[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.69,0:00:03.46,Default,,0000,0000,0000,,What I want to start thinking\Nabout in this video is,
Dialogue: 0,0:00:03.46,0:00:06.29,Default,,0000,0000,0000,,given that we do have a\Nmonopoly on something,
Dialogue: 0,0:00:06.29,0:00:08.38,Default,,0000,0000,0000,,and in this example,\Nin this video,
Dialogue: 0,0:00:08.38,0:00:10.44,Default,,0000,0000,0000,,we're going to have a\Nmonopoly on oranges.
Dialogue: 0,0:00:10.44,0:00:12.41,Default,,0000,0000,0000,,Given that we have a\Nmonopoly on oranges
Dialogue: 0,0:00:12.41,0:00:16.36,Default,,0000,0000,0000,,and a demand curve for\Noranges in the market,
Dialogue: 0,0:00:16.36,0:00:18.19,Default,,0000,0000,0000,,how do we maximize our profit?
Dialogue: 0,0:00:18.19,0:00:19.61,Default,,0000,0000,0000,,And to answer that\Nquestion, we're
Dialogue: 0,0:00:19.61,0:00:21.19,Default,,0000,0000,0000,,going to think about\Nour total revenue
Dialogue: 0,0:00:21.19,0:00:23.01,Default,,0000,0000,0000,,for different quantities.
Dialogue: 0,0:00:23.01,0:00:24.84,Default,,0000,0000,0000,,And from that we'll get\Nthe marginal revenue
Dialogue: 0,0:00:24.84,0:00:25.98,Default,,0000,0000,0000,,for different quantities.
Dialogue: 0,0:00:25.98,0:00:28.50,Default,,0000,0000,0000,,And then we can compare that\Nto our marginal cost curve.
Dialogue: 0,0:00:28.50,0:00:30.29,Default,,0000,0000,0000,,And that should give\Nus a pretty good sense
Dialogue: 0,0:00:30.29,0:00:34.55,Default,,0000,0000,0000,,of what quantity we should\Nproduce to optimize things.
Dialogue: 0,0:00:34.55,0:00:37.26,Default,,0000,0000,0000,,So let's just figure\Nout total revenue first.
Dialogue: 0,0:00:37.26,0:00:39.01,Default,,0000,0000,0000,,So obviously, if\Nwe produce nothing,
Dialogue: 0,0:00:39.01,0:00:42.93,Default,,0000,0000,0000,,if we produces 0 quantity,\Nwe'll have nothing to sell.
Dialogue: 0,0:00:42.93,0:00:44.53,Default,,0000,0000,0000,,Total revenue is\Nprice times quantity.
Dialogue: 0,0:00:44.53,0:00:46.99,Default,,0000,0000,0000,,Your price is 6 but\Nyour quantity is 0.
Dialogue: 0,0:00:46.99,0:00:51.24,Default,,0000,0000,0000,,So your total revenue is going\Nto be 0 if you produce nothing.
Dialogue: 0,0:00:51.24,0:00:53.88,Default,,0000,0000,0000,,If you produce 1 unit--\Nand this over here
Dialogue: 0,0:00:53.88,0:00:55.88,Default,,0000,0000,0000,,is actually 1,000\Npounds per day.
Dialogue: 0,0:00:55.88,0:00:58.58,Default,,0000,0000,0000,,And we'll call a unit\N1,000 pounds per day.
Dialogue: 0,0:00:58.58,0:01:00.60,Default,,0000,0000,0000,,If you produce 1 unit,\Nthen your total revenue
Dialogue: 0,0:01:00.60,0:01:04.02,Default,,0000,0000,0000,,is 1 unit times $5 per pound.
Dialogue: 0,0:01:04.02,0:01:08.48,Default,,0000,0000,0000,,So it'll be $5 times, actually\N1,000, so it'll be $5,000.
Dialogue: 0,0:01:08.48,0:01:13.26,Default,,0000,0000,0000,,And you can also view it as\Nthe area right over here.
Dialogue: 0,0:01:13.26,0:01:17.20,Default,,0000,0000,0000,,You have the height is price\Nand the width is quantity.
Dialogue: 0,0:01:17.20,0:01:19.00,Default,,0000,0000,0000,,But we can plot that, 5 times 1.
Dialogue: 0,0:01:19.00,0:01:22.46,Default,,0000,0000,0000,,If you produce 1 unit,\Nyou're going to get $5,000.
Dialogue: 0,0:01:22.46,0:01:27.55,Default,,0000,0000,0000,,So this right over here\Nis in thousands of dollars
Dialogue: 0,0:01:27.55,0:01:29.88,Default,,0000,0000,0000,,and this right over here\Nis in thousands of pounds.
Dialogue: 0,0:01:33.17,0:01:35.46,Default,,0000,0000,0000,,Just to make sure that we're\Nconsistent with this right
Dialogue: 0,0:01:35.46,0:01:36.41,Default,,0000,0000,0000,,over here.
Dialogue: 0,0:01:36.41,0:01:37.34,Default,,0000,0000,0000,,Let's keep going.
Dialogue: 0,0:01:37.34,0:01:41.20,Default,,0000,0000,0000,,So that was this point, or\Nwhen we produce 1,000 pounds,
Dialogue: 0,0:01:41.20,0:01:43.16,Default,,0000,0000,0000,,we get $5,000.
Dialogue: 0,0:01:43.16,0:01:47.26,Default,,0000,0000,0000,,If we produce 2,000\Npounds, now we're
Dialogue: 0,0:01:47.26,0:01:50.79,Default,,0000,0000,0000,,talking about our price\Nis going to be $4.
Dialogue: 0,0:01:50.79,0:01:52.84,Default,,0000,0000,0000,,Or if we could say\Nour price is $4
Dialogue: 0,0:01:52.84,0:01:55.84,Default,,0000,0000,0000,,we can sell 2,000 pounds,\Ngiven this demand curve.
Dialogue: 0,0:01:55.84,0:01:57.34,Default,,0000,0000,0000,,And our total revenue\Nis going to be
Dialogue: 0,0:01:57.34,0:01:59.90,Default,,0000,0000,0000,,the area of this\Nrectangle right over here.
Dialogue: 0,0:01:59.90,0:02:02.05,Default,,0000,0000,0000,,Height is price,\Nwidth is quantity.
Dialogue: 0,0:02:02.05,0:02:03.96,Default,,0000,0000,0000,,4 times 2 is 8.
Dialogue: 0,0:02:03.96,0:02:06.64,Default,,0000,0000,0000,,So if I produce\N2,000 pounds then
Dialogue: 0,0:02:06.64,0:02:10.17,Default,,0000,0000,0000,,I will get a total\Nrevenue of $8,000.
Dialogue: 0,0:02:10.17,0:02:12.21,Default,,0000,0000,0000,,So this is 7 and 1/2,\N8 is going to put
Dialogue: 0,0:02:12.21,0:02:16.32,Default,,0000,0000,0000,,us something right about there.
Dialogue: 0,0:02:16.32,0:02:18.07,Default,,0000,0000,0000,,And then we can keep going.
Dialogue: 0,0:02:18.07,0:02:22.31,Default,,0000,0000,0000,,If I produce, or if the\Nprice is $3 per pound,
Dialogue: 0,0:02:22.31,0:02:24.65,Default,,0000,0000,0000,,I can sell 3,000 pounds.
Dialogue: 0,0:02:24.65,0:02:27.69,Default,,0000,0000,0000,,My total revenue is this\Nrectangle right over here,
Dialogue: 0,0:02:27.69,0:02:30.63,Default,,0000,0000,0000,,$3 times 3 is $9,000.
Dialogue: 0,0:02:30.63,0:02:32.92,Default,,0000,0000,0000,,So if I produce\N3,000 pounds, I can
Dialogue: 0,0:02:32.92,0:02:35.26,Default,,0000,0000,0000,,get a total revenue of $9,000.
Dialogue: 0,0:02:35.26,0:02:37.99,Default,,0000,0000,0000,,So right about there.
Dialogue: 0,0:02:37.99,0:02:39.68,Default,,0000,0000,0000,,And let's keep going.
Dialogue: 0,0:02:39.68,0:02:45.98,Default,,0000,0000,0000,,If I produce, or if the\Nprice, is $2 per pound,
Dialogue: 0,0:02:45.98,0:02:47.66,Default,,0000,0000,0000,,I can sell 4,000 pounds.
Dialogue: 0,0:02:47.66,0:02:51.83,Default,,0000,0000,0000,,My total revenue is $2\Ntimes 4, which is $8,000.
Dialogue: 0,0:02:51.83,0:02:54.33,Default,,0000,0000,0000,,So if I produce\N4,000 pounds I can
Dialogue: 0,0:02:54.33,0:02:55.98,Default,,0000,0000,0000,,get a total revenue of $8,000.
Dialogue: 0,0:02:55.98,0:02:59.66,Default,,0000,0000,0000,,It should be even with that\None right over there, just
Dialogue: 0,0:02:59.66,0:03:00.85,Default,,0000,0000,0000,,like that.
Dialogue: 0,0:03:00.85,0:03:13.40,Default,,0000,0000,0000,,And then if the price is $1 per\Npound I can sell 5,000 pounds.
Dialogue: 0,0:03:13.40,0:03:17.87,Default,,0000,0000,0000,,My total revenue is going\Nto be $1 times 5, or $5,000.
Dialogue: 0,0:03:17.87,0:03:19.88,Default,,0000,0000,0000,,So it's going to be\Neven with this here.
Dialogue: 0,0:03:19.88,0:03:24.56,Default,,0000,0000,0000,,So if I produce 5,000 units\NI can get $5,000 of revenue.
Dialogue: 0,0:03:24.56,0:03:27.70,Default,,0000,0000,0000,,And if the price\Nis 0, the market
Dialogue: 0,0:03:27.70,0:03:29.75,Default,,0000,0000,0000,,will demand 6,000 pounds\Nper day if it's free.
Dialogue: 0,0:03:29.75,0:03:31.96,Default,,0000,0000,0000,,But I'm not going to generate\Nany revenue because I'm
Dialogue: 0,0:03:31.96,0:03:33.94,Default,,0000,0000,0000,,going to be giving\Nit away for free.
Dialogue: 0,0:03:33.94,0:03:37.70,Default,,0000,0000,0000,,So I will not be generating\Nany revenue in this situation.
Dialogue: 0,0:03:37.70,0:03:40.24,Default,,0000,0000,0000,,So our total revenue curve,\Nit looks like-- and if you've
Dialogue: 0,0:03:40.24,0:03:41.82,Default,,0000,0000,0000,,taken algebra you\Nwould recognize this
Dialogue: 0,0:03:41.82,0:03:48.27,Default,,0000,0000,0000,,as a downward facing\Nparabola-- our total revenue
Dialogue: 0,0:03:48.27,0:03:51.38,Default,,0000,0000,0000,,looks like this.
Dialogue: 0,0:03:51.38,0:03:54.54,Default,,0000,0000,0000,,It's easier for me to draw\Na curve with a dotted line.
Dialogue: 0,0:03:54.54,0:03:58.45,Default,,0000,0000,0000,,Our total revenue looks\Nsomething like that.
Dialogue: 0,0:03:58.45,0:04:00.41,Default,,0000,0000,0000,,And you can even\Nsolve it algebraically
Dialogue: 0,0:04:00.41,0:04:03.36,Default,,0000,0000,0000,,to show that it is this\Ndownward facing parabola.
Dialogue: 0,0:04:03.36,0:04:07.12,Default,,0000,0000,0000,,The formula right over\Nhere of the demand curve,
Dialogue: 0,0:04:07.12,0:04:08.50,Default,,0000,0000,0000,,its y-intercept is 6.
Dialogue: 0,0:04:08.50,0:04:10.97,Default,,0000,0000,0000,,So if I wanted to write price\Nas a function of quantity
Dialogue: 0,0:04:10.97,0:04:16.48,Default,,0000,0000,0000,,we have price is equal\Nto 6 minus quantity.
Dialogue: 0,0:04:16.48,0:04:18.98,Default,,0000,0000,0000,,Or if you wanted to write in\Nthe traditional slope intercept
Dialogue: 0,0:04:18.98,0:04:22.75,Default,,0000,0000,0000,,form, or mx plus b form-- and\Nif that doesn't make any sense
Dialogue: 0,0:04:22.75,0:04:25.22,Default,,0000,0000,0000,,you might want to review some\Nof our algebra playlist--
Dialogue: 0,0:04:25.22,0:04:28.64,Default,,0000,0000,0000,,you could write it as p is\Nequal to negative q plus 6.
Dialogue: 0,0:04:28.64,0:04:30.83,Default,,0000,0000,0000,,Obviously these are\Nthe same exact thing.
Dialogue: 0,0:04:30.83,0:04:36.01,Default,,0000,0000,0000,,You have a y-intercept of\Nsix and you have a negative 1
Dialogue: 0,0:04:36.01,0:04:37.23,Default,,0000,0000,0000,,slope.
Dialogue: 0,0:04:37.23,0:04:40.90,Default,,0000,0000,0000,,If you increase quantity by\N1, you decrease price by 1.
Dialogue: 0,0:04:40.90,0:04:43.63,Default,,0000,0000,0000,,Or another way to think about\Nit, if you decrease price by 1
Dialogue: 0,0:04:43.63,0:04:45.82,Default,,0000,0000,0000,,you increase quantity by 1.
Dialogue: 0,0:04:45.82,0:04:48.34,Default,,0000,0000,0000,,So that's why you have\Na negative 1 slope.
Dialogue: 0,0:04:48.34,0:04:50.57,Default,,0000,0000,0000,,So this is price is a\Nfunction of quantity.
Dialogue: 0,0:04:50.57,0:04:52.08,Default,,0000,0000,0000,,What is total revenue?
Dialogue: 0,0:04:52.08,0:04:57.87,Default,,0000,0000,0000,,Well, total revenue is equal\Nto price times quantity.
Dialogue: 0,0:04:57.87,0:05:00.46,Default,,0000,0000,0000,,But we can write price as\Na function of quantity.
Dialogue: 0,0:05:00.46,0:05:01.41,Default,,0000,0000,0000,,We did it just now.
Dialogue: 0,0:05:01.41,0:05:02.93,Default,,0000,0000,0000,,This is what it is.
Dialogue: 0,0:05:02.93,0:05:06.99,Default,,0000,0000,0000,,So we can rewrite it, or we\Ncould even write it like this,
Dialogue: 0,0:05:06.99,0:05:09.51,Default,,0000,0000,0000,,we can rewrite the\Nprice part as-- so this
Dialogue: 0,0:05:09.51,0:05:14.28,Default,,0000,0000,0000,,is going to be equal to negative\Nq plus 6 times quantity.
Dialogue: 0,0:05:17.04,0:05:19.78,Default,,0000,0000,0000,,And this is equal\Nto total revenue.
Dialogue: 0,0:05:19.78,0:05:21.20,Default,,0000,0000,0000,,And then if you\Nmultiply this out,
Dialogue: 0,0:05:21.20,0:05:24.07,Default,,0000,0000,0000,,you get total\Nrevenue is equal to q
Dialogue: 0,0:05:24.07,0:05:30.01,Default,,0000,0000,0000,,times q is negative q\Nsquared plus 6 plus 6q.
Dialogue: 0,0:05:30.01,0:05:31.92,Default,,0000,0000,0000,,So you might recognize this.
Dialogue: 0,0:05:31.92,0:05:33.82,Default,,0000,0000,0000,,This is clearly a quadratic.
Dialogue: 0,0:05:33.82,0:05:38.06,Default,,0000,0000,0000,,Since you have a negative out\Nfront before the second degree
Dialogue: 0,0:05:38.06,0:05:39.92,Default,,0000,0000,0000,,term right over here,\Nbefore the q squared,
Dialogue: 0,0:05:39.92,0:05:42.12,Default,,0000,0000,0000,,it is a downward\Nopening parabola.
Dialogue: 0,0:05:42.12,0:05:44.30,Default,,0000,0000,0000,,So it makes complete sense.
Dialogue: 0,0:05:44.30,0:05:46.50,Default,,0000,0000,0000,,Now, I'm going to leave\Nyou there in this video.
Dialogue: 0,0:05:46.50,0:05:48.00,Default,,0000,0000,0000,,Because I'm trying\Nto make an effort
Dialogue: 0,0:05:48.00,0:05:50.02,Default,,0000,0000,0000,,not to make my videos too long.
Dialogue: 0,0:05:50.02,0:05:51.60,Default,,0000,0000,0000,,But in the next video\Nwhat we're going
Dialogue: 0,0:05:51.60,0:05:54.54,Default,,0000,0000,0000,,to think about is, what\Nis the marginal revenue we
Dialogue: 0,0:05:54.54,0:05:57.56,Default,,0000,0000,0000,,get for each of\Nthese quantities?
Dialogue: 0,0:05:57.56,0:06:03.61,Default,,0000,0000,0000,,And just as a review,\Nmarginal revenue
Dialogue: 0,0:06:03.61,0:06:08.82,Default,,0000,0000,0000,,is equal to change in\Ntotal revenue divided
Dialogue: 0,0:06:08.82,0:06:10.77,Default,,0000,0000,0000,,by change in quantity.
Dialogue: 0,0:06:10.77,0:06:13.22,Default,,0000,0000,0000,,Or another way to think about\Nit, the marginal revenue
Dialogue: 0,0:06:13.22,0:06:17.00,Default,,0000,0000,0000,,at any one of these\Nquantities is the slope
Dialogue: 0,0:06:17.00,0:06:18.61,Default,,0000,0000,0000,,of the line tangent\Nto that point.
Dialogue: 0,0:06:18.61,0:06:20.69,Default,,0000,0000,0000,,And you really have to do\Na little bit of calculus
Dialogue: 0,0:06:20.69,0:06:23.82,Default,,0000,0000,0000,,in order to actually calculate\Nslopes of tangent lines.
Dialogue: 0,0:06:23.82,0:06:26.35,Default,,0000,0000,0000,,But we'll approximate it\Nwith a little bit of algebra.
Dialogue: 0,0:06:26.35,0:06:28.49,Default,,0000,0000,0000,,But what we essentially want\Nto do is figure out the slope.
Dialogue: 0,0:06:28.49,0:06:31.03,Default,,0000,0000,0000,,So if we wanted to figure out\Nthe marginal revenue when we're
Dialogue: 0,0:06:31.03,0:06:34.08,Default,,0000,0000,0000,,selling 1,000 pounds--\Nso exactly how much more
Dialogue: 0,0:06:34.08,0:06:37.51,Default,,0000,0000,0000,,total revenue do we get if\Nwe just barely increase,
Dialogue: 0,0:06:37.51,0:06:40.42,Default,,0000,0000,0000,,if we just started selling\Nanother millionth of a pound
Dialogue: 0,0:06:40.42,0:06:42.48,Default,,0000,0000,0000,,of oranges-- what's\Ngoing to happen?
Dialogue: 0,0:06:42.48,0:06:44.06,Default,,0000,0000,0000,,And so what we do\Nis we're essentially
Dialogue: 0,0:06:44.06,0:06:47.27,Default,,0000,0000,0000,,trying to figure out the\Nslope of the tangent line
Dialogue: 0,0:06:47.27,0:06:49.36,Default,,0000,0000,0000,,at any point.
Dialogue: 0,0:06:49.36,0:06:50.23,Default,,0000,0000,0000,,And you can see that.
Dialogue: 0,0:06:50.23,0:06:53.82,Default,,0000,0000,0000,,Because the change\Nin total revenue
Dialogue: 0,0:06:53.82,0:07:00.75,Default,,0000,0000,0000,,is this and change in\Nquantity is that there.
Dialogue: 0,0:07:00.75,0:07:02.98,Default,,0000,0000,0000,,So we're trying to find\Nthe instantaneous slope
Dialogue: 0,0:07:02.98,0:07:04.60,Default,,0000,0000,0000,,at that point, or\Nyou could think of it
Dialogue: 0,0:07:04.60,0:07:07.19,Default,,0000,0000,0000,,as the slope of\Nthe tangent line.
Dialogue: 0,0:07:07.19,0:07:10.84,Default,,0000,0000,0000,,And we'll continue doing\Nthat in the next video.