0:00:00.690,0:00:03.460
What I want to start thinking[br]about in this video is,

0:00:03.460,0:00:06.290
given that we do have a[br]monopoly on something,

0:00:06.290,0:00:08.380
and in this example,[br]in this video,

0:00:08.380,0:00:10.440
we're going to have a[br]monopoly on oranges.

0:00:10.440,0:00:12.410
Given that we have a[br]monopoly on oranges

0:00:12.410,0:00:16.360
and a demand curve for[br]oranges in the market,

0:00:16.360,0:00:18.194
how do we maximize our profit?

0:00:18.194,0:00:19.610
And to answer that[br]question, we're

0:00:19.610,0:00:21.193
going to think about[br]our total revenue

0:00:21.193,0:00:23.007
for different quantities.

0:00:23.007,0:00:24.840
And from that we'll get[br]the marginal revenue

0:00:24.840,0:00:25.980
for different quantities.

0:00:25.980,0:00:28.500
And then we can compare that[br]to our marginal cost curve.

0:00:28.500,0:00:30.291
And that should give[br]us a pretty good sense

0:00:30.291,0:00:34.550
of what quantity we should[br]produce to optimize things.

0:00:34.550,0:00:37.260
So let's just figure[br]out total revenue first.

0:00:37.260,0:00:39.010
So obviously, if[br]we produce nothing,

0:00:39.010,0:00:42.930
if we produces 0 quantity,[br]we'll have nothing to sell.

0:00:42.930,0:00:44.530
Total revenue is[br]price times quantity.

0:00:44.530,0:00:46.990
Your price is 6 but[br]your quantity is 0.

0:00:46.990,0:00:51.240
So your total revenue is going[br]to be 0 if you produce nothing.

0:00:51.240,0:00:53.880
If you produce 1 unit--[br]and this over here

0:00:53.880,0:00:55.880
is actually 1,000[br]pounds per day.

0:00:55.880,0:00:58.580
And we'll call a unit[br]1,000 pounds per day.

0:00:58.580,0:01:00.597
If you produce 1 unit,[br]then your total revenue

0:01:00.597,0:01:04.019
is 1 unit times $5 per pound.

0:01:04.019,0:01:08.480
So it'll be $5 times, actually[br]1,000, so it'll be $5,000.

0:01:08.480,0:01:13.260
And you can also view it as[br]the area right over here.

0:01:13.260,0:01:17.200
You have the height is price[br]and the width is quantity.

0:01:17.200,0:01:19.000
But we can plot that, 5 times 1.

0:01:19.000,0:01:22.460
If you produce 1 unit,[br]you're going to get $5,000.

0:01:22.460,0:01:27.550
So this right over here[br]is in thousands of dollars

0:01:27.550,0:01:29.885
and this right over here[br]is in thousands of pounds.

0:01:33.169,0:01:35.460
Just to make sure that we're[br]consistent with this right

0:01:35.460,0:01:36.410
over here.

0:01:36.410,0:01:37.340
Let's keep going.

0:01:37.340,0:01:41.200
So that was this point, or[br]when we produce 1,000 pounds,

0:01:41.200,0:01:43.165
we get $5,000.

0:01:43.165,0:01:47.260
If we produce 2,000[br]pounds, now we're

0:01:47.260,0:01:50.790
talking about our price[br]is going to be $4.

0:01:50.790,0:01:52.840
Or if we could say[br]our price is $4

0:01:52.840,0:01:55.840
we can sell 2,000 pounds,[br]given this demand curve.

0:01:55.840,0:01:57.340
And our total revenue[br]is going to be

0:01:57.340,0:01:59.900
the area of this[br]rectangle right over here.

0:01:59.900,0:02:02.050
Height is price,[br]width is quantity.

0:02:02.050,0:02:03.960
4 times 2 is 8.

0:02:03.960,0:02:06.640
So if I produce[br]2,000 pounds then

0:02:06.640,0:02:10.169
I will get a total[br]revenue of $8,000.

0:02:10.169,0:02:12.210
So this is 7 and 1/2,[br]8 is going to put

0:02:12.210,0:02:16.320
us something right about there.

0:02:16.320,0:02:18.070
And then we can keep going.

0:02:18.070,0:02:22.310
If I produce, or if the[br]price is $3 per pound,

0:02:22.310,0:02:24.650
I can sell 3,000 pounds.

0:02:24.650,0:02:27.690
My total revenue is this[br]rectangle right over here,

0:02:27.690,0:02:30.630
$3 times 3 is $9,000.

0:02:30.630,0:02:32.920
So if I produce[br]3,000 pounds, I can

0:02:32.920,0:02:35.260
get a total revenue of $9,000.

0:02:35.260,0:02:37.990
So right about there.

0:02:37.990,0:02:39.680
And let's keep going.

0:02:39.680,0:02:45.980
If I produce, or if the[br]price, is $2 per pound,

0:02:45.980,0:02:47.660
I can sell 4,000 pounds.

0:02:47.660,0:02:51.830
My total revenue is $2[br]times 4, which is $8,000.

0:02:51.830,0:02:54.330
So if I produce[br]4,000 pounds I can

0:02:54.330,0:02:55.976
get a total revenue of $8,000.

0:02:55.976,0:02:59.660
It should be even with that[br]one right over there, just

0:02:59.660,0:03:00.850
like that.

0:03:00.850,0:03:13.400
And then if the price is $1 per[br]pound I can sell 5,000 pounds.

0:03:13.400,0:03:17.870
My total revenue is going[br]to be $1 times 5, or $5,000.

0:03:17.870,0:03:19.880
So it's going to be[br]even with this here.

0:03:19.880,0:03:24.560
So if I produce 5,000 units[br]I can get $5,000 of revenue.

0:03:24.560,0:03:27.700
And if the price[br]is 0, the market

0:03:27.700,0:03:29.752
will demand 6,000 pounds[br]per day if it's free.

0:03:29.752,0:03:31.960
But I'm not going to generate[br]any revenue because I'm

0:03:31.960,0:03:33.940
going to be giving[br]it away for free.

0:03:33.940,0:03:37.700
So I will not be generating[br]any revenue in this situation.

0:03:37.700,0:03:40.237
So our total revenue curve,[br]it looks like-- and if you've

0:03:40.237,0:03:41.820
taken algebra you[br]would recognize this

0:03:41.820,0:03:48.270
as a downward facing[br]parabola-- our total revenue

0:03:48.270,0:03:51.380
looks like this.

0:03:51.380,0:03:54.540
It's easier for me to draw[br]a curve with a dotted line.

0:03:54.540,0:03:58.450
Our total revenue looks[br]something like that.

0:03:58.450,0:04:00.410
And you can even[br]solve it algebraically

0:04:00.410,0:04:03.360
to show that it is this[br]downward facing parabola.

0:04:03.360,0:04:07.120
The formula right over[br]here of the demand curve,

0:04:07.120,0:04:08.500
its y-intercept is 6.

0:04:08.500,0:04:10.970
So if I wanted to write price[br]as a function of quantity

0:04:10.970,0:04:16.480
we have price is equal[br]to 6 minus quantity.

0:04:16.480,0:04:18.980
Or if you wanted to write in[br]the traditional slope intercept

0:04:18.980,0:04:22.750
form, or mx plus b form-- and[br]if that doesn't make any sense

0:04:22.750,0:04:25.220
you might want to review some[br]of our algebra playlist--

0:04:25.220,0:04:28.640
you could write it as p is[br]equal to negative q plus 6.

0:04:28.640,0:04:30.830
Obviously these are[br]the same exact thing.

0:04:30.830,0:04:36.010
You have a y-intercept of[br]six and you have a negative 1

0:04:36.010,0:04:37.230
slope.

0:04:37.230,0:04:40.900
If you increase quantity by[br]1, you decrease price by 1.

0:04:40.900,0:04:43.630
Or another way to think about[br]it, if you decrease price by 1

0:04:43.630,0:04:45.820
you increase quantity by 1.

0:04:45.820,0:04:48.340
So that's why you have[br]a negative 1 slope.

0:04:48.340,0:04:50.570
So this is price is a[br]function of quantity.

0:04:50.570,0:04:52.080
What is total revenue?

0:04:52.080,0:04:57.870
Well, total revenue is equal[br]to price times quantity.

0:04:57.870,0:05:00.460
But we can write price as[br]a function of quantity.

0:05:00.460,0:05:01.410
We did it just now.

0:05:01.410,0:05:02.930
This is what it is.

0:05:02.930,0:05:06.990
So we can rewrite it, or we[br]could even write it like this,

0:05:06.990,0:05:09.510
we can rewrite the[br]price part as-- so this

0:05:09.510,0:05:14.280
is going to be equal to negative[br]q plus 6 times quantity.

0:05:17.040,0:05:19.784
And this is equal[br]to total revenue.

0:05:19.784,0:05:21.200
And then if you[br]multiply this out,

0:05:21.200,0:05:24.070
you get total[br]revenue is equal to q

0:05:24.070,0:05:30.010
times q is negative q[br]squared plus 6 plus 6q.

0:05:30.010,0:05:31.920
So you might recognize this.

0:05:31.920,0:05:33.820
This is clearly a quadratic.

0:05:33.820,0:05:38.060
Since you have a negative out[br]front before the second degree

0:05:38.060,0:05:39.920
term right over here,[br]before the q squared,

0:05:39.920,0:05:42.120
it is a downward[br]opening parabola.

0:05:42.120,0:05:44.300
So it makes complete sense.

0:05:44.300,0:05:46.500
Now, I'm going to leave[br]you there in this video.

0:05:46.500,0:05:48.000
Because I'm trying[br]to make an effort

0:05:48.000,0:05:50.017
not to make my videos too long.

0:05:50.017,0:05:51.600
But in the next video[br]what we're going

0:05:51.600,0:05:54.540
to think about is, what[br]is the marginal revenue we

0:05:54.540,0:05:57.560
get for each of[br]these quantities?

0:05:57.560,0:06:03.610
And just as a review,[br]marginal revenue

0:06:03.610,0:06:08.820
is equal to change in[br]total revenue divided

0:06:08.820,0:06:10.770
by change in quantity.

0:06:10.770,0:06:13.220
Or another way to think about[br]it, the marginal revenue

0:06:13.220,0:06:17.000
at any one of these[br]quantities is the slope

0:06:17.000,0:06:18.607
of the line tangent[br]to that point.

0:06:18.607,0:06:20.690
And you really have to do[br]a little bit of calculus

0:06:20.690,0:06:23.820
in order to actually calculate[br]slopes of tangent lines.

0:06:23.820,0:06:26.350
But we'll approximate it[br]with a little bit of algebra.

0:06:26.350,0:06:28.490
But what we essentially want[br]to do is figure out the slope.

0:06:28.490,0:06:31.031
So if we wanted to figure out[br]the marginal revenue when we're

0:06:31.031,0:06:34.080
selling 1,000 pounds--[br]so exactly how much more

0:06:34.080,0:06:37.510
total revenue do we get if[br]we just barely increase,

0:06:37.510,0:06:40.420
if we just started selling[br]another millionth of a pound

0:06:40.420,0:06:42.477
of oranges-- what's[br]going to happen?

0:06:42.477,0:06:44.060
And so what we do[br]is we're essentially

0:06:44.060,0:06:47.270
trying to figure out the[br]slope of the tangent line

0:06:47.270,0:06:49.356
at any point.

0:06:49.356,0:06:50.230
And you can see that.

0:06:50.230,0:06:53.820
Because the change[br]in total revenue

0:06:53.820,0:07:00.750
is this and change in[br]quantity is that there.

0:07:00.750,0:07:02.975
So we're trying to find[br]the instantaneous slope

0:07:02.975,0:07:04.600
at that point, or[br]you could think of it

0:07:04.600,0:07:07.190
as the slope of[br]the tangent line.

0:07:07.190,0:07:10.840
And we'll continue doing[br]that in the next video.