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Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.40,0:00:04.14,Default,,0000,0000,0000,,♪ [music] ♪
Dialogue: 0,0:00:13.42,0:00:15.89,Default,,0000,0000,0000,,- [Alex] In our last video, \Nwe introduced the variables
Dialogue: 0,0:00:15.94,0:00:18.72,Default,,0000,0000,0000,,in our Super Simple Solow Model.
Dialogue: 0,0:00:18.72,0:00:21.66,Default,,0000,0000,0000,,We have physical capital, \Nrepresented by "K,"
Dialogue: 0,0:00:21.66,0:00:25.45,Default,,0000,0000,0000,,human capital, represented by "e" \Ntimes "L," and ideas,
Dialogue: 0,0:00:25.53,0:00:27.11,Default,,0000,0000,0000,,represented by "A."
Dialogue: 0,0:00:27.61,0:00:32.54,Default,,0000,0000,0000,,In this video, we're going to hold \Nhuman capital and ideas constant.
Dialogue: 0,0:00:32.88,0:00:38.45,Default,,0000,0000,0000,,That will let us focus in on K\Nso we can show what happens
Dialogue: 0,0:00:38.45,0:00:42.35,Default,,0000,0000,0000,,to output when the amount \Nof physical capital changes.
Dialogue: 0,0:00:42.83,0:00:47.30,Default,,0000,0000,0000,,Since capital is the only input, \Noutput is a function
Dialogue: 0,0:00:47.30,0:00:49.73,Default,,0000,0000,0000,,just of the quantity of capital.
Dialogue: 0,0:00:49.96,0:00:52.67,Default,,0000,0000,0000,,Let's write output \Nwith the letter "Y."
Dialogue: 0,0:00:52.94,0:00:55.69,Default,,0000,0000,0000,,Then we can say that Y is \Na function of K.
Dialogue: 0,0:00:55.78,0:00:58.14,Default,,0000,0000,0000,,Output is a function \Nof the quantity of capital.
Dialogue: 0,0:00:58.50,0:01:01.41,Default,,0000,0000,0000,,What properties should \Nour production function have?
Dialogue: 0,0:01:01.41,0:01:05.32,Default,,0000,0000,0000,,First, it makes sense \Nthat more K increases output.
Dialogue: 0,0:01:05.59,0:01:08.33,Default,,0000,0000,0000,,Recall from our earlier\Nvideo, our farmer.
Dialogue: 0,0:01:08.43,0:01:11.50,Default,,0000,0000,0000,,A farmer with a tractor can \Nproduce a lot more output
Dialogue: 0,0:01:11.50,0:01:13.47,Default,,0000,0000,0000,,than a farmer with just a shovel.
Dialogue: 0,0:01:13.47,0:01:17.15,Default,,0000,0000,0000,,Similarly, a farmer with two \Ntractors can produce more output
Dialogue: 0,0:01:17.15,0:01:19.63,Default,,0000,0000,0000,,than a farmer with just one tractor.
Dialogue: 0,0:01:20.73,0:01:23.48,Default,,0000,0000,0000,,If we graph capital \Non the horizontal axis
Dialogue: 0,0:01:23.48,0:01:26.28,Default,,0000,0000,0000,,and output on the vertical axis,
Dialogue: 0,0:01:26.28,0:01:28.37,Default,,0000,0000,0000,,we're going to see \Na positive relationship.
Dialogue: 0,0:01:28.66,0:01:32.03,Default,,0000,0000,0000,,As capital goes up, \Noutput goes up.
Dialogue: 0,0:01:32.03,0:01:33.91,Default,,0000,0000,0000,,That seems pretty straightforward.
Dialogue: 0,0:01:34.84,0:01:37.18,Default,,0000,0000,0000,,The second property \Nour production function
Dialogue: 0,0:01:37.18,0:01:39.68,Default,,0000,0000,0000,,should have is \Nthat while more capital
Dialogue: 0,0:01:39.68,0:01:42.45,Default,,0000,0000,0000,,produces more output,\Nit should do so
Dialogue: 0,0:01:42.45,0:01:46.92,Default,,0000,0000,0000,,at a diminishing rate.\NWhat do I mean by that?
Dialogue: 0,0:01:46.94,0:01:48.76,Default,,0000,0000,0000,,Let's go back to our farmer.
Dialogue: 0,0:01:49.10,0:01:51.88,Default,,0000,0000,0000,,The first tractor he gets is\Nthe most productive.
Dialogue: 0,0:01:52.21,0:01:53.96,Default,,0000,0000,0000,,It helps him grow \Na lot more wheat.
Dialogue: 0,0:01:54.20,0:01:58.14,Default,,0000,0000,0000,,The second tractor he might use if \Nthe first tractor -- it breaks down.
Dialogue: 0,0:01:58.37,0:02:02.10,Default,,0000,0000,0000,,So the second tractor is \Nless productive than the first.
Dialogue: 0,0:02:02.78,0:02:06.14,Default,,0000,0000,0000,,The third tractor is maybe just \Na spare in case both break down.
Dialogue: 0,0:02:06.50,0:02:10.14,Default,,0000,0000,0000,,So the third tractor will boost \Nhis output even less
Dialogue: 0,0:02:10.22,0:02:11.73,Default,,0000,0000,0000,,than did the second.
Dialogue: 0,0:02:12.50,0:02:17.12,Default,,0000,0000,0000,,Said another way, the farmer will \Nallocate his tractors
Dialogue: 0,0:02:17.12,0:02:20.03,Default,,0000,0000,0000,,so that the first tractor, \Nhe's going to allocate
Dialogue: 0,0:02:20.03,0:02:23.33,Default,,0000,0000,0000,,to the most important, \Nthe most productive task.
Dialogue: 0,0:02:23.93,0:02:28.28,Default,,0000,0000,0000,,Meaning that subsequent tractors --\Nthe farmer will allocate them
Dialogue: 0,0:02:28.28,0:02:31.38,Default,,0000,0000,0000,,to less and less productive tasks.
Dialogue: 0,0:02:32.09,0:02:37.85,Default,,0000,0000,0000,,We call this the Iron Logic \Nof Diminishing Returns.
Dialogue: 0,0:02:39.24,0:02:41.52,Default,,0000,0000,0000,,To represent both \Nof these properties,
Dialogue: 0,0:02:41.52,0:02:43.66,Default,,0000,0000,0000,,we can use a simple \Nproduction function,
Dialogue: 0,0:02:43.66,0:02:47.14,Default,,0000,0000,0000,,one which we're already familiar\Nwith: the square root function.
Dialogue: 0,0:02:47.43,0:02:51.92,Default,,0000,0000,0000,,Output equals the square root \Nof the capital inputs.
Dialogue: 0,0:02:51.98,0:02:54.82,Default,,0000,0000,0000,,So if we input 1 unit of capital, \Noutput is 1.
Dialogue: 0,0:02:54.99,0:02:58.49,Default,,0000,0000,0000,,If we input 4 units of capital, \Noutput is 2.
Dialogue: 0,0:02:58.91,0:03:04.22,Default,,0000,0000,0000,,If we input 9 units of capital, \Noutput is… 3.
Dialogue: 0,0:03:05.10,0:03:08.92,Default,,0000,0000,0000,,The marginal product \Nof capital describes how much
Dialogue: 0,0:03:08.92,0:03:13.79,Default,,0000,0000,0000,,additional output is produced \Nwith each additional unit
Dialogue: 0,0:03:13.79,0:03:14.96,Default,,0000,0000,0000,,of capital.
Dialogue: 0,0:03:15.94,0:03:19.21,Default,,0000,0000,0000,,Notice that the marginal product\Nof the first unit of capital
Dialogue: 0,0:03:19.21,0:03:20.57,Default,,0000,0000,0000,,is really high.
Dialogue: 0,0:03:20.78,0:03:26.03,Default,,0000,0000,0000,,But as the capital stock grows, \Nthe marginal product of capital
Dialogue: 0,0:03:26.03,0:03:30.96,Default,,0000,0000,0000,,is less and less and less.
Dialogue: 0,0:03:31.43,0:03:34.53,Default,,0000,0000,0000,,Already, we can explain \None of our puzzles.
Dialogue: 0,0:03:34.85,0:03:38.59,Default,,0000,0000,0000,,Recall that growth was fast \Nin Germany and Japan
Dialogue: 0,0:03:38.59,0:03:40.03,Default,,0000,0000,0000,,after World War II.
Dialogue: 0,0:03:40.31,0:03:42.80,Default,,0000,0000,0000,,That makes sense, \Nbecause after the war,
Dialogue: 0,0:03:42.80,0:03:45.03,Default,,0000,0000,0000,,those countries -- they \Ndidn't have a lot of capital.
Dialogue: 0,0:03:45.17,0:03:49.04,Default,,0000,0000,0000,,So that meant that the first units \Nof capital had a very high
Dialogue: 0,0:03:49.04,0:03:52.74,Default,,0000,0000,0000,,marginal product. \NThe first road between two cities
Dialogue: 0,0:03:52.74,0:03:56.64,Default,,0000,0000,0000,,or the first tractor on a farm, \Nor the first new steel factory --
Dialogue: 0,0:03:56.95,0:03:59.76,Default,,0000,0000,0000,,that gets you a lot \Nof additional output.
Dialogue: 0,0:04:00.30,0:04:04.06,Default,,0000,0000,0000,,Capital's very productive \Nwhen you don't have a lot of it.
Dialogue: 0,0:04:04.46,0:04:08.68,Default,,0000,0000,0000,,But don't forget that Germany \Nand Japan were growing
Dialogue: 0,0:04:08.68,0:04:10.30,Default,,0000,0000,0000,,from a low base.
Dialogue: 0,0:04:10.64,0:04:12.98,Default,,0000,0000,0000,,You can grow fast \Nwhen you don't have a lot,
Dialogue: 0,0:04:13.03,0:04:15.87,Default,,0000,0000,0000,,but all else being the same, \Nyou'd rather have more
Dialogue: 0,0:04:15.87,0:04:17.44,Default,,0000,0000,0000,,and grow slower.
Dialogue: 0,0:04:17.71,0:04:22.86,Default,,0000,0000,0000,,So, capital can drive growth, \Nbut because of the iron logic
Dialogue: 0,0:04:22.86,0:04:25.92,Default,,0000,0000,0000,,of diminishing returns, \Nthe same additions
Dialogue: 0,0:04:25.99,0:04:29.64,Default,,0000,0000,0000,,to the capital stock may get \Nyou less and less output.
Dialogue: 0,0:04:30.36,0:04:34.97,Default,,0000,0000,0000,,Unfortunately for K, \Nin the next video we'll show
Dialogue: 0,0:04:34.97,0:04:37.83,Default,,0000,0000,0000,,that capital has another\Nproblem to deal with.
Dialogue: 0,0:04:38.37,0:04:42.10,Default,,0000,0000,0000,,- [Announcer] If you want to test \Nyourself, click “Practice Questions.”
Dialogue: 0,0:04:42.10,0:04:46.42,Default,,0000,0000,0000,,Or, if you're ready to move on, you \Ncan click “Go to the Next Video.”
Dialogue: 0,0:04:47.24,0:04:49.43,Default,,0000,0000,0000,,♪ [music] ♪
Dialogue: 0,0:04:49.63,0:04:53.56,Default,,0000,0000,0000,,You can also visit MRUniversity.com \Nto see our entire library
Dialogue: 0,0:04:53.56,0:04:55.22,Default,,0000,0000,0000,,of videos and resources.
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