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GREG HUTKO: Today we're going
to do Fall 2010, P Set Six,

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Problem Number Four.

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And for this problem we're going
to shift away from what

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we've usually been talking
about, where we're dealing

00:00:33.220 --> 00:00:36.000
with a straight equilibrium,
setting the demand curve equal

00:00:36.000 --> 00:00:37.440
to the supply curve.

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And now we're going to think
about what happens when the

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supplier has market power.

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When they're the only competitor
in the market, and

00:00:43.670 --> 00:00:46.560
they can decide how much
quantity they want to produce.

00:00:46.560 --> 00:00:49.550
And they don't have to worry
about other producers coming

00:00:49.550 --> 00:00:51.160
in and producing.

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Problem Number Four--

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I'll read through Part A--

00:00:53.430 --> 00:00:55.790
states, "A monopolist
firm faces the

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following cost curve.

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The cost equal Q squared plus
15, where Q is the output

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produced, the demand for its
product is given by P equals

00:01:05.420 --> 00:01:09.050
24 minus Q. We need to calculate
the non-price

00:01:09.050 --> 00:01:12.750
discriminating consumer surplus,
the producer surplus,

00:01:12.750 --> 00:01:17.210
and the deadweight loss
associated with the monopoly."

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Now, what this problem's really
going to look like-- we

00:01:19.620 --> 00:01:24.030
can think about it starting
with this graph.

00:01:24.030 --> 00:01:26.920
Is, instead of producing output
to the point of the

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equilibrium right here, the
supplier can actually make

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more money by saying I'm only
going to produce to a point

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right here, so this is what
we're looking for.

00:01:40.570 --> 00:01:43.470
We're wondering how much is the
supplier actually going to

00:01:43.470 --> 00:01:46.900
constrict the supply
in the market.

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And when they constrict this
supply, what happens is this

00:01:52.780 --> 00:01:55.790
small triangle right here
becomes the deadweight loss.

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This is potential surplus that
would have existed when this

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whole big triangle was
the consumer surplus

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plus producer surplus.

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So now nobody's getting
that triangle.

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But the producer surplus is much
bigger than it would have

00:02:10.625 --> 00:02:14.080
been when it was just the space
below the price level to

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the supply curve.

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So the producers
are better off.

00:02:16.870 --> 00:02:19.550
The consumers are going
to be worse off.

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And society as a whole-- adding
together the producers'

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and the consumers' surplus--

00:02:24.140 --> 00:02:26.210
is going to be worse off.

00:02:26.210 --> 00:02:29.030
Now, the way the producers
actually make their decision

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on how much to produce is, when
they're moving this line

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back and forth deciding how much
they want to constrict

00:02:35.260 --> 00:02:38.470
the quantity that they're going
to supply, and when

00:02:38.470 --> 00:02:42.300
they're supplying more, the
quantity they're supplying is

00:02:42.300 --> 00:02:44.540
going to be increasing.

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But as they supply more--

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since the demand curve
is downward sloping--

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the price is going
to be going down.

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And now the way the producer
actually makes their

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production decision is to say,
OK, I know I'm going to lose

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some money if I'm producing
more, because the price is

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going to be falling.

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What I want to know is I want to
produce as much as I can so

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that, at the margin, the cost
of producing that one

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additional unit is the same as
the revenue that I'm going to

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be taking in for that
additional unit.

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The point where I'm producing,
and the additional cost of

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that unit is more than the
additional money that I'm

00:03:17.690 --> 00:03:20.510
taking in, I'm going to stop
assuming that there's no

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competition.

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So the monopolist firm is going
to set the marginal cost

00:03:24.790 --> 00:03:26.960
equal to the marginal revenue.

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So we have a total cost
function, so calculating the

00:03:29.800 --> 00:03:32.780
marginal cost is pretty
straightforward.

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I'm just going to take the
derivative with respect to Q,

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and the marginal cost for
a monopolist firm

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is going to be 2Q.

00:03:41.420 --> 00:03:43.890
Now, it's tempting when we
look at this revenue

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function-- revenue just being
the total quantity I'm

00:03:46.770 --> 00:03:49.220
producing times the price
I'm receiving.

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It's tempting to just take the
derivative here with respect

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to Q, and say that marginal
revenue is going

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to be equal to price.

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But that's not what the
monopolist does.

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Because in a competitive
situation, we were setting

00:04:02.080 --> 00:04:04.770
marginal cost equal to P.

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In the monopolist situation,
the monopolist is going to

00:04:08.120 --> 00:04:12.190
look at this P right here, and
they're going to say I know

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how the consumers are going to
respond based on my decision

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to produce.

00:04:18.160 --> 00:04:25.030
So I'm going to replace this
P with the demand curve, 24

00:04:25.030 --> 00:04:29.880
minus Q. So I can plan how much
I'm producing based on

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what I know the consumer's
response to my production

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choice is going to be.

00:04:35.550 --> 00:04:38.910
So instead of taking the
derivative of this function,

00:04:38.910 --> 00:04:45.340
I'm going to plug-in 24 minus Q
and we're going to find the

00:04:45.340 --> 00:04:48.440
marginal revenue using
this function.

00:04:48.440 --> 00:04:53.690
When we do this, we find that
the marginal revenue is equal

00:04:53.690 --> 00:04:57.370
to 24 minus 2Q.

00:04:57.370 --> 00:05:01.730
And all we have to do now is
we have to set the marginal

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revenue and the marginal cost
equal, and we can find the

00:05:04.900 --> 00:05:07.140
quantity that's going
to be produced at

00:05:07.140 --> 00:05:08.390
the monopolist outcome.

00:05:10.960 --> 00:05:13.930
Solving for Q, you find that
the quantity is going to be

00:05:13.930 --> 00:05:15.490
equal to 6.

00:05:15.490 --> 00:05:18.890
And then we can solve for the
price just by going back to

00:05:18.890 --> 00:05:22.020
the demand curve that's
given on our graph.

00:05:22.020 --> 00:05:35.740
The price here in the
monopolist case

00:05:35.740 --> 00:05:39.740
is going to be 18.

00:05:39.740 --> 00:05:41.640
So now we can come back
to our graph.

00:05:41.640 --> 00:05:44.630
We know that the monopolist
level of output is going to be

00:05:44.630 --> 00:05:47.460
6, so we can label this 0.6.

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We know the price that's
going to be charged--

00:05:49.510 --> 00:05:52.710
which is not the intersection
with the supply curve, it's

00:05:52.710 --> 00:05:55.050
going to be the intersection
with the demand curve--

00:05:55.050 --> 00:05:58.950
this price is going to be 18.

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And on our graph it's going to
also be useful to label two

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more points.

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That'll just make it easier for
us to calculate consumer

00:06:06.600 --> 00:06:09.690
surplus, producer surplus,
and deadweight loss.

00:06:09.690 --> 00:06:13.720
We're going to want to label
this point right here so the

00:06:13.720 --> 00:06:18.010
equilibrium quantity is 8-- and
you'll see in a second why

00:06:18.010 --> 00:06:19.230
I'm labeling that.

00:06:19.230 --> 00:06:22.230
And you're also going to want
to label where, when the

00:06:22.230 --> 00:06:25.230
quantity is 6, the intersection

00:06:25.230 --> 00:06:26.150
with the supply curve.

00:06:26.150 --> 00:06:30.770
So when the quantity is 6, you
know that the marginal cost

00:06:30.770 --> 00:06:32.150
curve is given here.

00:06:32.150 --> 00:06:39.480
So that means the intersection
right here is going to be 12.

00:06:39.480 --> 00:06:42.530
And this is going to make our
calculations of the area of

00:06:42.530 --> 00:06:46.850
PS, the area of CS, and
the area of DWL just

00:06:46.850 --> 00:06:49.210
a little bit easier.

00:06:49.210 --> 00:06:52.060
Now, to calculate consumer
surplus, I'm just going to

00:06:52.060 --> 00:06:56.390
multiply the height of this
triangle right here by the

00:06:56.390 --> 00:06:57.930
length of the triangle,
and I'm going to

00:06:57.930 --> 00:06:59.440
take one half of that.

00:06:59.440 --> 00:07:13.210
So consumer surplus in
this situation is

00:07:13.210 --> 00:07:15.500
going to equal 18.

00:07:15.500 --> 00:07:16.910
And now we're going to
do the same thing

00:07:16.910 --> 00:07:18.460
for producer surplus.

00:07:18.460 --> 00:07:21.490
We're going to add the area of
this rectangle to the area of

00:07:21.490 --> 00:07:23.220
this triangle at the
bottom as well.

00:07:37.160 --> 00:07:41.400
So the first term here that's
given is the area of the

00:07:41.400 --> 00:07:46.100
rectangle, and the term here is
the area of the triangle.

00:07:46.100 --> 00:07:47.600
Adding these together, we're
going to find that the

00:07:47.600 --> 00:07:53.810
producer surplus is 72.

00:07:53.810 --> 00:07:55.900
And now, to calculate the
deadweight loss you really

00:07:55.900 --> 00:07:57.360
have two options.

00:07:57.360 --> 00:08:01.070
One, you could find the total
producer and consumer surplus

00:08:01.070 --> 00:08:01.990
at equilibrium--

00:08:01.990 --> 00:08:04.960
so the area of this large
triangle right here.

00:08:04.960 --> 00:08:08.270
And you could subtract out the
new consumer surplus and the

00:08:08.270 --> 00:08:11.100
new producer surplus, and you'll
be left with only the

00:08:11.100 --> 00:08:12.660
deadweight loss.

00:08:12.660 --> 00:08:14.720
For our purposes, it's going to
be a little bit easier to

00:08:14.720 --> 00:08:18.400
just take the height of the
triangle and the length of the

00:08:18.400 --> 00:08:21.110
base, and to multiply through.

00:08:21.110 --> 00:08:22.730
When we do that, we're going
to find that the deadweight

00:08:22.730 --> 00:08:38.220
loss is going to
be equal to 6.

00:08:44.150 --> 00:08:46.600
And so you can see that the
producer surplus is pretty

00:08:46.600 --> 00:08:48.570
high in this situation.

00:08:48.570 --> 00:08:50.590
And so the government's going
to come in in our next

00:08:50.590 --> 00:08:52.810
problem, and they're going to
say we have an intervention

00:08:52.810 --> 00:08:55.540
that might be able to correct
this problem that we see in

00:08:55.540 --> 00:08:56.900
the market.

00:08:56.900 --> 00:08:59.460
Part B says, "How does charging
the monopolist a

00:08:59.460 --> 00:09:05.050
specific tax of $8 per unit
affect the monopoly optimum,

00:09:05.050 --> 00:09:08.660
and the welfare of consumers,
the monopoly, and society,

00:09:08.660 --> 00:09:11.810
where society's welfare or
surplus includes the tax

00:09:11.810 --> 00:09:14.940
revenue?"

00:09:14.940 --> 00:09:19.050
So, what's basically happening
in this new case is we're

00:09:19.050 --> 00:09:21.630
going to start off with the same
sort of problem where the

00:09:21.630 --> 00:09:25.430
monopolist gets to decide how
much they're going to output.

00:09:25.430 --> 00:09:28.140
And we're interested in
the marginal cost and

00:09:28.140 --> 00:09:30.100
the marginal revenue.

00:09:30.100 --> 00:09:36.080
Now, the marginal revenue is
going to be represented by the

00:09:36.080 --> 00:09:39.460
same equation, and we're going
to substitute in for price the

00:09:39.460 --> 00:09:40.710
demand curve again.

00:09:45.610 --> 00:09:48.500
And when we solve through,
substituting in for the demand

00:09:48.500 --> 00:09:50.020
curve and taking the derivative,
we're going to

00:09:50.020 --> 00:09:58.060
find that the marginal revenue
is again going to be equal to

00:09:58.060 --> 00:10:02.810
24 minus 2Q.

00:10:02.810 --> 00:10:05.330
So the marginal revenue
hasn't changed at all.

00:10:05.330 --> 00:10:07.330
What is going to change is going
to be the total cost

00:10:07.330 --> 00:10:16.260
curve for the monopolist. So
this was the cost curve that

00:10:16.260 --> 00:10:19.670
we started off with, but now
for each unit Q that the

00:10:19.670 --> 00:10:22.680
monopolist produces, it's
going to be taxed

00:10:22.680 --> 00:10:24.790
at a rate of t.

00:10:24.790 --> 00:10:30.310
So we can add in the
cost of the tax.

00:10:30.310 --> 00:10:32.650
And in the next step, I'm going
to take the derivative

00:10:32.650 --> 00:10:37.160
with respect to Q, and I'm going
to substitute in for t

00:10:37.160 --> 00:10:39.950
the price of the tax, or 8.

00:10:39.950 --> 00:10:52.410
So now our new marginal cost
is equal to 2Q plus 8.

00:10:52.410 --> 00:10:54.200
And to solve for our new
equilibrium, we're just going

00:10:54.200 --> 00:10:59.100
to set marginal cost and
marginal revenue equal.

00:10:59.100 --> 00:11:00.370
And when we do that, we're
going to find that

00:11:00.370 --> 00:11:05.080
Q is equal to 4.

00:11:05.080 --> 00:11:17.960
And plugging into the demand
curve, you're going to find

00:11:17.960 --> 00:11:21.500
that the price is equal to 20.

00:11:21.500 --> 00:11:25.100
Now in this problem, you could
go through and you could go

00:11:25.100 --> 00:11:27.430
ahead and you could calculate
the consumer surplus, the

00:11:27.430 --> 00:11:30.220
producer surplus, the deadweight
loss and the tax

00:11:30.220 --> 00:11:33.510
revenue, and you could figure
out quantitatively how much

00:11:33.510 --> 00:11:34.560
they've changed.

00:11:34.560 --> 00:11:36.530
But we're just going to draw a
new graph, and we're going to

00:11:36.530 --> 00:11:39.710
look at the changes in consumer
surplus, producer

00:11:39.710 --> 00:11:43.110
surplus, and deadweight loss,
and make a qualitative

00:11:43.110 --> 00:11:47.770
assessment of how those
quantities have changed.

00:11:47.770 --> 00:11:55.130
So on a new axes, I'm going to
draw the old supply curve and

00:11:55.130 --> 00:11:56.380
the demand curve.

00:11:58.420 --> 00:12:01.060
Now, what's essentially
happening is, since the

00:12:01.060 --> 00:12:04.180
suppliers know for each unit
they're producing they're

00:12:04.180 --> 00:12:08.260
going to have to pay a tax
of 8, the supply curve is

00:12:08.260 --> 00:12:13.170
essentially shifting
up by 8 units.

00:12:13.170 --> 00:12:17.210
And I'm representing the new
supply curve with an s prime.

00:12:17.210 --> 00:12:20.800
So now, instead of the suppliers
making their

00:12:20.800 --> 00:12:23.250
monopolist decision based on
this supply curve and the

00:12:23.250 --> 00:12:26.680
demand curve, they're now
making it over here.

00:12:26.680 --> 00:12:28.860
And so what's going to happen is
they're going to have some

00:12:28.860 --> 00:12:31.690
new monopolist output.

00:12:31.690 --> 00:12:38.010
And in this case, we know the
new monopolist output is 4.

00:12:38.010 --> 00:12:41.800
We know that the new
monopolist price

00:12:41.800 --> 00:12:46.670
is going to be 20.

00:12:46.670 --> 00:12:51.780
And so we can see on this graph
that producer surplus is

00:12:51.780 --> 00:12:57.750
going to be represented
by this four-sided

00:12:57.750 --> 00:12:59.000
figure right here.

00:13:01.180 --> 00:13:03.960
We know that the tax revenue
is going to be-- since the

00:13:03.960 --> 00:13:08.130
distance from this point to this
point is 8, from 0 to 4--

00:13:08.130 --> 00:13:12.440
this is going to represent the
tax, this box right here.

00:13:14.980 --> 00:13:18.480
And we know that the consumer
surplus is going to be this

00:13:18.480 --> 00:13:23.270
small triangle up top.

00:13:23.270 --> 00:13:25.570
Meanwhile, the dead weight loss
is anything that's not

00:13:25.570 --> 00:13:28.340
represented that would have been
in our original producer

00:13:28.340 --> 00:13:30.850
surplus, plus consumer
surplus.

00:13:30.850 --> 00:13:36.410
So the deadweight loss is this
large triangle over here.

00:13:36.410 --> 00:13:39.670
So basically what's happened
is, compared to our initial

00:13:39.670 --> 00:13:43.950
case, the government's come
in and for society--

00:13:43.950 --> 00:13:45.910
since there's less
being produced--

00:13:45.910 --> 00:13:51.210
we've basically shifted
the monopolist

00:13:51.210 --> 00:13:53.430
quantity over to the left.

00:13:53.430 --> 00:13:57.590
This means that, overall, the
deadweight loss, this triangle

00:13:57.590 --> 00:14:01.120
over here, has increased
in size.

00:14:01.120 --> 00:14:06.620
So if the deadweight loss is
increasing, we can say that

00:14:06.620 --> 00:14:08.695
society is going to be worse
off in this situation.

00:14:11.700 --> 00:14:14.870
In another case, it's also clear
to see that the consumer

00:14:14.870 --> 00:14:18.760
surplus, since the consumers are
paying a higher price for

00:14:18.760 --> 00:14:22.980
a lower quantity, we can also
say that the consumer surplus

00:14:22.980 --> 00:14:24.230
is going to decrease.

00:14:26.940 --> 00:14:29.270
So we can safely say that the
consumers are going to be

00:14:29.270 --> 00:14:31.550
worse off as well.

00:14:31.550 --> 00:14:34.710
And then the last interpretation
is knowing that

00:14:34.710 --> 00:14:37.030
in the first case the producers
were allowed to make

00:14:37.030 --> 00:14:41.190
their production decision just
given the demand curve and

00:14:41.190 --> 00:14:43.350
their original supply curve.

00:14:43.350 --> 00:14:46.550
Now their production decision
also has to take into account

00:14:46.550 --> 00:14:49.150
the government taking away
some of their profits.

00:14:49.150 --> 00:14:51.500
If the government is taking
some away some of their

00:14:51.500 --> 00:14:56.230
profits, the producers
are necessarily going

00:14:56.230 --> 00:14:58.080
to have less surplus.

00:14:58.080 --> 00:15:01.200
So the producers are going
to be worse off as well.

00:15:01.200 --> 00:15:03.870
So overall, the only person
who might possibly benefit

00:15:03.870 --> 00:15:05.690
from this policy would
be the government.

00:15:05.690 --> 00:15:09.100
But overall, the producers, the
consumers, and society are

00:15:09.100 --> 00:15:12.180
going to be worse off.

00:15:12.180 --> 00:15:15.830
Now, the last part of this
problem is part C. And instead

00:15:15.830 --> 00:15:21.230
of implementing a tax on the per
unit production decision

00:15:21.230 --> 00:15:24.010
for the producers, now the
government's going to consider

00:15:24.010 --> 00:15:25.870
a different tax policy.

00:15:25.870 --> 00:15:29.170
Part C says "How does imposing
a tax on profits--

00:15:29.170 --> 00:15:32.600
profit after tax equals
1 minus t--

00:15:32.600 --> 00:15:36.930
affect the monopoly optimum, and
the welfare of consumers,

00:15:36.930 --> 00:15:40.440
the monopoly, and society?"

00:15:40.440 --> 00:15:43.660
Now basically, what's happening
in this situation is

00:15:43.660 --> 00:15:45.390
the government's going
to come in.

00:15:45.390 --> 00:15:47.800
And they're going to say all
right, after you've made your

00:15:47.800 --> 00:15:50.515
decision on how much to produce,
we're going to take a

00:15:50.515 --> 00:15:53.590
set percentage of the
producer's surplus.

00:15:53.590 --> 00:15:56.880
So if you get a producer's
surplus of this amount, then a

00:15:56.880 --> 00:16:04.870
certain chunk of it is going
to go to Uncle Sam at a tax

00:16:04.870 --> 00:16:09.150
percentage which we can
say is just x percent.

00:16:09.150 --> 00:16:13.520
Now that percentage of tax, it
doesn't change the fact that

00:16:13.520 --> 00:16:17.440
the producers want to have as
much surplus as possible.

00:16:17.440 --> 00:16:20.540
Just because they're going to
lose, say, 10% of it because

00:16:20.540 --> 00:16:23.010
of Uncle Sam, it's not actually
going to affect the

00:16:23.010 --> 00:16:25.120
fact that they want their
producer surplus to be as big

00:16:25.120 --> 00:16:26.530
as possible.

00:16:26.530 --> 00:16:29.340
So what happens in this
situation is that this after

00:16:29.340 --> 00:16:32.570
profit tax will not affect
the equilibrium at all.

00:16:32.570 --> 00:16:33.510
And we're going to
be left with the

00:16:33.510 --> 00:16:37.540
same consumer surplus.

00:16:37.540 --> 00:16:40.500
Producer surplus is going to be
lower because of the tax,

00:16:40.500 --> 00:16:42.710
but overall, society is going
to be left with the same

00:16:42.710 --> 00:16:44.510
social welfare.

00:16:44.510 --> 00:16:47.440
So really what this problem is
looking at through its three

00:16:47.440 --> 00:16:50.360
parts, we look at the monopolist
situation, and we

00:16:50.360 --> 00:16:54.910
look at how the government can
try to adjust with tax policy

00:16:54.910 --> 00:16:56.630
what's happening
in the market.

00:16:56.630 --> 00:17:00.710
And what we saw in our second
scenario is that when they

00:17:00.710 --> 00:17:04.839
charge a per unit tax on the
producers, societal welfare is

00:17:04.839 --> 00:17:06.119
going to go down.

00:17:06.119 --> 00:17:08.829
But in the third case, when
they're just taking a set

00:17:08.829 --> 00:17:14.069
percentage from the producer
surplus, the overall welfare

00:17:14.069 --> 00:17:16.930
for the society is going
to stay the same.

00:17:16.930 --> 00:17:20.890
So bundled in this problem we
had the monopolist situation,

00:17:20.890 --> 00:17:23.290
setting marginal cost equal
to marginal revenue.

00:17:23.290 --> 00:17:26.010
And we also looked at tax
implications on a per unit

00:17:26.010 --> 00:17:33.300
basis, and on a profit basis
with a set tax after the

00:17:33.300 --> 00:17:34.640
production decision is made.

00:17:34.640 --> 00:17:36.200
I hope you found this
problem helpful.