00:00:25.530 --> 00:00:26.630
of programmers.

00:00:26.630 --> 00:00:29.090
And then let's say based on
other studies or industry

00:00:29.090 --> 00:00:31.410
studies or our past
experience, this tells us

00:00:31.410 --> 00:00:34.800
how many lines of programming
code we can get per month.

00:00:34.800 --> 00:00:36.850
And obviously, lines
of code isn't maybe

00:00:36.850 --> 00:00:38.980
the best way to measure
things because someone

00:00:38.980 --> 00:00:41.290
can write good lines
or bad lines of code.

00:00:41.290 --> 00:00:44.150
But let's just say this is one
way of measuring productivity

00:00:44.150 --> 00:00:45.509
for software engineers.

00:00:45.509 --> 00:00:47.300
So the first thing I'm
going to think about

00:00:47.300 --> 00:00:48.990
is what are my fixed costs?

00:00:48.990 --> 00:00:50.690
So what am I going
to spend no matter

00:00:50.690 --> 00:00:54.080
how many software engineers
I hire for this project?

00:00:54.080 --> 00:00:56.750
And for the sake of this
video, my fixed costs

00:00:56.750 --> 00:00:59.750
will be the office space
and the electricity

00:00:59.750 --> 00:01:02.840
and let's assume I just have
an office that can accommodate

00:01:02.840 --> 00:01:04.670
any number of these programmers.

00:01:04.670 --> 00:01:05.770
So that's a fixed cost.

00:01:05.770 --> 00:01:07.430
That's not going
to change depending

00:01:07.430 --> 00:01:09.024
on the number of
programmers I have.

00:01:09.024 --> 00:01:10.690
And then the other
fixed cost, let's say

00:01:10.690 --> 00:01:12.830
I have a product manager
for this project.

00:01:12.830 --> 00:01:15.280
And I'm going to pay her
salary to essentially

00:01:15.280 --> 00:01:20.040
help spec out what this
software should actually do.

00:01:20.040 --> 00:01:22.680
So her salary is, let's
say, $10,000 a month

00:01:22.680 --> 00:01:26.350
and then another $5,000 a month
in office space for everybody.

00:01:26.350 --> 00:01:30.100
So it's going to come
out to $15,000 a month.

00:01:30.100 --> 00:01:32.660
And that's not going to
change regardless of however

00:01:32.660 --> 00:01:34.004
many programmers I have.

00:01:34.004 --> 00:01:36.420
So I'm going to go into Excel
and go to this little bottom

00:01:36.420 --> 00:01:37.380
right right over here.

00:01:37.380 --> 00:01:39.580
And I'm going to drag that down.

00:01:39.580 --> 00:01:42.120
And so it's going to be
$15,000 in fixed costs

00:01:42.120 --> 00:01:45.260
no matter how many
programmers I end up hiring.

00:01:45.260 --> 00:01:46.540
Now the variable cost.

00:01:49.950 --> 00:01:52.090
Well, let's just say that
the full compensation

00:01:52.090 --> 00:01:54.630
for a programmer
is $10,000 a month.

00:01:54.630 --> 00:01:57.685
So if you include the
cost of their salary,

00:01:57.685 --> 00:02:00.220
if you include the cost
of their health insurance,

00:02:00.220 --> 00:02:03.100
you include the extra
goodies that they

00:02:03.100 --> 00:02:05.860
will eat from the company
kitchen, whatever it might be.

00:02:05.860 --> 00:02:07.550
So it's going to
be $10,000 a month.

00:02:07.550 --> 00:02:10.400
So my variable my
total variable costs

00:02:10.400 --> 00:02:13.670
are going to be $10,000 times
the number of programmers.

00:02:13.670 --> 00:02:17.610
So here I'm going to write
equals, and I'm going to write,

00:02:17.610 --> 00:02:21.240
it's going to be $10,000
per programmer times--

00:02:21.240 --> 00:02:23.610
that little snowflake,
I pressed Shift +

00:02:23.610 --> 00:02:26.120
8 to get that snowflake--
times, and I could

00:02:26.120 --> 00:02:28.790
say times whatever
is in that cell.

00:02:28.790 --> 00:02:31.640
So you see it's cell D7.

00:02:31.640 --> 00:02:33.230
And actually let
me scroll this over

00:02:33.230 --> 00:02:36.630
so that you can see the cells.

00:02:36.630 --> 00:02:38.070
So that is cell D7.

00:02:38.070 --> 00:02:41.040
And let me press Enter.

00:02:41.040 --> 00:02:45.320
So it's $10,000 times D7, which
is this one right over here.

00:02:45.320 --> 00:02:46.770
And I just selected that.

00:02:46.770 --> 00:02:48.180
And I can press Enter.

00:02:48.180 --> 00:02:50.250
And right now, that's nothing.

00:02:50.250 --> 00:02:54.610
Let me scroll over so we can see
everything a little bit better.

00:02:54.610 --> 00:02:57.080
Let me scroll over a little bit.

00:02:57.080 --> 00:02:57.970
There you go.

00:02:57.970 --> 00:02:59.120
I'm having trouble.

00:02:59.120 --> 00:02:59.640
OK.

00:02:59.640 --> 00:03:00.650
There you go.

00:03:00.650 --> 00:03:03.010
Now, what are going
to be my total costs?

00:03:03.010 --> 00:03:06.690
My total costs are my fixed
costs plus my variable costs.

00:03:06.690 --> 00:03:11.180
So that's going to be equal
to-- and I'm just using my arrow

00:03:11.180 --> 00:03:14.680
keys right now-- it's going
to be equal to F7, right?

00:03:14.680 --> 00:03:21.970
That's cell F7 plus this
one, plus my variable costs.

00:03:21.970 --> 00:03:25.890
My total costs are my fixed
costs plus my variable costs.

00:03:25.890 --> 00:03:27.960
And so it's $15,000.

00:03:27.960 --> 00:03:30.520
And actually, I can make this
true for every row over here.

00:03:30.520 --> 00:03:32.311
And this is one of the
really useful things

00:03:32.311 --> 00:03:36.660
about a spreadsheet, is I
defined this cell as being

00:03:36.660 --> 00:03:41.970
$10,000 times whatever this
cell is right over here.

00:03:41.970 --> 00:03:45.710
And so what I can just do
is I can just take that,

00:03:45.710 --> 00:03:47.217
drag that all the way down.

00:03:47.217 --> 00:03:48.800
And for every one
of these, it's going

00:03:48.800 --> 00:03:52.170
to take $10,000
times the cell that's

00:03:52.170 --> 00:03:54.250
essentially three to its left.

00:03:54.250 --> 00:03:56.630
So now it's going to
be 10,000 times D8.

00:03:56.630 --> 00:03:59.990
This will be 10,000 times D9.

00:03:59.990 --> 00:04:00.794
Let's get that.

00:04:00.794 --> 00:04:02.210
So that we can see
it right there.

00:04:02.210 --> 00:04:04.080
10,000 times D9.

00:04:04.080 --> 00:04:05.802
And you could, if
you click on there,

00:04:05.802 --> 00:04:07.510
you can actually see
what the formula is.

00:04:07.510 --> 00:04:08.770
10,000 times D9.

00:04:08.770 --> 00:04:11.180
So by dragging that, I was
able to get the right formula

00:04:11.180 --> 00:04:13.120
all the way down.

00:04:13.120 --> 00:04:15.660
Now the total cost
for every row here

00:04:15.660 --> 00:04:19.075
is going to be two to the
left plus one to the left.

00:04:19.075 --> 00:04:20.450
And so if I drag
that down, it'll

00:04:20.450 --> 00:04:23.330
do that for every row over here.

00:04:23.330 --> 00:04:26.950
So now this is 25, is
the 15 plus the 10.

00:04:26.950 --> 00:04:28.590
105 is 15 plus 90,000.

00:04:28.590 --> 00:04:32.370
Our total costs are fixed
costs plus variable costs.

00:04:32.370 --> 00:04:34.862
Now let's think about
the average fixed cost.

00:04:34.862 --> 00:04:36.236
And the average
fixed cost, we're

00:04:36.236 --> 00:04:40.790
going to think about it in fixed
cost per line of code produced.

00:04:40.790 --> 00:04:43.030
And over here, line
of code produced is 0.

00:04:43.030 --> 00:04:46.480
So we're going to divide
by 0, which is undefined.

00:04:46.480 --> 00:04:47.860
So we could leave that blank.

00:04:47.860 --> 00:04:49.384
But we could fill this one in.

00:04:49.384 --> 00:04:50.800
So our total fixed
costs-- this is

00:04:50.800 --> 00:04:53.950
going to be our total fixed
costs, which is cell F8.

00:04:53.950 --> 00:04:58.140
I just used the arrow
keys to select F8.

00:04:58.140 --> 00:05:02.300
Divided by our total
lines of code per month.

00:05:02.300 --> 00:05:06.370
So divided by our total
lines of code per month.

00:05:06.370 --> 00:05:12.060
And so that gets me $3.75
fixed costs per line of code.

00:05:12.060 --> 00:05:14.990
And then I can do the same thing
that I've been doing before.

00:05:14.990 --> 00:05:16.870
I can drag this down.

00:05:16.870 --> 00:05:18.670
And then we see what
the fixed cost is.

00:05:18.670 --> 00:05:22.290
So if at any given point if I
take the fixed cost, $15,000,

00:05:22.290 --> 00:05:25.060
divided by the lines
of code, I get $1.38.

00:05:25.060 --> 00:05:28.730
And this actually makes sense
because the more programmers I

00:05:28.730 --> 00:05:31.600
add on to this project, the
more lines of code I get,

00:05:31.600 --> 00:05:33.480
I'm using the same
fixed costs I'm.

00:05:33.480 --> 00:05:35.350
Using the same project manager.

00:05:35.350 --> 00:05:36.920
I'm using the same office space.

00:05:36.920 --> 00:05:39.360
So the cost of that project
manager and that office space

00:05:39.360 --> 00:05:42.740
gets spread out along
more and more code.

00:05:42.740 --> 00:05:45.660
So the fixed cost
per line of code

00:05:45.660 --> 00:05:49.120
goes down as we add more
and more programmers.

00:05:49.120 --> 00:05:53.110
Now what is the average
of variable cost?

00:05:53.110 --> 00:05:54.750
So once again, the
variable cost is

00:05:54.750 --> 00:05:57.410
going to be whatever
the variable cost is

00:05:57.410 --> 00:05:59.550
per lines of code per month.

00:05:59.550 --> 00:06:01.050
So when we're talking
about average,

00:06:01.050 --> 00:06:04.240
we're talking about average
cost per line of code.

00:06:04.240 --> 00:06:06.640
So this is per line of code.

00:06:06.640 --> 00:06:08.790
Let me write it over here.

00:06:08.790 --> 00:06:12.570
Per line of code.

00:06:12.570 --> 00:06:15.010
And I can even say per month.

00:06:15.010 --> 00:06:16.424
Per line of code per month.

00:06:16.424 --> 00:06:18.090
Actually, I wanted
that spread out more.

00:06:18.090 --> 00:06:18.780
But the way I've set it up.

00:06:18.780 --> 00:06:19.696
So let me scroll down.

00:06:19.696 --> 00:06:21.340
Oops.

00:06:21.340 --> 00:06:22.590
I'm having issues here.

00:06:22.590 --> 00:06:23.090
All right.

00:06:23.090 --> 00:06:27.149
Well these are all average
lines of code per month.

00:06:27.149 --> 00:06:28.690
And so let's think
about what happens

00:06:28.690 --> 00:06:30.212
with our variable costs.

00:06:30.212 --> 00:06:31.920
So I'm also going to
start here because I

00:06:31.920 --> 00:06:33.520
don't want to divide by 0.

00:06:33.520 --> 00:06:38.050
So in this month, our total
variable costs were $10,000

00:06:38.050 --> 00:06:42.190
and our total lines of code
are going to be $4,000.

00:06:42.190 --> 00:06:44.710
G8 divided by E8.

00:06:44.710 --> 00:06:49.120
And so average variable cost
per line of code is 2.50 .

00:06:49.120 --> 00:06:50.350
And then what happens?

00:06:50.350 --> 00:06:52.617
So let's do that for
every row over here.

00:06:52.617 --> 00:06:55.200
So when we do it for every row,
something interesting happens.

00:06:55.200 --> 00:06:56.830
Our average fixed cost
went down because we're

00:06:56.830 --> 00:06:58.788
taking the same cost and
we're spreading it out

00:06:58.788 --> 00:07:00.370
amongst more code.

00:07:00.370 --> 00:07:02.900
But our average
variable cost went up.

00:07:02.900 --> 00:07:05.660
As we added more programmers,
per line of code,

00:07:05.660 --> 00:07:07.410
it actually costs
us a little bit more

00:07:07.410 --> 00:07:09.470
on average per line of code.

00:07:09.470 --> 00:07:11.420
And that's actually,
if you look here,

00:07:11.420 --> 00:07:14.452
as we add the incremental lines
of code we get per programmer

00:07:14.452 --> 00:07:15.410
is actually going down.

00:07:15.410 --> 00:07:17.390
That first programmer
by themselves,

00:07:17.390 --> 00:07:19.530
she can write 4,000
lines of code.

00:07:19.530 --> 00:07:22.710
But then that second programmer
you're not getting to 8,000,

00:07:22.710 --> 00:07:23.710
you're getting to 3,000.

00:07:23.710 --> 00:07:26.200
And probably because they have
to coordinate with each other.

00:07:26.200 --> 00:07:27.720
They have to plan
a little bit more.

00:07:27.720 --> 00:07:29.930
It's not all in
one person's head.

00:07:29.930 --> 00:07:31.490
Then, when you're
at the third one,

00:07:31.490 --> 00:07:33.281
you're not even adding
3,000 lines of code.

00:07:33.281 --> 00:07:35.077
You're only adding
2,000 lines of code.

00:07:35.077 --> 00:07:36.660
And this is actually
a real phenomenon

00:07:36.660 --> 00:07:38.118
that actually
happens in companies.

00:07:38.118 --> 00:07:41.020
The more people you
add on to a project,

00:07:41.020 --> 00:07:42.690
obviously they can
maybe do more work,

00:07:42.690 --> 00:07:44.050
but there's also
more coordination.

00:07:44.050 --> 00:07:45.250
There's going to
be more meetings.

00:07:45.250 --> 00:07:46.875
There's going to be
more interruptions.

00:07:46.875 --> 00:07:49.610
And so each person's
individual productivity

00:07:49.610 --> 00:07:50.981
is going to go down.

00:07:50.981 --> 00:07:53.230
And this isn't to say that
this third coder is somehow

00:07:53.230 --> 00:07:55.170
worse than the first coder.

00:07:55.170 --> 00:07:56.920
On average, all of
them are now only going

00:07:56.920 --> 00:08:01.400
to produce 3,000 lines of code
a month, when maybe individually

00:08:01.400 --> 00:08:03.696
they could have each
produced 4,000 lines of code,

00:08:03.696 --> 00:08:05.570
but they have to spend
some of their energies

00:08:05.570 --> 00:08:06.820
now coordinating it.

00:08:06.820 --> 00:08:10.890
And so that's why our average
variable cost per line of code

00:08:10.890 --> 00:08:12.010
is going up.

00:08:12.010 --> 00:08:15.290
As we add more and more
people, incrementally it's

00:08:15.290 --> 00:08:17.330
becoming more and more
expensive on average

00:08:17.330 --> 00:08:19.270
to write that line of code.

00:08:19.270 --> 00:08:21.540
And now if we look at
average total cost, that's

00:08:21.540 --> 00:08:23.380
going to be-- and
this is once again,

00:08:23.380 --> 00:08:25.380
this is per line
of code-- is going

00:08:25.380 --> 00:08:31.820
to be our total cost, H8 divided
by the total lines of code

00:08:31.820 --> 00:08:33.020
per month.

00:08:33.020 --> 00:08:36.390
So if we just hire
one engineer, we're

00:08:36.390 --> 00:08:42.195
going to have $6.25
spent per line of code.

00:08:42.195 --> 00:08:43.570
And this is actually
just the sum

00:08:43.570 --> 00:08:45.200
of these two right over here.

00:08:45.200 --> 00:08:50.350
And then, let me set that
formula for every row.

00:08:50.350 --> 00:08:52.370
And so we see
something interesting.

00:08:52.370 --> 00:08:55.160
When we start to
hire a few engineers,

00:08:55.160 --> 00:08:57.260
we're able to spread out
our fixed costs, even

00:08:57.260 --> 00:09:00.590
though our average variable cost
per line of code are going up,

00:09:00.590 --> 00:09:02.470
our fixed costs are going down.

00:09:02.470 --> 00:09:05.060
So it's actually we're getting
a little bit of a benefit

00:09:05.060 --> 00:09:08.120
because we're spreading our
fixed cost per line of code.

00:09:08.120 --> 00:09:09.960
But then it starts to
get expensive again

00:09:09.960 --> 00:09:11.870
because, as we said,
the more people you

00:09:11.870 --> 00:09:13.370
have working on the
project, they're

00:09:13.370 --> 00:09:15.850
going to have spend more time
coordinating with each other

00:09:15.850 --> 00:09:17.800
and maybe even undoing
each other's work

00:09:17.800 --> 00:09:20.480
or redoing each other's work
as opposed to just writing

00:09:20.480 --> 00:09:22.510
the actual software.

00:09:22.510 --> 00:09:24.960
And now let's think
about the marginal cost.

00:09:24.960 --> 00:09:27.005
The marginal cost, the
best way to think about it

00:09:27.005 --> 00:09:31.300
is, what is the incremental
cost of that next set of line

00:09:31.300 --> 00:09:32.077
of code?

00:09:32.077 --> 00:09:33.660
So one way to think
about it-- so this

00:09:33.660 --> 00:09:35.740
is going to be how much
more you're spending

00:09:35.740 --> 00:09:39.650
divided by how much more
code you're getting.

00:09:39.650 --> 00:09:42.150
So for example, how much
more-- and this is going to be,

00:09:42.150 --> 00:09:46.200
once again, per line of code.

00:09:46.200 --> 00:09:50.000
So when we go from zero
programmers to one programmer,

00:09:50.000 --> 00:09:52.410
we're going from
$15,000 of total cost

00:09:52.410 --> 00:09:56.270
to $25,000 of total cost.

00:09:56.270 --> 00:09:58.180
We do it in parentheses.

00:09:58.180 --> 00:10:01.000
If we're going
from 15 to 25, that

00:10:01.000 --> 00:10:04.510
means we're increasing our
expenditure by 25 minus 15.

00:10:04.510 --> 00:10:07.060
And so that's why I'm
doing H8 minus H7.

00:10:07.060 --> 00:10:10.150
So that's how much more we're
spending in expenditures.

00:10:10.150 --> 00:10:12.370
And then, how much more
code are we getting?

00:10:12.370 --> 00:10:17.819
Well we're getting 4,000
minus 0 lines of code.

00:10:17.819 --> 00:10:19.860
And the reason why I'm
doing the formula this way

00:10:19.860 --> 00:10:22.590
is so that when we drag
it down on all the rows,

00:10:22.590 --> 00:10:24.640
the formula will be
right because it's

00:10:24.640 --> 00:10:27.430
relatively taking the
right cells into account.

00:10:27.430 --> 00:10:29.180
And the reason why I'm
saying it's average

00:10:29.180 --> 00:10:30.554
is because this
is saying, what's

00:10:30.554 --> 00:10:33.780
the incremental cost per line of
code for this first 4,000 lines

00:10:33.780 --> 00:10:34.700
of code?

00:10:34.700 --> 00:10:36.870
And then we can go from there.

00:10:36.870 --> 00:10:38.580
And we can drag it down.

00:10:38.580 --> 00:10:40.330
And now this tells us
the incremental cost

00:10:40.330 --> 00:10:43.002
per code for the next
3,000 lines of code.

00:10:43.002 --> 00:10:44.460
And once again, it
got a little bit

00:10:44.460 --> 00:10:46.880
more expensive because we're
getting a little bit less

00:10:46.880 --> 00:10:49.245
efficient as we add
more and more people.

00:10:49.245 --> 00:10:51.620
And there's something very
interesting that happens here.

00:10:51.620 --> 00:10:54.300
And you might have even noticed
it in these numbers over here.

00:10:54.300 --> 00:10:56.104
We actually get a
negative marginal cost.

00:10:56.104 --> 00:10:58.520
And this isn't meaning that
when we add more lines of code

00:10:58.520 --> 00:10:59.740
somehow we're getting money.

00:10:59.740 --> 00:11:02.890
It's actually saying that
as we spend more money,

00:11:02.890 --> 00:11:04.510
we're actually
killing lines of code.

00:11:04.510 --> 00:11:06.593
Because at some point, if
you have too many people

00:11:06.593 --> 00:11:08.680
on this one project
team, they actually

00:11:08.680 --> 00:11:10.627
start killing each
other's productivity.

00:11:10.627 --> 00:11:12.710
And you can even see it
right here in the numbers.

00:11:12.710 --> 00:11:14.120
When we had seven
people, we were

00:11:14.120 --> 00:11:15.942
able to write 11,400
lines of code.

00:11:15.942 --> 00:11:18.150
But then the eighth person,
because of coordination--

00:11:18.150 --> 00:11:20.130
it's not that this eighth
person is incompetent,

00:11:20.130 --> 00:11:22.088
it's just when you have
eight people on a team,

00:11:22.088 --> 00:11:23.830
everyone's productivity
goes down so

00:11:23.830 --> 00:11:26.970
that you're only able to
produce 11,200 lines of code.

00:11:26.970 --> 00:11:29.377
And that's why you had this
negative marginal cost.

00:11:29.377 --> 00:11:31.460
Now, when you get to eight
people, all of a sudden

00:11:31.460 --> 00:11:33.330
by spending more
dollars, you're actually

00:11:33.330 --> 00:11:36.532
destroying some of what you
were actually trying to produce.

00:11:36.532 --> 00:11:37.990
So what I wanted
to do here is just

00:11:37.990 --> 00:11:39.610
to really get you
behind the numbers

00:11:39.610 --> 00:11:40.960
and really maybe give
you a little sense of how

00:11:40.960 --> 00:11:42.870
you can actually do
this with a spreadsheet.

00:11:42.870 --> 00:11:45.770
And get you thinking a little
bit about how a firm's cost

00:11:45.770 --> 00:11:48.840
structure might actually work.


Depreciation and opportunity cost of capital

WEBVTT
Kind: captions
Language: en

00:00:00.540 --> 00:00:02.707
Background voice: Let's
think about how we would

00:00:02.707 --> 00:00:04.030
have accounted for things,

00:00:04.030 --> 00:00:07.123
if instead of renting our
building for $200,000,

00:00:07.123 --> 00:00:10.137
instead we bought the
building for $2,000,000,

00:00:10.137 --> 00:00:11.605
how would that showed up …

00:00:11.605 --> 00:00:13.541
how would that have shown up

00:00:13.541 --> 00:00:15.457
from an accounting profit point of view

00:00:15.457 --> 00:00:18.290
and an economic profit point of view?

00:00:18.290 --> 00:00:22.939
We're going to buy our
building for $2,000,000.

00:00:22.939 --> 00:00:25.137
That is the market value of our building

00:00:25.137 --> 00:00:26.963
at the beginning of our period,

00:00:26.963 --> 00:00:29.271
at the beginning of year 1.

00:00:29.271 --> 00:00:31.404
Let's say, at the end of year 1,

00:00:31.404 --> 00:00:34.935
so this is year 1 right
over here, that occurs.

00:00:34.935 --> 00:00:35.936
Maybe, to a large degree,

00:00:35.936 --> 00:00:37.627
this is because I used the building,

00:00:37.627 --> 00:00:39.545
there was a lot of traffic in there.

00:00:39.545 --> 00:00:40.805
Maybe it was a brand new building before

00:00:40.805 --> 00:00:42.004
and now it's essentially kind of ...

00:00:42.004 --> 00:00:44.544
the building itself has
taken some wear and tear.

00:00:44.544 --> 00:00:47.404
Because of that, the market
value of the building

00:00:47.404 --> 00:00:51.295
is now, 1.9 million dollars.

00:00:51.295 --> 00:00:53.045
Essentially, through this year,

00:00:53.045 --> 00:00:59.338
the building's value has
depreciated by $100,000.

00:00:59.338 --> 00:01:03.805
We'll say the depreciation is $100,000.

00:01:03.805 --> 00:01:06.963
Notice, I didn't pay anyone that $100,000.

00:01:06.963 --> 00:01:11.405
It was not an explicit opportunity cost,

00:01:11.405 --> 00:01:13.378
but this really is an opportunity cost,

00:01:13.378 --> 00:01:18.071
because this $100,000
is the opportunity cost

00:01:18.071 --> 00:01:20.404
of not selling the building a year ago.

00:01:20.404 --> 00:01:21.938
Instead, using that building,

00:01:21.938 --> 00:01:25.295
I have essentially lost out on $100,000.

00:01:25.295 --> 00:01:27.963
That's not all that I have lost out on.

00:01:27.963 --> 00:01:31.558
I have also lost out on
the ability to invest

00:01:31.558 --> 00:01:33.869
this $2,000,000 in other things.

00:01:33.869 --> 00:01:36.877
Maybe I could have
invested the $2,000,000

00:01:36.877 --> 00:01:41.270
at a 5% rate and gotten
some interest on it.

00:01:41.270 --> 00:01:44.004
I also have the opportunity cost,

00:01:44.004 --> 00:01:46.472
opportunity cost

00:01:46.472 --> 00:01:51.110
of capital, of not
investing that $2,000,000

00:01:51.110 --> 00:01:52.804
some place else.

00:01:52.804 --> 00:01:54.337
The opportunity cost of capital,

00:01:54.337 --> 00:01:58.737
let's say I could have
gotten 5% on my $2,000,000.

00:01:58.737 --> 00:02:03.137
5% of 2,000,000 is $100,000.

00:02:03.137 --> 00:02:07.360
My opportunity cost of
capital is $100,000.

00:02:07.360 --> 00:02:09.337
Another way to think about it is,

00:02:09.337 --> 00:02:11.026
let's just say that I buy the building

00:02:11.026 --> 00:02:12.805
and I sell it at the end of the year.

00:02:12.805 --> 00:02:15.360
Then, I would have literally lost $100,000

00:02:15.360 --> 00:02:16.870
on that transaction

00:02:16.870 --> 00:02:18.610
and although I might have used it,

00:02:18.610 --> 00:02:20.694
so I got some value out of it,

00:02:20.694 --> 00:02:23.360
and I would have lost another $100,000

00:02:23.360 --> 00:02:26.276
by not having that money
invested in some other use

00:02:26.276 --> 00:02:27.804
during that period.

00:02:27.804 --> 00:02:30.026
These are the 2 non-explicit cost

00:02:30.026 --> 00:02:32.203
that will come into ...

00:02:32.203 --> 00:02:34.610
that would show up in
our profit statements.

00:02:34.610 --> 00:02:39.803
Now, depreciation is something
that is accounted for

00:02:39.803 --> 00:02:41.137
by accountants.

00:02:41.137 --> 00:02:42.610
When you look at a company's financials,

00:02:42.610 --> 00:02:45.070
you will see something
called a depreciation.

00:02:45.070 --> 00:02:47.610
Which is a measure of, how are you ...

00:02:47.610 --> 00:02:49.693
You're kind of using
up your capital goods,

00:02:49.693 --> 00:02:51.403
you are using up your building,

00:02:51.403 --> 00:02:52.777
you are using up your equipment,

00:02:52.777 --> 00:02:55.275
you are using up your vehicles,

00:02:55.275 --> 00:02:57.275
or whatever else you might have.

00:02:57.275 --> 00:02:59.526
Economist are very pure
about depreciation.

00:02:59.526 --> 00:03:01.138
They say, what was the market value

00:03:01.138 --> 00:03:01.871
at the beginning of the period,

00:03:01.871 --> 00:03:03.806
what is the market value at the end,

00:03:03.806 --> 00:03:05.943
the difference is how
much it has depreciated.

00:03:05.943 --> 00:03:07.203
This is kind of ...

00:03:07.203 --> 00:03:08.776
it's actually almost a more natural way.

00:03:08.776 --> 00:03:10.361
In accounting, and I
won't go into the details,

00:03:10.361 --> 00:03:12.402
there are many ways to
depreciate something.

00:03:12.402 --> 00:03:13.403
You might be able to say,

00:03:13.403 --> 00:03:15.442
"Well, if the thing is worth $2,000,000"

00:03:15.442 --> 00:03:18.026
"and if it's going to last me 10 years,"

00:03:18.026 --> 00:03:21.138
"I can depreciate $100,000 a year,"

00:03:21.138 --> 00:03:22.536
"or actually $200,000 a year."

00:03:22.536 --> 00:03:25.070
2,000,000 divided by 10 years.

00:03:25.070 --> 00:03:26.870
There is different incentives based on

00:03:26.870 --> 00:03:28.870
if you are the owner of a firm,

00:03:28.870 --> 00:03:30.276
of how you depreciate.

00:03:30.276 --> 00:03:31.203
You might want to actually want to have

00:03:31.203 --> 00:03:33.070
a lot of depreciation for tax purposes,

00:03:33.070 --> 00:03:36.942
so that you can somehow
hide a profit or whatever.

00:03:36.942 --> 00:03:38.610
For the sake of this video,
we're going to assume

00:03:38.610 --> 00:03:40.671
that both the accountants
and the economist

00:03:40.671 --> 00:03:45.274
will mark off $100,000 of depreciation,

00:03:45.274 --> 00:03:47.609
if we were to buy the building.

00:03:47.609 --> 00:03:50.276
Let's redo our 2 financial statements,

00:03:50.276 --> 00:03:53.525
the accounting version
and the economic version.

00:03:53.525 --> 00:03:54.804
In the accounting version ...

00:03:54.804 --> 00:03:59.360
Let me copy and paste all of this.

00:03:59.360 --> 00:04:03.943
Copy and let me go down here and paste it.

00:04:03.943 --> 00:04:06.070
Let me paste it.

00:04:06.070 --> 00:04:09.270
Now, we don't have any rent expense.

00:04:09.270 --> 00:04:10.204
Instead of renting the building,

00:04:10.204 --> 00:04:11.943
we've gone off and we've
bought the building.

00:04:11.943 --> 00:04:13.736
Let me get rid of that.

00:04:13.736 --> 00:04:18.537
Our rent expense is now going to be 0,

00:04:18.537 --> 00:04:20.471
is now going to be 0.

00:04:20.471 --> 00:04:22.609
We do have a depreciation expense.

00:04:22.609 --> 00:04:24.204
I'll write that in another color.

00:04:24.204 --> 00:04:30.942
We do have a depreciation
expense of $100,000.

00:04:30.942 --> 00:04:33.443
We don't think about the
opportunity cost of capital.

00:04:33.443 --> 00:04:35.471
What we could have done ...

00:04:35.471 --> 00:04:37.204
This is opportunity cost of capital.

00:04:37.204 --> 00:04:38.942
What we could have done
with that $2,000,000

00:04:38.942 --> 00:04:41.805
that we used to buy the building.

00:04:41.805 --> 00:04:44.026
Our pretax profit,

00:04:44.026 --> 00:04:46.941
our pretax accounting profit,

00:04:46.941 --> 00:04:50.941
pretax profit from an
accounting point of view,

00:04:50.941 --> 00:04:54.609
is going to be … Let's see, 50 minus 200

00:04:54.609 --> 00:04:58.290
is 300, minus another ...

00:04:58.290 --> 00:04:59.443
Let me make sure that I get this right.

00:04:59.443 --> 00:05:00.943
I have …

00:05:00.943 --> 00:05:01.942
Actually, it's gotten better,

00:05:01.942 --> 00:05:03.337
because my rent was 200

00:05:03.337 --> 00:05:05.203
and now I only have a depreciation of 100.

00:05:05.203 --> 00:05:13.622
It's 50 minus 350 gives me
a pretax profit of $150,000.

00:05:13.622 --> 00:05:16.204
That was because I was renting it for more

00:05:16.204 --> 00:05:18.609
and now my depreciation, based on how ...

00:05:18.609 --> 00:05:19.860
what happened with the market rate,

00:05:19.860 --> 00:05:21.072
actually changed less

00:05:21.072 --> 00:05:22.609
than what my rent would have been.

00:05:22.609 --> 00:05:23.681
The economic profit,

00:05:23.681 --> 00:05:25.529
at least based on the way
we've done the numbers here

00:05:25.529 --> 00:05:26.794
it will actually come out neutral.

00:05:26.794 --> 00:05:27.724
Which it should,

00:05:27.724 --> 00:05:29.029
because really economic profit,

00:05:29.029 --> 00:05:30.113
we're just trying to decide,

00:05:30.113 --> 00:05:33.458
does it make sense for us to
run this business in this way.

00:05:33.458 --> 00:05:35.792
When we look at the economic profit ...

00:05:35.792 --> 00:05:39.980
Let's copy and paste this again.

00:05:39.980 --> 00:05:42.425
Let me copy just this part.

00:05:42.425 --> 00:05:46.991
Copy and paste.

00:05:46.991 --> 00:05:48.759
Maybe if things actually did improve,

00:05:48.759 --> 00:05:52.192
when we actually changed
whether we owned or rent,

00:05:52.192 --> 00:05:54.663
then that would say that's the
more economic way to do it.

00:05:54.663 --> 00:05:59.060
Let's say that it's year
2 or this is year 1 again.

00:05:59.060 --> 00:06:02.859
Now we're doing, this is
economic profit, year 1.

00:06:02.859 --> 00:06:03.747
Our food is the same.

00:06:03.747 --> 00:06:04.723
Our labor is the same.

00:06:04.723 --> 00:06:06.792
Our rent disappears.

00:06:06.792 --> 00:06:08.997
Let me get rid of that.

00:06:08.997 --> 00:06:10.125
Let me get rid of the rent.

00:06:10.125 --> 00:06:12.192
The rent is now going to be 0.

00:06:12.192 --> 00:06:13.997
We now own our building.

00:06:13.997 --> 00:06:15.330
Rent is 0.

00:06:15.330 --> 00:06:17.095
These are all our explicit cost.

00:06:17.095 --> 00:06:22.193
These are direct payments
of money to someone else.

00:06:22.193 --> 00:06:24.758
Now, let's think about our implicit cost.

00:06:24.758 --> 00:06:27.728
Implicit cost.

00:06:27.728 --> 00:06:29.457
We still have the same implicit cost

00:06:29.457 --> 00:06:30.527
that we had up here.

00:06:30.527 --> 00:06:32.007
We have the wages foregone.

00:06:32.007 --> 00:06:33.524
We talked about maybe I was a doctor

00:06:33.524 --> 00:06:35.992
and I'm not working as a
doctor to run this restaurant,

00:06:35.992 --> 00:06:39.256
so my wages foregone are $150,000.

00:06:39.256 --> 00:06:46.773
Wages foregone are $150,000.

00:06:46.773 --> 00:06:47.857
Actually, I think ...

00:06:47.857 --> 00:06:54.189
Wages lost are $150,000.

00:06:54.189 --> 00:06:57.457
Now, we have the
depreciation on top of that.

00:06:57.457 --> 00:06:59.857
I'll do this in magenta
to show what is new.

00:06:59.857 --> 00:07:03.925
We have the depreciation of $100,000.

00:07:03.925 --> 00:07:04.939
On top of that,

00:07:04.939 --> 00:07:07.024
we have the opportunity cost of capital.

00:07:07.024 --> 00:07:09.260
The return we could have
gotten on that $2,000,000,

00:07:09.260 --> 00:07:11.607
that instead we used to buy the building.

00:07:11.607 --> 00:07:16.792
I'll call it OCC,
opportunity cost of capital,

00:07:16.792 --> 00:07:20.458
in this situation was
the 5% of $2,000,000,

00:07:20.458 --> 00:07:24.940
another $100,000.

00:07:24.940 --> 00:07:26.993
The way that I've worked
out the numbers here,

00:07:26.993 --> 00:07:29.273
we didn't have to spend 200,000 on rent,

00:07:29.273 --> 00:07:32.392
but we increased our implicit
cost by owning the building,

00:07:32.392 --> 00:07:35.356
by 200,000, so it all comes out the same.

00:07:35.356 --> 00:07:38.106
We still get what we
got in the previous one,

00:07:38.106 --> 00:07:41.992
of an economic profit
of negative $100,000.

00:07:41.992 --> 00:07:48.124
Negative 100,000 of economic profit.

00:07:48.124 --> 00:07:50.122
Economic profit.

00:07:50.122 --> 00:07:54.392
This of course was accounting profit.

00:07:54.392 --> 00:07:56.025
I wanted to really just highlight in this,

00:07:56.025 --> 00:07:57.773
is that you don't get kind of a freebie

00:07:57.773 --> 00:08:00.811
on the economic profit
when you decide to buy

00:08:00.811 --> 00:08:03.348
instead of rent, or rent verses buy.

00:08:03.348 --> 00:08:05.059
There are still ways of accounting for,

00:08:05.059 --> 00:08:06.939
essentially, the opportunity cost

00:08:06.939 --> 00:08:10.000
of doing any of these actions.