AP Microeconomics FRQ on perfect competition

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:00.890
- [Instructor] This is
the type of question

00:00:00.890 --> 00:00:03.690
that you might see on
an AP Economics exam,

00:00:03.690 --> 00:00:06.600
and it's talking about
perfectly competitive markets.

00:00:06.600 --> 00:00:09.900
So it says, a typical
profit-maximizing firm

00:00:09.900 --> 00:00:13.690
in a perfectly competitive
constant-cost industry

00:00:13.690 --> 00:00:17.550
is earning a positive economic profit.

00:00:17.550 --> 00:00:19.220
So the first question they ask us is,

00:00:19.220 --> 00:00:22.150
is the market price
greater than, less than,

00:00:22.150 --> 00:00:24.250
or equal to the firm's price?

00:00:24.250 --> 00:00:25.880
Explain.

00:00:25.880 --> 00:00:27.620
So pause this video and
see if you can answer

00:00:27.620 --> 00:00:30.170
this on your own before we do it together.

00:00:30.170 --> 00:00:31.410
All right now let's do it together.

00:00:31.410 --> 00:00:32.890
So remember, we are talking

00:00:32.890 --> 00:00:36.730
about a perfectly competitive market.

00:00:36.730 --> 00:00:38.660
So in a perfectly competitive market,

00:00:38.660 --> 00:00:42.100
all of the players in that
market have to be price takers.

00:00:42.100 --> 00:00:44.230
They have no pricing power.

00:00:44.230 --> 00:00:49.230
So the market price has to
be equal to the firm's price.

00:00:49.310 --> 00:00:53.440
So market, market price

00:00:54.730 --> 00:00:59.400
equal, equal to firm price, firm price

00:01:01.390 --> 00:01:05.943
because in perfectly,

00:01:07.070 --> 00:01:11.490
perfectly competitive market, market,

00:01:12.660 --> 00:01:14.770
firms are price takers,

00:01:14.770 --> 00:01:19.530
firms are price takers.

00:01:19.530 --> 00:01:20.960
They have no pricing power.

00:01:20.960 --> 00:01:22.770
All right, part b.

00:01:22.770 --> 00:01:25.780
Draw correctly labeled
side-by-side graphs for both

00:01:25.780 --> 00:01:28.030
the market and a typical firm

00:01:28.030 --> 00:01:30.350
and show each of the following.

00:01:30.350 --> 00:01:32.390
And they ask us to do
a bunch of stuff here.

00:01:32.390 --> 00:01:34.210
So once again, pause this video
and actually get out paper.

00:01:34.210 --> 00:01:36.928
This will be very valuable
for you to have a go at this.

00:01:36.928 --> 00:01:40.170
All right, so let's see we wanna do

00:01:40.170 --> 00:01:42.870
these side-by-side graphs,
and we wanna think about

00:01:42.870 --> 00:01:44.670
the market and the firm.

00:01:44.670 --> 00:01:47.140
And we've done this in
multiple videos before.

00:01:47.140 --> 00:01:50.090
So let's think about what
they're talking about is,

00:01:50.090 --> 00:01:52.103
so this is the market right over here.

00:01:53.210 --> 00:01:54.513
That's the market.

00:01:55.380 --> 00:01:59.130
And this is, on this axis
is going to be price.

00:01:59.130 --> 00:02:01.483
On this axis is going to be quantity.

00:02:02.500 --> 00:02:06.110
And then let me do a similar
thing for a firm here.

00:02:06.110 --> 00:02:10.697
So that would be the
firm's price axis, price.

00:02:12.110 --> 00:02:17.093
And then this would be quantity
for the firm, quantity.

00:02:18.720 --> 00:02:21.720
Let me make it clear, this is the market,

00:02:21.720 --> 00:02:26.720
and then this right over here is the firm.

00:02:26.740 --> 00:02:29.190
And let's see, they say,
market price and quantity.

00:02:29.190 --> 00:02:31.800
So the equilibrium price
and quantity in the market.

00:02:31.800 --> 00:02:35.540
So we could draw the supply
curve for the market.

00:02:35.540 --> 00:02:38.040
It might look something like this,

00:02:38.040 --> 00:02:39.970
upward-sloping, we've
seen that multiple times.

00:02:39.970 --> 00:02:42.230
We could do the demand
curve for the market.

00:02:42.230 --> 00:02:43.950
It would look something like that.

00:02:43.950 --> 00:02:47.670
And then we have the
equilibrium price in the market,

00:02:47.670 --> 00:02:50.840
which they want us to
use P sub m, so P sub m.

00:02:50.840 --> 00:02:54.370
And then we have the equilibrium
quantity in the market,

00:02:54.370 --> 00:02:57.220
which they want us to use Q sub m.

00:02:57.220 --> 00:02:59.900
So we've done this first part.

00:02:59.900 --> 00:03:01.490
All right now let's see
what else they want.

00:03:01.490 --> 00:03:03.950
The firm's quantity, labeled Q sub f,

00:03:03.950 --> 00:03:07.530
the firm's average
revenue curve, labeled AR,

00:03:07.530 --> 00:03:10.598
the firm's average total
cost curve, labeled ATC,

00:03:10.598 --> 00:03:14.780
the area representing total
cost shaded completely.

00:03:14.780 --> 00:03:16.330
So in order to do this first part,

00:03:16.330 --> 00:03:18.350
the quantity that it would be rational

00:03:18.350 --> 00:03:22.138
for this profit-seeking firm
or the profit-maximizing firm

00:03:22.138 --> 00:03:24.210
to produce, to think about that,

00:03:24.210 --> 00:03:25.340
we'd actually also have to think about

00:03:25.340 --> 00:03:27.170
the firm's average revenue.

00:03:27.170 --> 00:03:30.000
And the average revenue, which
is going to be the same thing

00:03:30.000 --> 00:03:31.620
as the demand curve for that firm,

00:03:31.620 --> 00:03:33.240
is going to be based on this market price.

00:03:33.240 --> 00:03:36.390
Remember, the firm, in this
perfectly competitive market,

00:03:36.390 --> 00:03:38.350
has to be a price taker.

00:03:38.350 --> 00:03:41.170
So this horizontal line right over there,

00:03:41.170 --> 00:03:46.010
that is the firm's average revenue, AR,

00:03:46.010 --> 00:03:48.690
which is equal to its marginal revenue,

00:03:48.690 --> 00:03:50.860
which is equal to its demand curve,

00:03:50.860 --> 00:03:53.750
which is equal to this market price.

00:03:53.750 --> 00:03:56.010
And the quantity that it's
rational for this firm

00:03:56.010 --> 00:03:58.770
to produce is where this
marginal revenue curve,

00:03:58.770 --> 00:04:01.260
which is also the average
revenue curve in this case,

00:04:01.260 --> 00:04:04.170
intersects our marginal cost curve.

00:04:04.170 --> 00:04:07.780
So the marginal cost curve
might look something,

00:04:07.780 --> 00:04:09.800
something like this.

00:04:09.800 --> 00:04:12.263
So marginal cost.

00:04:13.190 --> 00:04:18.190
And so this right over
here is our Q sub f.

00:04:19.230 --> 00:04:22.280
So we've done this part and this part.

00:04:22.280 --> 00:04:24.878
The firm's average total cost curve,

00:04:24.878 --> 00:04:28.700
well the average total
cost at this quantity

00:04:28.700 --> 00:04:31.567
needs to be below the marginal revenue

00:04:31.567 --> 00:04:33.450
and the average revenue at that quantity

00:04:33.450 --> 00:04:35.120
because we know that the firm is earning

00:04:35.120 --> 00:04:38.010
a positive economic profit.

00:04:38.010 --> 00:04:41.530
So we are dealing with
a situation that likely

00:04:41.530 --> 00:04:42.470
looks like this.

00:04:42.470 --> 00:04:47.470
So the average total cost
might look something like this.

00:04:47.830 --> 00:04:51.900
And I drew it that way to
ensure that at this quantity,

00:04:51.900 --> 00:04:56.060
Q sub f, our marginal revenue
and our average revenue

00:04:56.060 --> 00:04:58.680
is above our average total cost.

00:04:58.680 --> 00:05:01.030
That tells us that we're
earning economic profit

00:05:01.030 --> 00:05:02.360
in this situation.

00:05:02.360 --> 00:05:04.180
So I've done part iv.

00:05:04.180 --> 00:05:07.800
The area representing total
cost shaded completely,

00:05:07.800 --> 00:05:10.413
well the area representing
total cost would be

00:05:10.413 --> 00:05:14.030
the cost per unit, the
average cost per unit,

00:05:14.030 --> 00:05:17.495
which is that much, times
the total number of units.

00:05:17.495 --> 00:05:21.930
And the total number of units
is going to be this length,

00:05:21.930 --> 00:05:23.690
which is equal to Q sub f.

00:05:23.690 --> 00:05:28.340
And so your total cost is
going to be this shaded area.

00:05:28.340 --> 00:05:30.860
If they were asking us
our total economic profit,

00:05:30.860 --> 00:05:33.540
then we would be talking
about this area up here,

00:05:33.540 --> 00:05:34.373
but they're not.

00:05:34.373 --> 00:05:36.780
They're talking about our total cost,

00:05:36.780 --> 00:05:39.370
which is this area right over there.

00:05:39.370 --> 00:05:41.050
So we have done those parts.

00:05:41.050 --> 00:05:42.758
Now let's go to part c.

00:05:42.758 --> 00:05:46.490
If one firm in the market
were to raise its price,

00:05:46.490 --> 00:05:48.060
what would happen to its total revenue?

00:05:48.060 --> 00:05:48.893
Explain.

00:05:48.893 --> 00:05:50.188
Pause this video, see
if you can answer that.

00:05:50.188 --> 00:05:52.590
Well remember, we're dealing

00:05:52.590 --> 00:05:55.000
with a perfectly competitive market,

00:05:55.000 --> 00:05:56.530
a perfectly competitive industry.

00:05:56.530 --> 00:05:58.810
There's no differentiation
between anyone's products.

00:05:58.810 --> 00:06:01.430
So if all of a sudden, someone
were to stick their head out

00:06:01.430 --> 00:06:03.890
and try to raise price, no one would buy

00:06:03.890 --> 00:06:05.606
their product anymore
because people can get

00:06:05.606 --> 00:06:09.210
identical products from other
people for a lower price.

00:06:09.210 --> 00:06:11.333
And so, its total revenue,

00:06:12.300 --> 00:06:15.750
its total revenue

00:06:17.090 --> 00:06:22.090
would go to zero

00:06:22.100 --> 00:06:27.100
since product is undifferentiated,
undifferentiated,

00:06:32.330 --> 00:06:37.330
and consumers could

00:06:37.520 --> 00:06:41.480
buy from others

00:06:42.580 --> 00:06:44.240
at lower price,

00:06:44.240 --> 00:06:47.310
at lower price.

00:06:47.310 --> 00:06:48.865
And this is another way to think about it.

00:06:48.865 --> 00:06:51.280
They have to be price takers

00:06:51.280 --> 00:06:53.523
in a perfectly competitive market.


Long run supply when industry costs are increasing or decreasing

WEBVTT
Kind: captions
Language: en

00:00:00.310 --> 00:00:01.830
- [Instructor] What we
have here we can view

00:00:01.830 --> 00:00:04.984
as the long run equilibrium
or long run steady state

00:00:04.984 --> 00:00:07.600
for a perfectly competitive market.

00:00:07.600 --> 00:00:09.420
Let's say this is the market for apples

00:00:09.420 --> 00:00:11.530
and this is idealized
perfectly competitive

00:00:11.530 --> 00:00:14.340
situation where you have
many firms producing,

00:00:14.340 --> 00:00:16.750
they're non-differentiated,
they have the same

00:00:16.750 --> 00:00:19.460
cost structure, there's no
barriers to entry or exit.

00:00:19.460 --> 00:00:20.870
And on the left you can see that

00:00:20.870 --> 00:00:22.954
this equilibrium price which is set by

00:00:22.954 --> 00:00:25.445
the intersection of the
supply and demand curves,

00:00:25.445 --> 00:00:27.770
that that's just going
to be the price that

00:00:27.770 --> 00:00:29.610
the firms have to take and we've talked

00:00:29.610 --> 00:00:31.240
about that at length in other videos.

00:00:31.240 --> 00:00:33.430
That's going to define that the firm's

00:00:33.430 --> 00:00:34.830
marginal revenue, not just this firm,

00:00:34.830 --> 00:00:36.514
but all of the participants of the market.

00:00:36.514 --> 00:00:38.956
In other videos we've
talked about the fact that

00:00:38.956 --> 00:00:41.681
the rational quantity
for this firm to produce

00:00:41.681 --> 00:00:43.760
would be where marginal revenue

00:00:43.760 --> 00:00:45.230
intersects marginal cost.

00:00:45.230 --> 00:00:46.890
And it's also gonna be the point where

00:00:46.890 --> 00:00:48.660
you have zero economic profit,

00:00:48.660 --> 00:00:50.560
where at that quantity, let's say the

00:00:50.560 --> 00:00:54.220
quantity for the firm,
your average total cost

00:00:54.220 --> 00:00:56.248
is equal to your marginal revenue.

00:00:56.248 --> 00:00:58.470
If marginal revenue were higher than

00:00:58.470 --> 00:01:00.744
average total cost at this quantity,

00:01:00.744 --> 00:01:02.810
well then you would have other entrants

00:01:02.810 --> 00:01:03.870
into the market because you're having

00:01:03.870 --> 00:01:05.490
positive economic profit.

00:01:05.490 --> 00:01:08.260
If marginal revenue is
below average total cost

00:01:08.260 --> 00:01:10.650
at that quantity, well
then firms are running

00:01:10.650 --> 00:01:12.930
economic losses and you will have people

00:01:12.930 --> 00:01:14.034
exiting the industry.

00:01:14.034 --> 00:01:16.310
And either of those
situations would get us

00:01:16.310 --> 00:01:17.980
back to an equilibrium state that looks

00:01:17.980 --> 00:01:18.881
something like this.

00:01:18.881 --> 00:01:21.708
But now let's imagine
a shock to the market

00:01:21.708 --> 00:01:24.979
somehow, let's say a new
research study comes out

00:01:24.979 --> 00:01:28.520
that says that the apples that this market

00:01:28.520 --> 00:01:31.130
produces, that it's
incredibly good for you,

00:01:31.130 --> 00:01:33.000
it'll make you live longer,
it'll make you happier,

00:01:33.000 --> 00:01:34.530
it'll make you have more friends.

00:01:34.530 --> 00:01:36.573
Well then the demand for apples goes up,

00:01:36.573 --> 00:01:39.621
and so you have a new demand curve

00:01:39.621 --> 00:01:42.358
that looks something like this, D prime.

00:01:42.358 --> 00:01:44.993
Well in that situation,
what's going to happen?

00:01:44.993 --> 00:01:47.230
Well now you have a new equilibrium price,

00:01:47.230 --> 00:01:49.240
you also have a new
equilibrium quantity over here,

00:01:49.240 --> 00:01:50.620
let's call that P Prime.

00:01:50.620 --> 00:01:54.560
This is going to define a
new marginal revenue curve,

00:01:54.560 --> 00:01:57.750
for the participants in the industry.

00:01:57.750 --> 00:01:59.680
So M, marginal revenue, prime.

00:01:59.680 --> 00:02:02.170
And now all of a sudden,
the rational quantity

00:02:02.170 --> 00:02:03.900
for them to produce would be out here,

00:02:03.900 --> 00:02:07.506
at least for this firm to
produce, so Q prime for,

00:02:07.506 --> 00:02:09.500
this firm is out here and you notice

00:02:09.500 --> 00:02:12.336
at that quantity, it is
making economic profit.

00:02:12.336 --> 00:02:14.490
For every unit it gets that much,

00:02:14.490 --> 00:02:17.010
it costs that much on
average for every unit,

00:02:17.010 --> 00:02:19.040
so it's making that much per unit,

00:02:19.040 --> 00:02:21.450
and then you multiply
that times the number

00:02:21.450 --> 00:02:22.641
of units or the quantity.

00:02:22.641 --> 00:02:24.450
This whole area is going to be

00:02:24.450 --> 00:02:27.130
the economic profit that
this firm is getting,

00:02:27.130 --> 00:02:28.450
and it's like that all of the firms,

00:02:28.450 --> 00:02:30.120
or most of the firms in this perfectly

00:02:30.120 --> 00:02:31.860
competitive market are
going to be getting it

00:02:31.860 --> 00:02:33.570
'cause they all have
the same cost structure.

00:02:33.570 --> 00:02:36.351
But as we said before,
when you have this positive

00:02:36.351 --> 00:02:39.350
economic profit, and there's
no barriers to entry,

00:02:39.350 --> 00:02:42.010
in the long run, more firms will enter

00:02:42.010 --> 00:02:44.690
because there's economic profit to be had.

00:02:44.690 --> 00:02:47.380
And in previous videos, we've talked about

00:02:47.380 --> 00:02:50.390
a situation where as
firms enter into a market,

00:02:50.390 --> 00:02:51.754
or exit a market, it doesn't change

00:02:51.754 --> 00:02:54.346
the cost structures of
the individual firms.

00:02:54.346 --> 00:02:56.350
So let's imagine for a second that because

00:02:56.350 --> 00:02:58.350
of everyone entering into this market

00:02:58.350 --> 00:03:00.040
that seems to have economic profit

00:03:00.040 --> 00:03:02.040
for the firms that are
participating into it,

00:03:02.040 --> 00:03:04.160
some of the inputs of say, growing apples,

00:03:04.160 --> 00:03:05.420
which is is what these firms do,

00:03:05.420 --> 00:03:06.810
start to go up in costs.

00:03:06.810 --> 00:03:08.340
So we're not talking about constant costs,

00:03:08.340 --> 00:03:09.880
perfectly competitive
market, now we're not

00:03:09.880 --> 00:03:11.510
talking about an increasing cost,

00:03:11.510 --> 00:03:12.693
perfectly competitive market.

00:03:12.693 --> 00:03:15.760
Well then firm A and every
firm's cost structure

00:03:15.760 --> 00:03:17.589
is going to change because as more firms

00:03:17.589 --> 00:03:19.498
come in, you're going to have to pay more

00:03:19.498 --> 00:03:22.720
for maybe apple seeds, pay
more for maybe pesticides,

00:03:22.720 --> 00:03:25.200
or wax, or maybe you pay more for land

00:03:25.200 --> 00:03:26.150
on which to grow them.

00:03:26.150 --> 00:03:28.643
And so you would have a
different marginal cost curve.

00:03:28.643 --> 00:03:31.880
We have the marginal cost
curve now looks like this.

00:03:31.880 --> 00:03:33.923
So marginal cost curve prime.

00:03:33.923 --> 00:03:36.978
You would also have a new
average total cost curve,

00:03:36.978 --> 00:03:41.978
maybe it looks something like this.

00:03:42.720 --> 00:03:45.710
So average total cost prime.

00:03:45.710 --> 00:03:47.580
And so, you can imagine that firms

00:03:47.580 --> 00:03:50.870
will jump into the market
in order to capture

00:03:50.870 --> 00:03:52.470
or think that they might
be able to get some

00:03:52.470 --> 00:03:54.650
economic profit, but they would only do so

00:03:54.650 --> 00:03:57.960
until the economic profit
for all firms goes to zero.

00:03:57.960 --> 00:04:00.800
So what point will the
economic profit go to zero?

00:04:00.800 --> 00:04:02.430
Well that's when the marginal revenue for

00:04:02.430 --> 00:04:04.800
the firms is equal to our marginal cost

00:04:04.800 --> 00:04:06.670
is equal to our average total cost.

00:04:06.670 --> 00:04:08.373
So it's that point right over there.

00:04:08.373 --> 00:04:11.920
So we would get to this
point right over here,

00:04:11.920 --> 00:04:14.379
let's call that marginal revenue prime.

00:04:14.379 --> 00:04:17.610
And so, more and more firms would enter

00:04:17.610 --> 00:04:19.123
into the market up until the point

00:04:19.123 --> 00:04:22.072
that the equilibrium
price gets us to P prime.

00:04:22.072 --> 00:04:24.120
And so the supply would increase,

00:04:24.120 --> 00:04:25.860
those folks wanna get that economic profit

00:04:25.860 --> 00:04:29.000
but it would increase until this point.

00:04:29.000 --> 00:04:30.557
So it'd shift a little bit to the right,

00:04:30.557 --> 00:04:33.009
and then we would get to S prime.

00:04:33.009 --> 00:04:35.740
As you can see, based on this we can now

00:04:35.740 --> 00:04:38.410
start to imagine a long run supply curve

00:04:38.410 --> 00:04:41.521
in this increasing cost,
perfectly competitive market.

00:04:41.521 --> 00:04:45.380
We were over here, that
was our equilibrium

00:04:45.380 --> 00:04:48.417
point before, now we are over here.

00:04:48.417 --> 00:04:53.000
And so our long run supply curve in this

00:04:53.000 --> 00:04:55.618
increasing cost environment,

00:04:55.618 --> 00:04:57.530
even though it's perfectly competitive,

00:04:57.530 --> 00:04:59.580
might look something like this.

00:04:59.580 --> 00:05:03.060
So in a constant cost
world, this was a flat line.

00:05:03.060 --> 00:05:04.695
Now in an increasing cost
world, as more and more

00:05:04.695 --> 00:05:07.070
people enter the market,
the cost structure,

00:05:07.070 --> 00:05:09.139
the inputs into producing an apple go up,

00:05:09.139 --> 00:05:11.160
now long run supply is that.

00:05:11.160 --> 00:05:13.360
Remember, the long run is enough time

00:05:13.360 --> 00:05:15.582
to go by for people to
enter and exit the market.

00:05:15.582 --> 00:05:18.513
Or enough time to go by so fixed costs

00:05:18.513 --> 00:05:21.680
aren't fixed anymore,
that they can be shed

00:05:21.680 --> 00:05:23.648
or that they could be increased.

00:05:23.648 --> 00:05:25.970
Now you could do another thought exercise.

00:05:25.970 --> 00:05:27.230
Let's say we're dealing with a market

00:05:27.230 --> 00:05:29.110
where the more people
that enter the market,

00:05:29.110 --> 00:05:30.960
the inputs actually get cheaper.

00:05:30.960 --> 00:05:32.470
And if that seems hard to believe,

00:05:32.470 --> 00:05:34.290
you can imagine, well, now people are able

00:05:34.290 --> 00:05:37.520
to produce seeds or wax at a new scale,

00:05:37.520 --> 00:05:39.310
so the inputs actually get cheaper.

00:05:39.310 --> 00:05:41.100
Well then you would
see the opposite thing.

00:05:41.100 --> 00:05:43.000
Then you would see that as more entrants

00:05:43.000 --> 00:05:45.420
enter the market, this
cost structure goes down,

00:05:45.420 --> 00:05:48.110
and so the supply can
increase more and more

00:05:48.110 --> 00:05:49.700
and more and more, to a point that

00:05:49.700 --> 00:05:52.430
the equilibrium price is now lower

00:05:52.430 --> 00:05:53.920
than it was before,
and then you would have

00:05:53.920 --> 00:05:57.053
a downward sloping long run supply curve.


Long run supply curve in constant cost perfectly competitive markets

WEBVTT
Kind: captions
Language: en

00:00:00.530 --> 00:00:02.100
- [Man] Alright, now
let's dig a little bit

00:00:02.100 --> 00:00:05.060
more into analyzing perfectly
competitive markets,

00:00:05.060 --> 00:00:08.050
and in particular we're
gonna focus on the long run,

00:00:08.050 --> 00:00:11.180
and remember the long run
is the time span where

00:00:11.180 --> 00:00:14.610
firms can enter and exit the market.

00:00:14.610 --> 00:00:15.800
Or, another way to think about it is,

00:00:15.800 --> 00:00:19.130
in the long run, fixed costs
actually become variable,

00:00:19.130 --> 00:00:21.610
you can shutter factories,
or you can build factories,

00:00:21.610 --> 00:00:23.250
in the long run.

00:00:23.250 --> 00:00:25.370
Now, in previous videos, we talked about

00:00:25.370 --> 00:00:28.830
that in the long run, in a
perfectly competitive market,

00:00:28.830 --> 00:00:32.060
the firms that operate in that
perfective competitive market

00:00:32.060 --> 00:00:35.410
are going to be operating
at zero economic profit,

00:00:35.410 --> 00:00:37.660
and you can see that
example right over here.

00:00:37.660 --> 00:00:39.560
As we've talked about
it in many, many videos,

00:00:39.560 --> 00:00:40.980
in a perfectly competitive market,

00:00:40.980 --> 00:00:42.890
the firms are price takers,

00:00:42.890 --> 00:00:46.510
that price is set by that
equilibrium point between

00:00:46.510 --> 00:00:47.880
the supply and demand curves,

00:00:47.880 --> 00:00:49.210
and the firms just take that.

00:00:49.210 --> 00:00:51.860
And so, their marginal revenue curve,

00:00:51.860 --> 00:00:54.400
it would just be a horizontal line

00:00:54.400 --> 00:00:56.920
that you see right over there,

00:00:56.920 --> 00:00:59.940
and zero economic profit
happens when you produce

00:00:59.940 --> 00:01:03.860
a quantity where your average total cost

00:01:03.860 --> 00:01:06.180
is the same as your marginal revenue.

00:01:06.180 --> 00:01:08.110
For each unit, the amount that you get,

00:01:08.110 --> 00:01:09.670
which is that marginal unit,

00:01:09.670 --> 00:01:11.650
that's also how much it
costs you to produce it,

00:01:11.650 --> 00:01:14.080
now remember, when we're
talking about economic profit,

00:01:14.080 --> 00:01:15.760
that includes your opportunity costs,

00:01:15.760 --> 00:01:17.620
so, that doesn't mean that these firms

00:01:17.620 --> 00:01:21.290
are operating at zero accounting profit,

00:01:21.290 --> 00:01:22.950
they could still be making money,

00:01:22.950 --> 00:01:25.700
but, if you were to factor
in their opportunity costs,

00:01:25.700 --> 00:01:28.530
that's when you get things to zero.

00:01:28.530 --> 00:01:29.750
Now, what I want to think about,

00:01:29.750 --> 00:01:32.460
what happens in the short and long run,

00:01:32.460 --> 00:01:36.110
if something say happens to market demand.

00:01:36.110 --> 00:01:39.730
Let's say that this is
the market for apples,

00:01:39.730 --> 00:01:41.220
the fruit apples.

00:01:41.220 --> 00:01:43.600
So, this is the market for
apples we're talking about,

00:01:43.600 --> 00:01:44.570
this is the market as a whole,

00:01:44.570 --> 00:01:46.690
this is a firm that produces apples,

00:01:46.690 --> 00:01:48.160
it could be a farm of some kind.

00:01:48.160 --> 00:01:50.440
And let's say that a new study comes out

00:01:50.440 --> 00:01:54.190
that apples actually are
super good for your health,

00:01:54.190 --> 00:01:57.020
and they can be used as a
performance enhancer for sports,

00:01:57.020 --> 00:01:59.100
and all sorts of positive results.

00:01:59.100 --> 00:02:02.630
Well, what is likely to
happen in the short run,

00:02:02.630 --> 00:02:03.950
and this is a little bit of a review

00:02:03.950 --> 00:02:05.920
in terms of our supply and demand curves,

00:02:05.920 --> 00:02:09.300
and also what would happen
to Firm A's economic profits.

00:02:09.300 --> 00:02:12.020
Pause this video and think about that.

00:02:12.020 --> 00:02:13.790
Well, in the short run,

00:02:13.790 --> 00:02:17.120
your demand curve would
shift to the right,

00:02:17.120 --> 00:02:19.610
and so, because at a given price,

00:02:19.610 --> 00:02:21.350
people are willing to demand more apples

00:02:21.350 --> 00:02:23.480
because it has all these
new and exciting benefits.

00:02:23.480 --> 00:02:28.060
And so, the demand curve might
shift someplace like that,

00:02:28.060 --> 00:02:31.510
so, that is D Prime,

00:02:31.510 --> 00:02:33.940
and if the demand curve shifts like that,

00:02:33.940 --> 00:02:37.150
now we have a new equilibrium
price in the market,

00:02:37.150 --> 00:02:39.600
our new equilibrium price in the market

00:02:39.600 --> 00:02:42.260
is right over here, we also
have a new equilibrium quantity,

00:02:42.260 --> 00:02:45.850
so, our quantity is shifted
from there, to now there,

00:02:45.850 --> 00:02:47.440
so, a new equilibrium quantity,

00:02:47.440 --> 00:02:50.810
and we have a new equilibrium price,

00:02:50.810 --> 00:02:53.710
let's just call this P Prime.

00:02:53.710 --> 00:02:58.020
And, at that new equilibrium price,

00:02:58.020 --> 00:03:01.320
well now, we have a
higher marginal revenue

00:03:01.320 --> 00:03:03.190
curve for Firm A,

00:03:03.190 --> 00:03:06.060
and now, Firm A, it'd be
rational for them to produce,

00:03:06.060 --> 00:03:08.990
remember, it's rational for
them to produce up until

00:03:08.990 --> 00:03:11.960
the marginal revenue is
equal to marginal cost,

00:03:11.960 --> 00:03:14.290
because each of those incremental
units up to that point,

00:03:14.290 --> 00:03:16.570
they're going to be making money
on those incremental units,

00:03:16.570 --> 00:03:18.150
and so, now it's rational for them

00:03:18.150 --> 00:03:19.640
to produce at this quantity,

00:03:19.640 --> 00:03:20.513
let me call that,

00:03:21.400 --> 00:03:22.670
Q Prime,

00:03:22.670 --> 00:03:23.750
and at this level,

00:03:23.750 --> 00:03:26.830
now all of a sudden Firm A
is making economic profit,

00:03:26.830 --> 00:03:29.860
because at this quantity,
that's revenue per unit,

00:03:29.860 --> 00:03:32.310
this is average total cost per unit,

00:03:32.310 --> 00:03:35.420
so they're making this height per unit,

00:03:35.420 --> 00:03:38.220
and then you multiply it, times
your total number of units,

00:03:38.220 --> 00:03:39.880
which is the base of this rectangle,

00:03:39.880 --> 00:03:41.780
and so, this area would represent

00:03:41.780 --> 00:03:44.480
this positive economic profit.

00:03:44.480 --> 00:03:46.000
Now, you might be saying,
wait, hold on a second,

00:03:46.000 --> 00:03:47.420
I thought you said in the long run,

00:03:47.420 --> 00:03:49.710
firms don't make economic profit

00:03:49.710 --> 00:03:51.630
in a perfectly competitive market.

00:03:51.630 --> 00:03:52.780
And that is true,

00:03:52.780 --> 00:03:55.100
at least based on the models
that we are constructing,

00:03:55.100 --> 00:03:57.620
because what happens when you have

00:03:57.620 --> 00:03:59.630
this positive economic profit?

00:03:59.630 --> 00:04:02.030
Well, other firms will enter this market,

00:04:02.030 --> 00:04:02.863
remember, we're talking about

00:04:02.863 --> 00:04:04.400
a perfectly competitive market,

00:04:04.400 --> 00:04:06.690
there are no barriers to enter in,

00:04:06.690 --> 00:04:08.760
everyone is fairly non-differentiated,

00:04:08.760 --> 00:04:10.450
and they have similar cost structures.

00:04:10.450 --> 00:04:12.750
And so, what you could imagine is,

00:04:12.750 --> 00:04:16.310
in the long run, folks
will enter the market,

00:04:16.310 --> 00:04:20.600
and then, the supply curve
will also shift to the right,

00:04:20.600 --> 00:04:22.910
and assuming that that doesn't change

00:04:22.910 --> 00:04:25.940
the cost structure for
the individual firms,

00:04:25.940 --> 00:04:28.750
and actually, let me show someone
entering into this market,

00:04:28.750 --> 00:04:30.620
so now, Firm B is entering this market,

00:04:30.620 --> 00:04:32.420
and when Firm B enters the market,

00:04:32.420 --> 00:04:35.060
it has the same cost structure as Firm A,

00:04:35.060 --> 00:04:37.280
and it didn't shift either of their first,

00:04:37.280 --> 00:04:38.820
either of their cost structures,

00:04:38.820 --> 00:04:39.930
so, this is known as a

00:04:39.930 --> 00:04:43.200
constant cost, perfectly
competitive market,

00:04:43.200 --> 00:04:47.450
where the entering or the
exiting of firms does not

00:04:47.450 --> 00:04:50.910
affect the cost structures of
the firms that are entering,

00:04:50.910 --> 00:04:52.900
or that are in the market.

00:04:52.900 --> 00:04:56.110
And so, this situation,
these graphs look the same,

00:04:56.110 --> 00:04:58.740
but now we have more
firms entering the market,

00:04:58.740 --> 00:05:02.010
the supply curve will shift to the right,

00:05:02.010 --> 00:05:04.590
and it's going to keep
shifting to the right

00:05:04.590 --> 00:05:08.270
until these firms that all
have identical cost structures,

00:05:08.270 --> 00:05:11.900
are no longer making
economic profit again.

00:05:11.900 --> 00:05:13.990
It wouldn't shift further
to the right because

00:05:13.990 --> 00:05:16.610
no one's going to enter if
they're making economic loss,

00:05:16.610 --> 00:05:18.650
it'll keep shifting until no one

00:05:18.650 --> 00:05:20.560
is making that economic profit.

00:05:20.560 --> 00:05:24.530
And so, you see what happened
in this constant cost,

00:05:24.530 --> 00:05:26.510
perfectly competitive market,

00:05:26.510 --> 00:05:29.870
that now, we are back to
this equilibrium point

00:05:29.870 --> 00:05:32.410
where we are at a higher
quantity because people like all

00:05:32.410 --> 00:05:34.620
the benefits of these apples,

00:05:34.620 --> 00:05:36.200
but we're at the price we were before,

00:05:36.200 --> 00:05:40.270
which is the same marginal
revenue curve that we were before

00:05:40.270 --> 00:05:42.310
for the various players

00:05:44.080 --> 00:05:45.470
in this market.

00:05:45.470 --> 00:05:47.720
And so, when you see
something like this in

00:05:47.720 --> 00:05:49.930
a constant cost, perfectly
competitive market,

00:05:49.930 --> 00:05:52.410
you can actually create
a long run supply curve,

00:05:52.410 --> 00:05:53.910
you could view this S and S Prime as

00:05:53.910 --> 00:05:55.520
a short run supply curve,

00:05:55.520 --> 00:05:57.980
the long run supply
curve, on the other hand,

00:05:57.980 --> 00:06:00.900
for a perfectly competitive market,

00:06:00.900 --> 00:06:05.110
in which the cost structure
of the participating firms

00:06:05.110 --> 00:06:07.790
do not depend on the number of firms

00:06:07.790 --> 00:06:09.930
that are in or out of the market,

00:06:09.930 --> 00:06:11.740
then you're at long run supply curve

00:06:11.740 --> 00:06:12.660
in what we could call

00:06:12.660 --> 00:06:15.910
a constant cost, perfectly
competitive market,

00:06:15.910 --> 00:06:19.113
is going to be a
horizontal line like this.

00:06:20.050 --> 00:06:21.760
So, I will leave you there.

00:06:21.760 --> 00:06:22.830
In other videos, we'll think about,

00:06:22.830 --> 00:06:25.020
well, what happens if the
cost structure changes

00:06:25.020 --> 00:06:26.940
for these firms depending on

00:06:26.940 --> 00:06:29.030
how many firms are in
or out of the market,

00:06:29.030 --> 00:06:30.210
and that will be based on,

00:06:30.210 --> 00:06:33.440
how do the costs of the inputs
into their production change

00:06:33.440 --> 00:06:36.793
as you have people entering
or exiting that market.


Economic profit for firms in perfectly competitive markets

WEBVTT
Kind: captions
Language: en

00:00:00.180 --> 00:00:01.013
- [Instructor] In this video,

00:00:01.013 --> 00:00:03.250
we're going to dig a little
bit deeper into the notion

00:00:03.250 --> 00:00:04.950
of perfectly competitive markets.

00:00:04.950 --> 00:00:06.000
So we're gonna think about

00:00:06.000 --> 00:00:10.170
under what scenarios a firm
would make an economic profit

00:00:10.170 --> 00:00:12.830
or an economic loss in them.

00:00:12.830 --> 00:00:15.910
Now as a reminder, these
perfectly competitive markets

00:00:15.910 --> 00:00:18.640
are something of a theoretical ideal.

00:00:18.640 --> 00:00:20.600
There's few markets in the real world

00:00:20.600 --> 00:00:22.520
that are truly perfectly competitive.

00:00:22.520 --> 00:00:23.960
Some might get close,

00:00:23.960 --> 00:00:25.920
but most markets are
someplace in a spectrum

00:00:25.920 --> 00:00:28.500
between perfectly competitive
and, at the other extreme,

00:00:28.500 --> 00:00:30.250
say, something like a monopoly.

00:00:30.250 --> 00:00:32.490
But here we're talking
about perfect competition.

00:00:32.490 --> 00:00:33.970
And perfect competition,

00:00:33.970 --> 00:00:36.550
the firm's products aren't differentiated.

00:00:36.550 --> 00:00:39.500
There's no barriers to entry or exit.

00:00:39.500 --> 00:00:40.900
And so in that situation,

00:00:40.900 --> 00:00:43.000
the market supply and demand curves

00:00:43.000 --> 00:00:45.300
are going to define the
price in the market,

00:00:45.300 --> 00:00:46.800
which are also going to define

00:00:46.800 --> 00:00:50.210
the marginal revenue for these firms.

00:00:50.210 --> 00:00:52.380
They're all going to be price-takers.

00:00:52.380 --> 00:00:54.890
They're going to be
passive in terms of price.

00:00:54.890 --> 00:00:56.760
Whatever the market price
is, that's the price

00:00:56.760 --> 00:00:59.210
that they are going to
sell their products for.

00:00:59.210 --> 00:01:02.090
And their decision is
really what quantity does,

00:01:02.090 --> 00:01:06.750
to produce and sell and whether
to enter or exit the market.

00:01:06.750 --> 00:01:07.970
So let's look at that a little bit.

00:01:07.970 --> 00:01:10.360
So these are just your classic
and supply, demand curve,

00:01:10.360 --> 00:01:13.700
supply and demand curves
you might see for a market.

00:01:13.700 --> 00:01:15.130
The first few units in the market,

00:01:15.130 --> 00:01:17.080
there's a huge marginal benefit,

00:01:17.080 --> 00:01:18.800
so people are willing to pay a lot.

00:01:18.800 --> 00:01:20.420
But then each incremental unit,

00:01:20.420 --> 00:01:22.670
the marginal benefit's a
little bit lower and lower

00:01:22.670 --> 00:01:24.080
and lower and lower, and
that's why we have those,

00:01:24.080 --> 00:01:26.040
that downward-sloping demand curve.

00:01:26.040 --> 00:01:28.700
And then on the supply
curve, the first unit

00:01:28.700 --> 00:01:31.860
in the market might be fairly
inexpensive to produce,

00:01:31.860 --> 00:01:34.260
but then the marginal cost gets higher

00:01:34.260 --> 00:01:35.093
and higher and higher.

00:01:35.093 --> 00:01:36.360
And where they meet,

00:01:36.360 --> 00:01:37.990
where the supply and demand meet,

00:01:37.990 --> 00:01:40.000
that tells us the equilibrium price

00:01:40.000 --> 00:01:42.000
and equilibrium quantity in the market.

00:01:42.000 --> 00:01:44.810
And we can show that with that line,

00:01:44.810 --> 00:01:47.360
and let's just say that
equilibrium price is $10.

00:01:47.360 --> 00:01:48.660
And as I just mentioned,

00:01:48.660 --> 00:01:52.230
that's going to have to be the
price that all of the firms,

00:01:52.230 --> 00:01:54.330
and these might not be all
of the firms in the market,

00:01:54.330 --> 00:01:55.650
but all of the firms in the market,

00:01:55.650 --> 00:01:57.880
if we're talking about a
perfectly competitive market,

00:01:57.880 --> 00:02:00.610
would just have to take that price.

00:02:00.610 --> 00:02:02.027
So given that,

00:02:02.027 --> 00:02:06.800
what quantity would firms
A, B, and C produce?

00:02:06.800 --> 00:02:10.330
And which of these firms
would be profitable or not>

00:02:10.330 --> 00:02:11.740
I encourage you to pause the video

00:02:11.740 --> 00:02:13.310
and think about those two questions.

00:02:13.310 --> 00:02:14.450
If you could just answer,

00:02:14.450 --> 00:02:16.680
which of these firms would
be profitable or not?

00:02:16.680 --> 00:02:19.563
And we're talking about
economic profit in this context.

00:02:20.550 --> 00:02:23.730
All right, well let's
look at firm A first.

00:02:23.730 --> 00:02:26.350
Well, firm A, for any of them,

00:02:26.350 --> 00:02:29.040
it is not rational to produce a quantity

00:02:29.040 --> 00:02:31.870
where the marginal cost is higher

00:02:31.870 --> 00:02:35.110
than the marginal revenue
that the firm's getting.

00:02:35.110 --> 00:02:37.810
And remember, this line right over here,

00:02:37.810 --> 00:02:41.880
this line right here, which is
the price line, that's also,

00:02:41.880 --> 00:02:46.500
that is price, which is
equal to marginal revenue.

00:02:46.500 --> 00:02:48.910
And so for that extra unit,

00:02:48.910 --> 00:02:53.000
if you can't sell it for
more than you're producing,

00:02:53.000 --> 00:02:55.050
then you wouldn't produce that extra unit.

00:02:55.050 --> 00:02:57.950
So it's rational for them to
produce more and more and more.

00:02:57.950 --> 00:02:59.640
The marginal cost goes higher and higher

00:02:59.640 --> 00:03:01.830
until right at the
point that marginal cost

00:03:01.830 --> 00:03:04.550
is equal to marginal revenue,
which is equal to price,

00:03:04.550 --> 00:03:07.100
the market price, which
they're just going to take.

00:03:07.100 --> 00:03:09.260
So it's rational for this firm

00:03:09.260 --> 00:03:12.240
to produce this quantity right over here.

00:03:12.240 --> 00:03:13.680
So I'll just go quantity,

00:03:13.680 --> 00:03:16.110
I'll say quantity for that firm.

00:03:16.110 --> 00:03:18.580
Now is this firm going
to be profitable or not?

00:03:18.580 --> 00:03:21.510
Well, at this quantity,
what's its average total cost?

00:03:21.510 --> 00:03:25.540
Well, its average total
cost is right over there.

00:03:25.540 --> 00:03:27.520
And so for every unit,

00:03:27.520 --> 00:03:30.100
it's going to make this difference

00:03:30.100 --> 00:03:33.500
between the price or the
marginal revenue it's getting

00:03:33.500 --> 00:03:35.460
and its average total cost.

00:03:35.460 --> 00:03:39.340
And so one way to think about
the profit of this firm is,

00:03:39.340 --> 00:03:41.400
and we're talking about economic profit,

00:03:41.400 --> 00:03:46.400
it's going to be the area of
this rectangle right over here.

00:03:46.890 --> 00:03:51.890
So let's say if the average
total cost at that quantity is,

00:03:51.940 --> 00:03:53.463
let's say that this is $8,

00:03:55.240 --> 00:03:59.200
then this height of the
rectangle is 10 minus eight.

00:03:59.200 --> 00:04:00.410
The height right over here,

00:04:00.410 --> 00:04:02.520
let me do this in a different color,

00:04:02.520 --> 00:04:05.810
this height right over here is $2.

00:04:05.810 --> 00:04:08.940
And then the width is going to
be the quantity of that firm.

00:04:08.940 --> 00:04:11.060
And so let's say the
quantity of that firm,

00:04:11.060 --> 00:04:13.470
let's say it's 10,000 units a year,

00:04:13.470 --> 00:04:14.860
10,000,

00:04:14.860 --> 00:04:16.800
10,000 units per year.

00:04:16.800 --> 00:04:21.190
And so the area right over
here would be $2 times 10,000.

00:04:21.190 --> 00:04:24.027
It would be $20,000,

00:04:24.027 --> 00:04:27.200
$20,000 per time unit,

00:04:27.200 --> 00:04:28.410
per time unit if we're talking

00:04:28.410 --> 00:04:30.370
all of this as, say, per year.

00:04:30.370 --> 00:04:31.670
Now let's go to firm B.

00:04:31.670 --> 00:04:32.990
Using that same analysis,

00:04:32.990 --> 00:04:34.940
is firm B making an economic profit

00:04:34.940 --> 00:04:36.890
or is it not making an economic profit?

00:04:37.730 --> 00:04:41.400
Well, firm B is once again
going to be a price-taker.

00:04:41.400 --> 00:04:44.130
And so the price right over here,

00:04:44.130 --> 00:04:45.660
the equilibrium price in the market,

00:04:45.660 --> 00:04:47.670
is going to be equal to the price

00:04:47.670 --> 00:04:48.650
that that firm has to take,

00:04:48.650 --> 00:04:50.950
which is going to be its
marginal revenue curve.

00:04:50.950 --> 00:04:53.040
And that's why it's a flat
marginal revenue curve.

00:04:53.040 --> 00:04:54.660
Because no matter what
quantity they produce,

00:04:54.660 --> 00:04:56.640
they're gonna get that same price.

00:04:56.640 --> 00:05:00.540
And it wouldn't be rational
for them to produce a quantity

00:05:00.540 --> 00:05:04.480
where marginal cost is
higher than marginal revenue,

00:05:04.480 --> 00:05:07.140
and so they would
produce right over there.

00:05:07.140 --> 00:05:10.883
Now what is their economic
profit at this quantity?

00:05:11.950 --> 00:05:16.950
So this is quantity of
the second firm, firm B.

00:05:18.050 --> 00:05:18.883
I'll write it like that.

00:05:18.883 --> 00:05:20.250
Maybe that is firm A.

00:05:20.250 --> 00:05:23.550
And maybe this is also, eh,
it looks about the same.

00:05:23.550 --> 00:05:24.930
I'll make 'em a little bit different.

00:05:24.930 --> 00:05:28.653
Let's say that's 9,500
units per time period.

00:05:29.520 --> 00:05:31.560
Well, here the average total cost

00:05:31.560 --> 00:05:34.970
at that quantity is equal
to the marginal cost,

00:05:34.970 --> 00:05:38.060
so which is equal to the marginal revenue.

00:05:38.060 --> 00:05:39.760
So at that quantity,

00:05:39.760 --> 00:05:42.380
whatever, that $10
they're getting per unit,

00:05:42.380 --> 00:05:45.460
they're also spending
on average $10 per unit.

00:05:45.460 --> 00:05:46.293
Another way to think about it,

00:05:46.293 --> 00:05:48.430
the area of that rectangle
is going to be zero

00:05:48.430 --> 00:05:50.340
because it has no height.

00:05:50.340 --> 00:05:52.770
So this, this situation right over here,

00:05:52.770 --> 00:05:54.910
the firm has zero,

00:05:54.910 --> 00:05:57.510
zero economic,

00:05:57.510 --> 00:06:01.423
I'll write $0 of economic profit.

00:06:02.300 --> 00:06:05.530
And then last but not least,
let's think about firm C.

00:06:05.530 --> 00:06:06.870
Pause this video, and think about

00:06:06.870 --> 00:06:09.023
what its economic profit would be.

00:06:10.120 --> 00:06:11.650
Well, like we've seen,

00:06:11.650 --> 00:06:16.340
it would be rational for
it to produce the quantity

00:06:16.340 --> 00:06:18.410
where marginal cost is
equal to marginal revenue,

00:06:18.410 --> 00:06:20.270
which is equal to the market price.

00:06:20.270 --> 00:06:22.840
So it would produce this
quantity right over here.

00:06:22.840 --> 00:06:27.840
And let's say that that
quantity is 9,000 units.

00:06:28.000 --> 00:06:30.250
And what's its average total cost then?

00:06:30.250 --> 00:06:33.530
So at 9,000 units, its average total cost,

00:06:33.530 --> 00:06:36.490
let's say that that is
$12 right over there.

00:06:36.490 --> 00:06:38.810
So what's its economic profit?

00:06:38.810 --> 00:06:40.960
So for every unit it's selling,

00:06:40.960 --> 00:06:43.717
it's getting $10 and it's costing

00:06:43.717 --> 00:06:45.950
$12 on average to produce it.

00:06:45.950 --> 00:06:50.590
So it's taking an economic
loss of $2 per unit.

00:06:50.590 --> 00:06:54.023
So $2 per unit, so this
height right over here is $2,

00:06:54.970 --> 00:06:57.580
times the units, times 9,000,

00:06:57.580 --> 00:07:00.100
you're going to have two times 9,000,

00:07:00.100 --> 00:07:02.590
you're going to have an $18,000

00:07:02.590 --> 00:07:06.110
not economic profit but economic,

00:07:06.110 --> 00:07:09.530
economic loss.

00:07:09.530 --> 00:07:11.610
Now one thing to think about is

00:07:11.610 --> 00:07:14.880
why would any firm be in this situation?

00:07:14.880 --> 00:07:16.290
Well, it's important to think about things

00:07:16.290 --> 00:07:19.120
in the short run versus the long run.

00:07:19.120 --> 00:07:19.980
In the short run,

00:07:19.980 --> 00:07:22.350
we've talked about this
analysis right over here,

00:07:22.350 --> 00:07:25.750
where a firm can decide what
quantity it would produce

00:07:25.750 --> 00:07:27.200
that is rational.

00:07:27.200 --> 00:07:29.580
Its fixed costs are
fixed in the short run.

00:07:29.580 --> 00:07:31.940
We've studied that in multiple videos.

00:07:31.940 --> 00:07:35.490
But in the long run, its
fixed costs aren't fixed,

00:07:35.490 --> 00:07:38.940
and so the firm could decide
to enter or exit the market.

00:07:38.940 --> 00:07:41.050
And so for firm C,

00:07:41.050 --> 00:07:43.810
while they've already
put in those fixed costs,

00:07:43.810 --> 00:07:46.260
it is actually rational for them to do it

00:07:46.260 --> 00:07:49.230
because they're actually
able to make their,

00:07:49.230 --> 00:07:52.850
the marginal revenue they
get up to that quantity,

00:07:52.850 --> 00:07:53.800
it's at least,

00:07:53.800 --> 00:07:57.550
they're able to more than
cover their marginal costs.

00:07:57.550 --> 00:08:00.520
And then they're able to eat
up or I guess you could say

00:08:00.520 --> 00:08:02.840
take care of some of their fixed costs,

00:08:02.840 --> 00:08:05.900
But they're still not able
to run an economic profit.

00:08:05.900 --> 00:08:07.270
So in the long run,

00:08:07.270 --> 00:08:09.940
it wouldn't be rational for
this firm to stay in the market.

00:08:09.940 --> 00:08:12.423
They would likely exit the market.


Long-run economic profit for perfectly competitive firms

WEBVTT
Kind: captions
Language: en

00:00:00.230 --> 00:00:01.710
- [Instructor] Let's
dig a little bit deeper

00:00:01.710 --> 00:00:04.500
into what happens in
perfectly competitive markets

00:00:04.500 --> 00:00:06.580
in the long run.

00:00:06.580 --> 00:00:08.310
So what we have on the left-hand side,

00:00:08.310 --> 00:00:10.330
and we've seen this
multiple times already,

00:00:10.330 --> 00:00:12.640
is our supply and our demand curves

00:00:12.640 --> 00:00:15.140
for our perfectly competitive market,

00:00:15.140 --> 00:00:18.130
and you can see the equilibrium
price right over here,

00:00:18.130 --> 00:00:19.660
marked with this a dotted line,

00:00:19.660 --> 00:00:21.910
and as we've talked
about in multiple videos,

00:00:21.910 --> 00:00:24.690
the firms in that perfectly
competitive market,

00:00:24.690 --> 00:00:26.490
the perfectly competitive firms,

00:00:26.490 --> 00:00:28.610
they just have to price takers,

00:00:28.610 --> 00:00:30.660
so the market price is going

00:00:30.660 --> 00:00:32.330
to be their marginal revenue curve.

00:00:32.330 --> 00:00:33.960
It's gonna be this horizontal curve.

00:00:33.960 --> 00:00:36.960
And it would be rational for
them to produce the quantity.

00:00:36.960 --> 00:00:38.210
So they're not going to set the price,

00:00:38.210 --> 00:00:40.370
but they can choose what
quantity to produce,

00:00:40.370 --> 00:00:43.250
but it would be rational
for them to keep producing

00:00:43.250 --> 00:00:46.710
while the marginal revenue is
higher than the marginal cost

00:00:46.710 --> 00:00:48.730
up to including when the marginal revenue

00:00:48.730 --> 00:00:50.870
is equal to the marginal cost.

00:00:50.870 --> 00:00:53.520
So for this firm at this
current state of affairs,

00:00:53.520 --> 00:00:55.130
it would be rational for them

00:00:55.130 --> 00:00:58.590
to produce this quantity right over there.

00:00:58.590 --> 00:01:00.350
And as we've talked about in other videos,

00:01:00.350 --> 00:01:03.870
at that quantity, they're going
to make an economic profit.

00:01:03.870 --> 00:01:05.530
And the way that we can see that

00:01:05.530 --> 00:01:09.430
is at this quantity, this
is the average total cost,

00:01:09.430 --> 00:01:11.990
that is your marginal revenue,

00:01:11.990 --> 00:01:16.990
and so you are going to
get this much per unit

00:01:17.610 --> 00:01:18.880
and then you multiply,

00:01:18.880 --> 00:01:21.220
so the height is how much you get per unit

00:01:21.220 --> 00:01:25.170
and then you multiply that
times the number of units,

00:01:25.170 --> 00:01:28.110
so the area of this rectangle

00:01:28.110 --> 00:01:32.900
is that positive economic
profit that this firm will have.

00:01:32.900 --> 00:01:36.160
Now, that's in the short run,
but now let's think about

00:01:36.160 --> 00:01:38.640
what will likely happen in the long run.

00:01:38.640 --> 00:01:43.210
If folks see other folks making
a positive economic profit,

00:01:43.210 --> 00:01:45.860
remember, economic profit
doesn't just account

00:01:45.860 --> 00:01:49.110
for regular cost, it also
includes opportunity cost,

00:01:49.110 --> 00:01:51.670
so a lot of you will say hey,
I would wanna put my resources

00:01:51.670 --> 00:01:53.880
into this market so that I can make

00:01:53.880 --> 00:01:56.580
that positive economic profit as well.

00:01:56.580 --> 00:01:57.560
But what's gonna happen

00:01:57.560 --> 00:02:01.100
as you have entrance into this market?

00:02:01.100 --> 00:02:03.940
Well, that's gonna shift the
supply curve to the right.

00:02:03.940 --> 00:02:07.400
At any given price, you're
gonna have more supplies,

00:02:07.400 --> 00:02:08.560
one way to think about it.

00:02:08.560 --> 00:02:10.070
So that's a supply curve.

00:02:10.070 --> 00:02:12.030
Let's just call that one.

00:02:12.030 --> 00:02:14.210
Now, you're gonna have more entrance.

00:02:14.210 --> 00:02:16.973
More entrance.

00:02:18.190 --> 00:02:19.490
And what's going to happen?

00:02:19.490 --> 00:02:22.660
Well, you might get to
something like you might get

00:02:22.660 --> 00:02:26.320
to a situation like this.

00:02:26.320 --> 00:02:28.080
Let me see if I can draw it well.

00:02:28.080 --> 00:02:29.950
You might get to a situation like this

00:02:29.950 --> 00:02:31.250
where you have more entrance

00:02:31.250 --> 00:02:33.620
and you got the supply curve two.

00:02:33.620 --> 00:02:35.730
Now, what's going to be the quantity

00:02:35.730 --> 00:02:37.470
that firm A produces in that one?

00:02:37.470 --> 00:02:40.130
Remember, firm A is one of many firms.

00:02:40.130 --> 00:02:43.050
Well, in this situation, we
have a new equilibrium price.

00:02:43.050 --> 00:02:45.620
So if this was P sub one,

00:02:45.620 --> 00:02:49.920
now we have this new
equilibrium price, P sub two,

00:02:49.920 --> 00:02:53.630
which is going to define a
new marginal revenue curve

00:02:53.630 --> 00:02:57.620
for all of the players in this
perfectly competitive market

00:02:57.620 --> 00:02:59.630
and so the new marginal revenue curve

00:02:59.630 --> 00:03:02.183
is gonna be right over there.

00:03:03.030 --> 00:03:06.390
Now, in this situation, what
is the rational quantity

00:03:06.390 --> 00:03:08.090
for firm A to produce?

00:03:08.090 --> 00:03:10.370
Well, once again, as
long as marginal revenue

00:03:10.370 --> 00:03:12.360
is higher than marginal cost,

00:03:12.360 --> 00:03:14.490
it makes sense for them to
produce more and more and more,

00:03:14.490 --> 00:03:18.020
up until the point that they are equal.

00:03:18.020 --> 00:03:23.020
So now, firm A would want to produce less

00:03:23.340 --> 00:03:27.320
because the market price that
it just has to take is less.

00:03:27.320 --> 00:03:29.987
But notice what happens
as more and more entrants

00:03:29.987 --> 00:03:31.670
got into the market.

00:03:31.670 --> 00:03:33.850
The market price, which also defines

00:03:33.850 --> 00:03:37.830
this horizontal marginal revenue
curve, went lower and lower

00:03:37.830 --> 00:03:42.230
to the point where firm
A now in this situation

00:03:42.230 --> 00:03:44.980
is making no economic profit.

00:03:44.980 --> 00:03:48.350
At this point, where not
only as marginal revenue

00:03:48.350 --> 00:03:50.030
intersecting marginal cost,

00:03:50.030 --> 00:03:51.330
but that's exactly the point

00:03:51.330 --> 00:03:56.070
in which marginal cost is
equaling average total cost.

00:03:56.070 --> 00:03:57.880
So one way to think about it is

00:03:57.880 --> 00:04:00.440
in a perfectly competitive firm,

00:04:00.440 --> 00:04:02.650
they're productively efficient.

00:04:02.650 --> 00:04:05.040
They are producing the quantity

00:04:05.040 --> 00:04:07.320
that minimizes their average total cost.

00:04:07.320 --> 00:04:08.640
We've already talked about that point

00:04:08.640 --> 00:04:12.140
where marginal cost and
average total cost intersect.

00:04:12.140 --> 00:04:14.300
That's gonna be the minimum
point for average total cost.

00:04:14.300 --> 00:04:15.450
And why is that?

00:04:15.450 --> 00:04:20.300
Well, while marginal cost
is below average total cost,

00:04:20.300 --> 00:04:22.560
average total cost is gonna
get lower and lower and lower,

00:04:22.560 --> 00:04:24.900
and then once marginal cost gets higher

00:04:24.900 --> 00:04:26.230
than average total cost,

00:04:26.230 --> 00:04:27.710
well, then the average total cost curve

00:04:27.710 --> 00:04:29.670
will starting going curving up.

00:04:29.670 --> 00:04:30.920
So we just saw a situation

00:04:30.920 --> 00:04:33.710
that even where we see economic
profit in the short run,

00:04:33.710 --> 00:04:37.240
in the long run, entrants are
going to go into that market

00:04:37.240 --> 00:04:40.880
and it's going to reduce the
economic profit down to zero

00:04:40.880 --> 00:04:45.240
and at that point, the firm
that has a zero economic profit,

00:04:45.240 --> 00:04:47.230
they're productively efficient.

00:04:47.230 --> 00:04:49.340
They are producing at the minimum point

00:04:49.340 --> 00:04:51.090
of the average total cost curve.

00:04:51.090 --> 00:04:52.840
And we've already talked before

00:04:52.840 --> 00:04:55.980
that this equilibrium point
right over here in our market,

00:04:55.980 --> 00:04:59.260
because our demand and supply curves,

00:04:59.260 --> 00:05:02.710
the intersection point defines the price,

00:05:02.710 --> 00:05:04.740
our equilibrium price and quantities,

00:05:04.740 --> 00:05:06.450
we're also allocatably efficient.

00:05:06.450 --> 00:05:08.710
We've talked about things like
dead weight lost in the past.

00:05:08.710 --> 00:05:10.640
That is not happening right over here.

00:05:10.640 --> 00:05:13.530
Our marginal benefit is
equal to our marginal cost

00:05:13.530 --> 00:05:16.620
right at that equilibrium
price and quantity.

00:05:16.620 --> 00:05:18.780
Now, some of you might be saying, well,

00:05:18.780 --> 00:05:20.050
what about the other situation?

00:05:20.050 --> 00:05:23.450
What about if for some
reason we were in a,

00:05:23.450 --> 00:05:24.830
let's call the supply curve here.

00:05:24.830 --> 00:05:26.390
Let's say people overshot.

00:05:26.390 --> 00:05:28.620
Too many people joined into this market.

00:05:28.620 --> 00:05:31.660
So let's say we went
to supply curve three,

00:05:31.660 --> 00:05:32.640
well what's going to happen?

00:05:32.640 --> 00:05:33.550
Let me label this.

00:05:33.550 --> 00:05:38.470
This is right over here, this
is marginal revenue curve one,

00:05:38.470 --> 00:05:41.010
which is equal to price one.

00:05:41.010 --> 00:05:43.360
This is marginal revenue curve two,

00:05:43.360 --> 00:05:44.960
which is equal to price two.

00:05:44.960 --> 00:05:47.590
And then this would define,
so this right over here

00:05:47.590 --> 00:05:51.740
would be price three, price three,

00:05:51.740 --> 00:05:55.530
which would define marginal
revenue curve three.

00:05:55.530 --> 00:05:58.470
So marginal revenue curve three,

00:05:58.470 --> 00:06:00.290
which is equal to price three.

00:06:00.290 --> 00:06:02.990
Well if too many entrants
joined into that market,

00:06:02.990 --> 00:06:07.180
now firm A has a more difficult scenario.

00:06:07.180 --> 00:06:09.130
They are, would produce at this quantity,

00:06:09.130 --> 00:06:11.010
we've talked about many times already,

00:06:11.010 --> 00:06:15.010
but at that quantity, each
unit their average total cost

00:06:15.010 --> 00:06:17.520
is higher than that
revenue they're getting.

00:06:17.520 --> 00:06:19.820
So they're going to be
running at an economic loss

00:06:19.820 --> 00:06:21.320
in the short run.

00:06:21.320 --> 00:06:23.000
But what would happen in the long run?

00:06:23.000 --> 00:06:26.200
Well firm A in the long run
would probably exit the market

00:06:26.200 --> 00:06:28.620
and other firms who are
running at economic loss

00:06:28.620 --> 00:06:31.000
would exit the market,
and so that would shift

00:06:31.000 --> 00:06:33.490
the supply curve back to the left.

00:06:33.490 --> 00:06:35.370
And so we would eventually
get, once again,

00:06:35.370 --> 00:06:40.040
to that reality where firms
have no economic profit

00:06:40.040 --> 00:06:43.210
in there and we have a market
that is allocatably efficient,

00:06:43.210 --> 00:06:46.620
no dead weight loss,
and firms are producing

00:06:46.620 --> 00:06:49.260
at the minimum point of their
average total cost curve,

00:06:49.260 --> 00:06:51.370
which is known as productive efficiency

00:06:51.370 --> 00:06:52.993
or productively efficient.


Logistic growth versus exponential growth

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:01.950
- [Instructor] Let's now
think a little bit more

00:00:01.950 --> 00:00:04.570
about how we might
model population growth,

00:00:04.570 --> 00:00:06.070
and as we do so, we're gonna become

00:00:06.070 --> 00:00:09.010
a little bit more familiar
with the types of formulas

00:00:09.010 --> 00:00:12.390
that you might see in an
AP Biology formula sheet.

00:00:12.390 --> 00:00:14.900
So in a previous video,
we introduced the idea

00:00:14.900 --> 00:00:18.030
of per capita growth rate of a population,

00:00:18.030 --> 00:00:20.800
and we used the letter r for that.

00:00:20.800 --> 00:00:23.610
And so let's say that the
per capita growth rate

00:00:23.610 --> 00:00:27.080
for a population is 0.2.

00:00:27.080 --> 00:00:29.850
That means that on average,

00:00:29.850 --> 00:00:33.350
for every one individual
in that population,

00:00:33.350 --> 00:00:37.100
a year later, it would have
grown by 20%, by two-tenths.

00:00:37.100 --> 00:00:41.920
So for every one, you would
now have 1.2 of that population

00:00:41.920 --> 00:00:43.120
a year later.

00:00:43.120 --> 00:00:46.130
Now, as we mentioned, many populations,

00:00:46.130 --> 00:00:47.810
or the ones that reproduced sexually,

00:00:47.810 --> 00:00:50.030
you'd need at least two,
a male and a female,

00:00:50.030 --> 00:00:52.180
but there's populations of certain things

00:00:52.180 --> 00:00:55.010
that can just reproduce on their own.

00:00:55.010 --> 00:00:56.910
They can just bud, or they can divide,

00:00:56.910 --> 00:00:59.880
if we're talking about
especially unicellular organisms.

00:00:59.880 --> 00:01:03.160
And from this notion, we
can get a related notion,

00:01:03.160 --> 00:01:06.590
which is our maximum per capita
growth rate of a population

00:01:06.590 --> 00:01:08.380
and let me just write that there.

00:01:08.380 --> 00:01:10.610
You could view this as
your per capita growth rate

00:01:10.610 --> 00:01:13.120
if the population is
not limited in any way,

00:01:13.120 --> 00:01:15.030
if there's ample resources.

00:01:15.030 --> 00:01:17.360
Water, food, land, territory,

00:01:17.360 --> 00:01:19.600
whatever that population needs to grow,

00:01:19.600 --> 00:01:22.760
but that still is talking
about per capita growth rate

00:01:22.760 --> 00:01:23.980
of population, we're just viewing as,

00:01:23.980 --> 00:01:26.380
this is the unfettered
one, this is the maximum.

00:01:26.380 --> 00:01:30.680
And from that, we can set up
an exponential growth equation,

00:01:30.680 --> 00:01:32.700
and we've seen this in other videos

00:01:32.700 --> 00:01:36.140
where the rate of change of our population

00:01:36.140 --> 00:01:38.860
with respect to time, N is our population,

00:01:38.860 --> 00:01:42.750
so dN dt is our rate
of change of population

00:01:42.750 --> 00:01:44.220
with respect to time.

00:01:44.220 --> 00:01:46.580
Or our population growth
rate right over here,

00:01:46.580 --> 00:01:47.480
let me write this down.

00:01:47.480 --> 00:01:51.780
Population growth rate.

00:01:51.780 --> 00:01:54.520
If we're dealing with a population

00:01:54.520 --> 00:01:58.150
that in no way is being
limited by its ecosystem,

00:01:58.150 --> 00:01:59.870
which in reality is not realistic,

00:01:59.870 --> 00:02:01.340
at some point you would be.

00:02:01.340 --> 00:02:05.370
Well then, the rate of
growth of population

00:02:05.370 --> 00:02:08.820
is going to be your maximum per capita

00:02:08.820 --> 00:02:10.473
growth rate of population,

00:02:11.360 --> 00:02:14.250
times your population itself.

00:02:14.250 --> 00:02:16.460
And we could see it set
up a little table here

00:02:16.460 --> 00:02:18.390
to see how these would
relate to each other,

00:02:18.390 --> 00:02:22.400
so let me do that, let me set up a table.

00:02:22.400 --> 00:02:25.190
And so let's think about
what the rate of change

00:02:25.190 --> 00:02:27.880
of population will be, our
population growth rate,

00:02:27.880 --> 00:02:29.450
for certain populations.

00:02:29.450 --> 00:02:31.930
So let's think about
what it's going to be,

00:02:31.930 --> 00:02:36.020
when our population is 100.

00:02:36.020 --> 00:02:38.690
When our population is 500,

00:02:38.690 --> 00:02:42.890
and when our population is 900.

00:02:42.890 --> 00:02:45.230
So, given these populations,

00:02:45.230 --> 00:02:48.570
what would be your population
growth rate for each of them?

00:02:48.570 --> 00:02:50.570
Pause this video and try to answer that.

00:02:51.490 --> 00:02:53.270
Well, when our population is 100,

00:02:53.270 --> 00:02:54.610
our population growth rate

00:02:54.610 --> 00:02:57.650
is just going to be 0.2 times that.

00:02:57.650 --> 00:03:00.130
So 0.2, let me write this down,

00:03:00.130 --> 00:03:03.930
this is just going to be, dN
dt is just going to be 0.2,

00:03:03.930 --> 00:03:06.760
our maximum per capita
growth rate of population

00:03:06.760 --> 00:03:10.700
times our population, times 100,

00:03:10.700 --> 00:03:13.220
which is equal to 20.

00:03:13.220 --> 00:03:16.040
So we're going to grow per year by 20

00:03:16.040 --> 00:03:18.470
when our population is 100.

00:03:18.470 --> 00:03:20.740
Now what about when our population is 500?

00:03:20.740 --> 00:03:22.530
What is going to be our
population growth rate?

00:03:22.530 --> 00:03:25.210
Pause the video again
and try to answer that.

00:03:25.210 --> 00:03:27.310
Well, once again, we just take our maximum

00:03:27.310 --> 00:03:30.488
per capita growth rate and
multiply it times our population,

00:03:30.488 --> 00:03:35.488
so .2 times 500, our population
growth rate is now 100.

00:03:36.020 --> 00:03:37.800
If we're talking about bunnies,

00:03:37.800 --> 00:03:39.030
and if our time is in years,

00:03:39.030 --> 00:03:40.840
this would be 100 bunnies per year,

00:03:40.840 --> 00:03:42.950
or 100 individuals per year.

00:03:42.950 --> 00:03:45.750
And let's think about it
when our population is 900.

00:03:45.750 --> 00:03:47.360
What's our population growth rate then?

00:03:47.360 --> 00:03:49.160
Pause the video again.

00:03:49.160 --> 00:03:52.140
Alright, well we're just
gonna take 0.2 times 900,

00:03:52.140 --> 00:03:56.890
so it is going to be 180
individuals per year.

00:03:56.890 --> 00:03:58.880
Now, as I just mentioned,

00:03:58.880 --> 00:04:01.240
this is talking about a
somewhat unrealistic situation

00:04:01.240 --> 00:04:03.650
where a population can
just grow and grow and grow

00:04:03.650 --> 00:04:05.880
and never be limited in any way.

00:04:05.880 --> 00:04:09.360
We know that land is
limited, food is limited,

00:04:09.360 --> 00:04:10.960
water is limited.

00:04:10.960 --> 00:04:15.600
And so, there's this notion
of a natural carrying capacity

00:04:15.600 --> 00:04:19.200
of a given population
in a given environment.

00:04:19.200 --> 00:04:22.630
And to describe that,
we'll use the letter K.

00:04:22.630 --> 00:04:25.070
And so let's say, for the organisms

00:04:25.070 --> 00:04:27.250
that we're studying here,
let's say they're bunnies,

00:04:27.250 --> 00:04:30.870
and they're bunnies on a
relatively small island,

00:04:30.870 --> 00:04:32.940
let's say that the
natural carrying capacity

00:04:32.940 --> 00:04:35.420
for that island is 1000.

00:04:35.420 --> 00:04:39.600
The the island really can't
support more than 1000 bunnies.

00:04:39.600 --> 00:04:43.340
So how would we change this
exponential growth equation

00:04:43.340 --> 00:04:46.110
right over here, exponential,

00:04:46.110 --> 00:04:47.273
to reflect that?

00:04:48.140 --> 00:04:50.840
Well, what mathematicians
and biologists have done

00:04:50.840 --> 00:04:52.090
is they've modified this,

00:04:52.090 --> 00:04:54.020
they multiplied this times the factor,

00:04:54.020 --> 00:04:56.840
to get us what's known as logistic growth.

00:04:56.840 --> 00:04:59.273
Logistic growth.

00:05:00.240 --> 00:05:01.993
So this is exponential growth,

00:05:02.955 --> 00:05:05.560
and what we're gonna now talk
about is logistic growth.

00:05:05.560 --> 00:05:08.220
And what they do is they start
with the exponential growth,

00:05:08.220 --> 00:05:11.390
so my population growth rate

00:05:11.390 --> 00:05:16.390
you could view as your maximum
per capita growth rate,

00:05:16.410 --> 00:05:19.350
times your population, so
that's exactly what we had

00:05:19.350 --> 00:05:22.890
right over here, but then they
multiplied that by a factor

00:05:22.890 --> 00:05:24.690
so that this thing slows down

00:05:24.690 --> 00:05:27.290
the closer and closer we get
to the carrying capacity.

00:05:27.290 --> 00:05:29.410
And the factor that they add is,

00:05:29.410 --> 00:05:34.410
your carrying capacity
minus your population,

00:05:34.870 --> 00:05:38.950
over your carrying capacity.

00:05:38.950 --> 00:05:41.350
Now let's see if this
makes intuitive sense.

00:05:41.350 --> 00:05:43.170
So let's set up another table here.

00:05:43.170 --> 00:05:45.270
And I'll do it with the same values.

00:05:45.270 --> 00:05:49.850
So let's say we have N,

00:05:49.850 --> 00:05:52.370
so our population, what's going
to be our population growth

00:05:52.370 --> 00:05:55.440
when our population's 100, when it's 500,

00:05:55.440 --> 00:05:57.420
and when it's 900?

00:05:57.420 --> 00:05:59.580
So I encourage you, pause this video,

00:05:59.580 --> 00:06:02.983
and figure out what dN dt
is at these various times.

00:06:03.910 --> 00:06:06.160
Well, at 100, it's going to be,

00:06:06.160 --> 00:06:07.430
I'll do this one, I'll write it out,

00:06:07.430 --> 00:06:12.430
it's going to be 0.2 times 100,

00:06:12.710 --> 00:06:17.710
times the carrying capacity is 1000,

00:06:17.900 --> 00:06:22.367
so it's gonna be 1000 minus 100,

00:06:23.310 --> 00:06:27.120
all of that over 1000.

00:06:27.120 --> 00:06:31.110
So this is 900 over 1000,
this is going to be 0.9.

00:06:31.110 --> 00:06:36.110
And then 0.2 times 100
is 20, so 20 times 0.9,

00:06:36.500 --> 00:06:40.080
this is going to be equal to 18.

00:06:40.080 --> 00:06:41.420
So it's a little bit lower,

00:06:41.420 --> 00:06:44.070
it's being slowed down a little
bit, but it's pretty close.

00:06:44.070 --> 00:06:46.130
Now let's see what happens
when we get to N equals 500.

00:06:46.130 --> 00:06:48.150
Pause this video and figure what dN dt,

00:06:48.150 --> 00:06:51.320
our population growth rate,
would be at that time.

00:06:51.320 --> 00:06:56.320
So in this case, it's
going to be 0.2 times 500,

00:06:56.390 --> 00:06:59.490
times 500, times this factor here,

00:06:59.490 --> 00:07:03.120
which is now going to be 1000

00:07:03.120 --> 00:07:07.370
minus 500, that's our population now,

00:07:07.370 --> 00:07:10.350
minus 500, all of that over 1000.

00:07:11.510 --> 00:07:12.890
Now what's this going to be?

00:07:12.890 --> 00:07:14.860
This is 100, which we had there,

00:07:14.860 --> 00:07:17.500
but it's going to be
multiplied by 500 over 1000,

00:07:17.500 --> 00:07:18.930
which is .5.

00:07:18.930 --> 00:07:20.730
So we're only going to grow half as fast

00:07:20.730 --> 00:07:22.130
as we were in this situation.

00:07:22.130 --> 00:07:23.260
'Cause once again, we don't have

00:07:23.260 --> 00:07:25.370
an infinite amount of resources here.

00:07:25.370 --> 00:07:29.600
So this is going to be 100 times .5,

00:07:29.600 --> 00:07:32.660
which is equal to 50.

00:07:32.660 --> 00:07:34.800
And then if you look at
this scenario over here,

00:07:34.800 --> 00:07:37.860
when our population is 900, what is dN dt?

00:07:37.860 --> 00:07:38.960
Pause the video again.

00:07:39.830 --> 00:07:44.537
Well, it is going to be 0.2 times 900,

00:07:45.490 --> 00:07:48.330
which is 180, times this factor,

00:07:48.330 --> 00:07:53.330
which is going to be 1000 minus 900,

00:07:55.780 --> 00:07:59.520
all of that over 1000.

00:07:59.520 --> 00:08:02.400
So now this factor's going to be,

00:08:02.400 --> 00:08:05.900
100 over 1000, which is .1, 0.1.

00:08:05.900 --> 00:08:08.190
This part right over here is,

00:08:08.190 --> 00:08:10.530
this part right over here is 180.

00:08:10.530 --> 00:08:13.770
180 times 1/10th is
going to be equal to 18.

00:08:13.770 --> 00:08:16.130
So now our population
growth has slowed down.

00:08:16.130 --> 00:08:17.160
Why is that happening?

00:08:17.160 --> 00:08:18.910
Here, your population rate,

00:08:18.910 --> 00:08:20.730
the rate of growth is growing
and growing and growing,

00:08:20.730 --> 00:08:23.020
because the more bunnies or
whatever types of individuals

00:08:23.020 --> 00:08:25.100
you have, there's just more to reproduce,

00:08:25.100 --> 00:08:27.310
and they're just gonna
keep growing exponentially.

00:08:27.310 --> 00:08:28.990
But here, they're
getting closer and closer

00:08:28.990 --> 00:08:31.840
to the carrying capacity of
whatever environment they're at.

00:08:31.840 --> 00:08:33.700
And so at 900, they're awfully close,

00:08:33.700 --> 00:08:34.820
so now you're gonna have some bunnies

00:08:34.820 --> 00:08:35.653
that are going hungry,

00:08:35.653 --> 00:08:37.620
and maybe they're not in the
mood to reproduce as much,

00:08:37.620 --> 00:08:39.220
or maybe they're getting killed,

00:08:39.220 --> 00:08:42.340
or they're dying of, this
is very unpleasant thinking,

00:08:42.340 --> 00:08:44.520
they're dying of starvation,

00:08:44.520 --> 00:08:46.470
or they're not able to
get water, dehydration.

00:08:46.470 --> 00:08:48.550
Who knows what might be happening?

00:08:48.550 --> 00:08:51.600
And we could also think
about this visually.

00:08:51.600 --> 00:08:55.350
If we were to make a quick
graph right over here,

00:08:55.350 --> 00:08:56.720
where if this is time,

00:08:56.720 --> 00:08:58.800
and if this is population,

00:08:58.800 --> 00:09:00.850
our exponential growth right here

00:09:00.850 --> 00:09:03.610
would describe something
that looks like this.

00:09:03.610 --> 00:09:06.920
So, for exponential growth, our population

00:09:06.920 --> 00:09:08.900
will grow like this.

00:09:08.900 --> 00:09:10.960
The more our population
is, the faster it grows,

00:09:10.960 --> 00:09:12.260
the more it is, the faster it grows,

00:09:12.260 --> 00:09:13.490
the more it is, the faster it grows,

00:09:13.490 --> 00:09:15.390
and it'll just keep
going forever until it,

00:09:15.390 --> 00:09:18.110
just, there's no limit in theory.

00:09:18.110 --> 00:09:19.870
And obviously, we know
that's not realistic.

00:09:19.870 --> 00:09:22.920
Now with logistic growth,
I'll do this in red,

00:09:22.920 --> 00:09:24.660
in logistic growth, in
the beginning it looks

00:09:24.660 --> 00:09:25.940
a lot like exponential growth,

00:09:25.940 --> 00:09:28.020
it's just a little bit slower.

00:09:28.020 --> 00:09:31.970
But then as the population
gets higher and higher,

00:09:31.970 --> 00:09:33.880
it gets a good bit slower,

00:09:33.880 --> 00:09:36.880
and it's limited by the
natural carrying capacity

00:09:36.880 --> 00:09:38.900
of the environment for that population.

00:09:38.900 --> 00:09:42.020
So K would be right over there.

00:09:42.020 --> 00:09:46.000
It would asymptote up to it,
but not quite approach it.

00:09:46.000 --> 00:09:48.270
And if you wanted to get the
limit, what would happen?

00:09:48.270 --> 00:09:49.850
Well, what happens at a population

00:09:49.850 --> 00:09:51.740
of 1000 in this circumstance?

00:09:51.740 --> 00:09:55.150
Well then, this factor right
over here just becomes zero,

00:09:55.150 --> 00:09:57.690
so your population at that point

00:09:57.690 --> 00:10:00.540
just wouldn't grow anymore if
you were to even get there.


Per capita population growth and exponential growth

WEBVTT
Kind: captions
Language: en

00:00:00.823 --> 00:00:01.760
- [Instructor] In a previous video,

00:00:01.760 --> 00:00:04.930
we started thinking about things
like population growth rate

00:00:04.930 --> 00:00:06.880
and how it relates to the birth rate

00:00:06.880 --> 00:00:08.670
and the death rate within a population,

00:00:08.670 --> 00:00:10.190
and we related that to some

00:00:10.190 --> 00:00:12.770
of the seemingly complex formulas

00:00:12.770 --> 00:00:16.380
that you might see on an
AP Biology formula sheet.

00:00:16.380 --> 00:00:18.370
Now we're going to
extend that conversation

00:00:18.370 --> 00:00:20.490
to discuss some of the other
formulas you might see,

00:00:20.490 --> 00:00:23.380
but to realize that they
really are just intuition

00:00:23.380 --> 00:00:25.930
using a little bit of fancy math notation.

00:00:25.930 --> 00:00:27.170
So just as a little bit of review,

00:00:27.170 --> 00:00:29.080
we looked at an example where,

00:00:29.080 --> 00:00:32.260
in a population, the birth
rate is 60 bunnies per year,

00:00:32.260 --> 00:00:33.240
we're talking about bunnies here,

00:00:33.240 --> 00:00:34.530
it's a population of bunnies,

00:00:34.530 --> 00:00:37.580
and the death rate is 15 bunnies per year,

00:00:37.580 --> 00:00:39.630
well, what's the population growth rate?

00:00:39.630 --> 00:00:40.890
Well, in a given year,

00:00:40.890 --> 00:00:42.910
you would expect 60 bunnies to be born,

00:00:42.910 --> 00:00:44.630
so that would add to the population.

00:00:44.630 --> 00:00:46.610
And you would expect 15 bunnies to die,

00:00:46.610 --> 00:00:48.730
so that would take away
from the population,

00:00:48.730 --> 00:00:52.720
for a net increase of 49 bunnies per year.

00:00:52.720 --> 00:00:54.170
And to put that in the language

00:00:54.170 --> 00:00:56.640
of your AP Biology formula sheet,

00:00:56.640 --> 00:00:59.890
the notation they use for
population growth rate,

00:00:59.890 --> 00:01:01.810
they use a fancy notation,

00:01:01.810 --> 00:01:03.310
so actually, let me
just write it over here,

00:01:03.310 --> 00:01:07.163
they say N is equal to your population,

00:01:08.656 --> 00:01:09.710
N is equal to population,

00:01:09.710 --> 00:01:11.350
and then your population growth rate,

00:01:11.350 --> 00:01:13.240
they use calculus notation.

00:01:13.240 --> 00:01:18.240
So our change in population
per change in time.

00:01:19.060 --> 00:01:20.940
This is really talking
about something in calculus

00:01:20.940 --> 00:01:22.470
known as instantaneous change,

00:01:22.470 --> 00:01:23.990
but we don't have to get too bogged down

00:01:23.990 --> 00:01:25.150
with that just yet.

00:01:25.150 --> 00:01:26.610
But your population growth rate,

00:01:26.610 --> 00:01:28.310
which you could use this notation for,

00:01:28.310 --> 00:01:32.990
is equal to your birth
rate, 60 bunnies per year,

00:01:32.990 --> 00:01:36.830
and the notation they use
for birth rate is just B.

00:01:36.830 --> 00:01:39.250
They don't use the same
rate notation for that.

00:01:39.250 --> 00:01:41.490
I probably would have, but that's fine,

00:01:41.490 --> 00:01:42.990
I'm just trying to make you familiar

00:01:42.990 --> 00:01:44.130
with what you might see.

00:01:44.130 --> 00:01:47.100
And then minus the death rate.

00:01:47.100 --> 00:01:48.780
Minus D.

00:01:48.780 --> 00:01:50.700
So this right over here is something

00:01:50.700 --> 00:01:52.460
that you would see on that formula sheet,

00:01:52.460 --> 00:01:54.940
but it makes fairly intuitive sense.

00:01:54.940 --> 00:01:57.310
Now the next idea we're
going to think about

00:01:57.310 --> 00:02:00.410
is something known as a per capita

00:02:00.410 --> 00:02:02.270
growth rate of population.

00:02:02.270 --> 00:02:04.500
Let me write it out in words first.

00:02:04.500 --> 00:02:06.440
So, here we're going to think about

00:02:06.440 --> 00:02:09.290
a per capita

00:02:10.750 --> 00:02:15.270
growth rate, or population growth rate.

00:02:15.270 --> 00:02:18.150
Per capita population growth rate.

00:02:18.150 --> 00:02:20.010
Now per capita means you could view it

00:02:20.010 --> 00:02:23.240
as on average per individual.

00:02:23.240 --> 00:02:26.010
What is the average growth
rate per individual?

00:02:26.010 --> 00:02:27.010
What is that going to be?

00:02:27.010 --> 00:02:29.930
Pause this video and
try to think about it.

00:02:29.930 --> 00:02:31.340
Well, one way you could think about it,

00:02:31.340 --> 00:02:33.500
is the total population growth rate,

00:02:33.500 --> 00:02:35.650
divided by the population,

00:02:35.650 --> 00:02:38.040
divided by the number of people there are.

00:02:38.040 --> 00:02:42.570
So it's going to be our
population growth rate,

00:02:42.570 --> 00:02:46.520
growth rate, divided by,

00:02:46.520 --> 00:02:49.670
divided by our population.

00:02:49.670 --> 00:02:50.503
Population.

00:02:52.090 --> 00:02:56.850
Now, let's say that we have
a population of 300 bunnies.

00:02:56.850 --> 00:02:58.350
Actually, let's make the
math a little bit simpler.

00:02:58.350 --> 00:03:02.660
Let's say we have a
population of 450 bunnies.

00:03:02.660 --> 00:03:04.350
So what is going to be our per capita

00:03:04.350 --> 00:03:07.460
population growth rate?

00:03:07.460 --> 00:03:10.490
Pause this video and
try to figure that out.

00:03:10.490 --> 00:03:14.020
Well, if we have a
population of 450 bunnies,

00:03:14.020 --> 00:03:17.690
450 bunnies.

00:03:17.690 --> 00:03:21.350
Our population growth rate
per the number of people,

00:03:21.350 --> 00:03:23.040
or number of bunnies, I should say,

00:03:23.040 --> 00:03:24.840
is going to be equal to,

00:03:24.840 --> 00:03:29.410
our population growth rate is 45 bunnies,

00:03:29.410 --> 00:03:32.003
bunnies per year.

00:03:32.880 --> 00:03:34.690
And that's going to be

00:03:34.690 --> 00:03:38.090
for every 450 bunnies.

00:03:38.090 --> 00:03:41.660
450 bunnies.

00:03:41.660 --> 00:03:43.860
Which will get us to,

00:03:43.860 --> 00:03:47.750
45 divided by 450 is 0.1,

00:03:47.750 --> 00:03:50.490
and then the units, bunnies
cancel with bunnies,

00:03:50.490 --> 00:03:54.350
so it's 0.1 per year.

00:03:54.350 --> 00:03:57.870
Now why is per capita population
growth rate interesting?

00:03:57.870 --> 00:04:00.480
Well, it tells us just how likely,

00:04:00.480 --> 00:04:02.190
and in most populations,

00:04:02.190 --> 00:04:04.570
you need at least a male and a female

00:04:04.570 --> 00:04:05.500
in order to reproduce,

00:04:05.500 --> 00:04:06.880
but there are some organisms

00:04:06.880 --> 00:04:10.510
that can just split and
reproduce asexually.

00:04:10.510 --> 00:04:15.510
But it tells on average
per individual organism

00:04:16.150 --> 00:04:20.370
how much are they going to grow per year?

00:04:20.370 --> 00:04:21.900
So it gives you a sense of that.

00:04:21.900 --> 00:04:23.340
Now connecting it to the notation

00:04:23.340 --> 00:04:26.170
that you might see on an
AP Biology formula sheet,

00:04:26.170 --> 00:04:27.250
it would look like this,

00:04:27.250 --> 00:04:30.000
the per capita population growth rate

00:04:30.000 --> 00:04:34.050
is usually denoted by
the lowercase letter r,

00:04:34.050 --> 00:04:36.020
and then they would say that
that is going to be equal

00:04:36.020 --> 00:04:38.120
to our population growth rate.

00:04:38.120 --> 00:04:39.630
Which, we've already seen that notation.

00:04:39.630 --> 00:04:43.800
The rate of change of our
population with respect to time,

00:04:43.800 --> 00:04:47.990
dN dt, divided by our population,

00:04:47.990 --> 00:04:50.870
divided by our population.

00:04:50.870 --> 00:04:53.640
Now we can algebraically
manipulate this a little bit,

00:04:53.640 --> 00:04:55.330
to get another expression.

00:04:55.330 --> 00:04:59.270
We could multiply both
sides times our uppercase N,

00:04:59.270 --> 00:05:01.330
times our population.

00:05:01.330 --> 00:05:04.860
And we're going to get dN
dt is equal to N times r,

00:05:04.860 --> 00:05:06.660
or r times N, let me rewrite it.

00:05:06.660 --> 00:05:10.930
We can rewrite this as dN dt

00:05:10.930 --> 00:05:15.930
is equal to our per capita
population growth rate,

00:05:16.530 --> 00:05:18.833
times our population.

00:05:19.780 --> 00:05:22.220
Now, this once again makes sense.

00:05:22.220 --> 00:05:24.100
If you say, okay, this is how many people,

00:05:24.100 --> 00:05:26.400
how many individuals I have,

00:05:26.400 --> 00:05:31.260
and if in a given year, they
grow by this much on average,

00:05:31.260 --> 00:05:32.300
well, if you multiply the two,

00:05:32.300 --> 00:05:34.810
you'll know how much the
whole population has grown.

00:05:34.810 --> 00:05:36.940
So if we didn't know these
numbers and someone said,

00:05:36.940 --> 00:05:38.990
hey, well, actually, we
can think about this,

00:05:38.990 --> 00:05:42.210
let's think about now a
population of 1000 bunnies.

00:05:42.210 --> 00:05:44.930
So if N was equal to 1000.

00:05:44.930 --> 00:05:46.760
And I'll say they're
the same type of bunnies

00:05:46.760 --> 00:05:50.340
that have the same
probability of reproducing,

00:05:50.340 --> 00:05:51.310
and the same likelihood,

00:05:51.310 --> 00:05:56.020
so we know that r is equal 0.1 per year.

00:05:56.020 --> 00:05:58.260
For this population of bunnies,

00:05:58.260 --> 00:06:00.130
what is going to be our
population growth rate?

00:06:00.130 --> 00:06:02.330
Pause this video and
try to figure that out.

00:06:04.870 --> 00:06:07.160
Well in this situation,

00:06:07.160 --> 00:06:12.160
dN dt is going to be our per
capita population growth rate,

00:06:12.860 --> 00:06:17.860
so it's going to 0.1 per year,

00:06:19.330 --> 00:06:21.650
times our population.

00:06:21.650 --> 00:06:25.560
Times 1000 bunnies,

00:06:25.560 --> 00:06:29.430
bunnies, I'll keep my units here, bunnies,

00:06:29.430 --> 00:06:31.350
and so this is going to be equal to,

00:06:31.350 --> 00:06:36.334
1000 times a tenth is 100,

00:06:36.334 --> 00:06:37.360
we're in that color.

00:06:37.360 --> 00:06:42.360
It's 100 bunnies, bunnies per year.

00:06:42.620 --> 00:06:44.080
So hopefully you're
getting an appreciation

00:06:44.080 --> 00:06:46.060
for why these types of formulas,

00:06:46.060 --> 00:06:47.130
which are fairly straightforward,

00:06:47.130 --> 00:06:49.780
they're using just a fancy
notation, are useful.

00:06:49.780 --> 00:06:53.620
Now, this is also an
interesting thing to look at.

00:06:53.620 --> 00:06:56.810
Because even though this is
in fancy calculus notation,

00:06:56.810 --> 00:06:59.060
and they're saying that our
rate of change of population

00:06:59.060 --> 00:07:01.910
is equal to r times our population,

00:07:01.910 --> 00:07:03.960
this is actually a differential equation,

00:07:03.960 --> 00:07:06.520
if you were to think about
what this population,

00:07:06.520 --> 00:07:08.670
the type of population
this would describe,

00:07:08.670 --> 00:07:10.060
this would actually be a population

00:07:10.060 --> 00:07:12.920
that's growing exponentially.

00:07:12.920 --> 00:07:16.840
So this is often known as an
exponential growth equation,

00:07:16.840 --> 00:07:18.453
let me write that down.

00:07:18.453 --> 00:07:23.380
Exponential, exponential growth.

00:07:23.380 --> 00:07:25.460
And, in other, in your math classes,

00:07:25.460 --> 00:07:26.460
in your calculus classes,

00:07:26.460 --> 00:07:28.490
or even in your precalculus classes,

00:07:28.490 --> 00:07:30.310
you will study exponential growth.

00:07:30.310 --> 00:07:32.600
In a biology class, you're
really just thinking about

00:07:32.600 --> 00:07:33.890
how to manipulate this a little bit.

00:07:33.890 --> 00:07:35.480
But just to give you a little sense

00:07:35.480 --> 00:07:38.440
of what's going on with
exponential growth,

00:07:38.440 --> 00:07:40.400
if you have a population of bunnies

00:07:40.400 --> 00:07:42.850
with this type of exponential growth,

00:07:42.850 --> 00:07:44.810
what is happening here, this is time,

00:07:44.810 --> 00:07:46.140
and this is your population,

00:07:46.140 --> 00:07:48.700
so you're going to have some
starting population here,

00:07:48.700 --> 00:07:51.410
and it's just going to grow exponentially.

00:07:51.410 --> 00:07:52.970
And the higher the r is,

00:07:52.970 --> 00:07:57.430
the steeper this exponential
growth curve is going to be.

00:07:57.430 --> 00:07:59.700
But this describes how
populations can grow

00:07:59.700 --> 00:08:02.840
if they are not constrained
by the environment in any way.

00:08:02.840 --> 00:08:05.660
They have just as much
land, as much water,

00:08:05.660 --> 00:08:07.390
and as much food as they need,

00:08:07.390 --> 00:08:10.960
eventually, the bunnies will
fill the surface of the earth,

00:08:10.960 --> 00:08:12.670
and the universe, and now, obviously,

00:08:12.670 --> 00:08:15.220
we know that that is not
a realistic situation,

00:08:15.220 --> 00:08:18.430
that any ecosystem has some
natural carrying capacity,

00:08:18.430 --> 00:08:21.010
there's only so much food,
there's only so much land.

00:08:21.010 --> 00:08:23.180
At some point, there's
just going to be bunnies

00:08:23.180 --> 00:08:26.030
falling from trees, and
it's going to be much easier

00:08:26.030 --> 00:08:28.110
for predators to get them,
and all these other things.

00:08:28.110 --> 00:08:30.494
And we will discuss
that in the next video.

00:08:30.494 --> 00:08:33.670
How do we adapt the
exponential growth equation

00:08:33.670 --> 00:08:35.250
right over here to factor
in a little bit more

00:08:35.250 --> 00:08:36.730
of a real-world situation,

00:08:36.730 --> 00:08:41.130
where at some population,
you're going to be hitting up

00:08:41.130 --> 00:08:44.363
against the carrying
capacity of the environment?


Population growth rate based on birth and death rates

WEBVTT
Kind: captions
Language: en

00:00:00.350 --> 00:00:02.100
- [Instructor] When you
take an AP Biology exam

00:00:02.100 --> 00:00:04.210
it is likely that will
include a formula sheet

00:00:04.210 --> 00:00:06.270
that will include formulas like this one

00:00:06.270 --> 00:00:08.420
and it can be a little
bit intimidating at first

00:00:08.420 --> 00:00:10.930
because we're not used to
seeing formulas like this

00:00:10.930 --> 00:00:13.530
that involve, in fact this is
formally calculus notation,

00:00:13.530 --> 00:00:15.020
in a biology class.

00:00:15.020 --> 00:00:17.690
But, what we'll see in this
video is that this formula

00:00:17.690 --> 00:00:19.320
is actually just trying
to express something

00:00:19.320 --> 00:00:21.200
that's fairly intuitive and
something that you actually

00:00:21.200 --> 00:00:24.560
don't even need calculus
or even much algebra,

00:00:24.560 --> 00:00:25.590
but then we'll connect it to this

00:00:25.590 --> 00:00:27.460
to see that it all makes sense.

00:00:27.460 --> 00:00:28.750
So, putting this aside,

00:00:28.750 --> 00:00:31.110
let me just ask you a simple question.

00:00:31.110 --> 00:00:33.280
Let's say we're studying a population

00:00:33.280 --> 00:00:36.280
and we see that the birth rate,

00:00:36.280 --> 00:00:38.420
the birth rate

00:00:38.420 --> 00:00:42.500
of this population is equal to 60,

00:00:42.500 --> 00:00:44.540
let's say we're studying
a population of bunnies,

00:00:44.540 --> 00:00:45.903
60 bunnies,

00:00:46.930 --> 00:00:48.430
bunnies per year

00:00:49.420 --> 00:00:53.370
and let's say we know that
the death rate of bunnies,

00:00:53.370 --> 00:00:57.910
death rate, is equal to 15 bunnies,

00:00:59.140 --> 00:01:01.890
bunnies per year.

00:01:01.890 --> 00:01:03.160
Now, without even paying attention

00:01:03.160 --> 00:01:04.870
to this formula sheet up there,

00:01:04.870 --> 00:01:07.610
what do you think, given this data,

00:01:07.610 --> 00:01:12.200
is the population, population

00:01:12.200 --> 00:01:17.070
growth rate for this
population of bunnies?

00:01:17.070 --> 00:01:20.080
Pause this video and see
if you can answer that.

00:01:20.080 --> 00:01:21.710
Well, your population growth rate,

00:01:21.710 --> 00:01:24.060
if you think about just
even say a given year,

00:01:24.060 --> 00:01:26.130
in that year you'll grow your population

00:01:26.130 --> 00:01:28.030
by 60 bunnies per year.

00:01:28.030 --> 00:01:30.260
So, you will grow

00:01:30.260 --> 00:01:33.020
by 60 bunnies

00:01:34.670 --> 00:01:37.020
per year and then you would shrink

00:01:37.020 --> 00:01:38.330
by the 15 that died.

00:01:38.330 --> 00:01:42.170
So, it would shrink by 15 bunnies,

00:01:42.170 --> 00:01:45.230
bunnies per year

00:01:45.230 --> 00:01:48.590
and so in that year you
would net out 45 bunnies

00:01:48.590 --> 00:01:50.690
and that's a rate 'cause
you're saying per year.

00:01:50.690 --> 00:01:54.410
So you would grow by 45 bunnies,

00:01:54.410 --> 00:01:56.450
bunnies in that year

00:01:56.450 --> 00:01:58.770
and that would be your
population growth rate.

00:01:58.770 --> 00:02:00.960
Now the thing that we
just did very intuitively,

00:02:00.960 --> 00:02:02.730
you don't need advanced
math to think through

00:02:02.730 --> 00:02:06.760
what we just did, that's exactly
what this formula's saying.

00:02:06.760 --> 00:02:09.470
This notation where
you say d something dt,

00:02:09.470 --> 00:02:11.480
this is the rate at which this something

00:02:11.480 --> 00:02:13.350
is changing with respect to time.

00:02:13.350 --> 00:02:15.150
So, this is just a fancy way of saying

00:02:15.150 --> 00:02:17.410
what is the rate at which our population

00:02:17.410 --> 00:02:19.400
is changing with respect to time?

00:02:19.400 --> 00:02:21.350
There's other ways that you
could have written that.

00:02:21.350 --> 00:02:22.960
If you didn't wanna use calculus notation

00:02:22.960 --> 00:02:25.650
you could of written change in population

00:02:25.650 --> 00:02:28.100
for a given change in time.

00:02:28.100 --> 00:02:31.160
The Greek letter delta
often denotes change in

00:02:31.160 --> 00:02:34.360
and what this formula says
is exactly what we did.

00:02:34.360 --> 00:02:37.530
It would be the difference
between the birth rate,

00:02:37.530 --> 00:02:39.790
which is the letter b in this formula,

00:02:39.790 --> 00:02:42.410
the birth rate, right over here,

00:02:42.410 --> 00:02:44.750
and the death rate.

00:02:44.750 --> 00:02:46.820
The death rate is the
letter d in this formula.

00:02:46.820 --> 00:02:48.090
You have it right over here

00:02:48.090 --> 00:02:50.090
and that's exactly what we did over there.

00:02:50.090 --> 00:02:51.800
So, it's all very intuitive.

00:02:51.800 --> 00:02:53.680
Now, if I were in charge
of the formula sheet

00:02:53.680 --> 00:02:55.340
I might have expressed it
a little bit different.

00:02:55.340 --> 00:02:57.120
Maybe I would have used
notation like this.

00:02:57.120 --> 00:02:58.970
Maybe I would have
written in plain English.

00:02:58.970 --> 00:03:01.420
I probably would have
used different notations

00:03:01.420 --> 00:03:03.670
for the b and the d to make
it a little bit clearer

00:03:03.670 --> 00:03:04.810
that those were rates,

00:03:04.810 --> 00:03:06.420
but as you see from this example,

00:03:06.420 --> 00:03:08.930
it's just trying to express
something very straightforward

00:03:08.930 --> 00:03:11.000
and frankly, something
that you probably actually

00:03:11.000 --> 00:03:12.663
don't need a formula sheet for.