Office Hours: The Solow Model
-
0:00 - 0:02♪ (music) ♪
-
0:03 - 0:06[Mary Clare] I've reviewed the data online.
I talked to ton of college students. -
0:06 - 0:09Everyone is missing this one question.
-
0:09 - 0:10It's time to make a video.
-
0:11 - 0:12♪ (music) ♪
-
0:15 - 0:18Today, we're gonna solve
the following problem from our video -
0:18 - 0:21on the Solow Model's steady state.
-
0:21 - 0:25Country A produces GDP
according to the following equation: -
0:25 - 0:28GDP equals five times the square root of K
-
0:28 - 0:30and has a capital stock of 10,000.
-
0:30 - 0:35If the country devotes 25% of its GDP
to making investment goods, -
0:35 - 0:38how much is this country investing?
-
0:38 - 0:42Additionally, if 1% of all capital
depreciates every year, -
0:42 - 0:44is the country's GDP increasing,
-
0:44 - 0:48decreasing, or remaining constant
in that steady state? -
0:48 - 0:51As always,
it's best to watch the video first -
0:51 - 0:53and try to solve this problem by yourself.
-
0:53 - 0:56If you have remaining questions,
you can always return, -
0:56 - 0:58and we'll work through
the problem together. -
0:58 - 1:01Ready? This question has two parts.
-
1:01 - 1:05First, finding how much
this country is investing, -
1:05 - 1:08and second, determining
whether or not its GDP is growing. -
1:08 - 1:10Fortunately, that first question
-
1:10 - 1:13is actually a necessary step
for solving the second one. -
1:14 - 1:15First things first.
-
1:15 - 1:17The relevant information from the problem
-
1:17 - 1:21is in that top right-hand corner
of the board for reference. -
1:21 - 1:25As always, it's best to identify steps
for solving the problem. -
1:26 - 1:29The first of the two questions
is fairly straightforward. -
1:29 - 1:33Simply derive the investment equation
from the GDP equation -
1:33 - 1:38and then solve for I, given the current
capital stock of 10,000. -
1:38 - 1:40To solve the second question,
-
1:40 - 1:42we'll need our answer from question one:
-
1:42 - 1:46the amount of capital we're accumulating
through investment. -
1:46 - 1:50We'll then find out how much capital
we're losing to depreciation, -
1:50 - 1:54and finally we'll compare the two,
investment to depreciation -
1:54 - 1:56to determine whether
the country's capital stock, -
1:56 - 2:00and therefore its GDP,
is increasing, decreasing, -
2:00 - 2:02or remaining constant
in the steady state. -
2:03 - 2:06Let's look a bit more in depth
at this problem by graphing it. -
2:06 - 2:09As you can see,
GDP is measured on the y-axis. -
2:09 - 2:11In previous Solow questions,
-
2:11 - 2:15you may have seen this labeled as
total output or Y instead of GDP. -
2:15 - 2:19And K, physical capital,
is measured on the x-axis -
2:19 - 2:23We know that this country's GDP is
five times the square root of K, -
2:23 - 2:26and we've actually already graphed it.
-
2:26 - 2:29This equation shows that GDP
is a function of K. -
2:29 - 2:32As K increases, GDP also increases,
-
2:32 - 2:36albeit by a smaller amount because
of the law of diminishing returns. -
2:36 - 2:38It's also worth noting
that we're actually holding -
2:38 - 2:41other variables that could affect
GDP constant. -
2:41 - 2:44Things like education,
or population, and ideas. -
2:44 - 2:49So increasing capital is the only way
this country's GDP grows. -
2:49 - 2:53In our example, this country
has $10,000 dollars worth of capital. -
2:53 - 2:57If we plug that into equation,
GDP is 500. -
2:59 - 3:02Now we know that GDP is
five times the square root of K. -
3:02 - 3:06And we also know that Investment
is 25% of GDP, -
3:07 - 3:13therefore, we can substitute five
times the square root of K in for GDP. -
3:18 - 3:20And that's it, for step one.
-
3:20 - 3:21To take a short cut,
-
3:21 - 3:28since we know GDP in this instance is 500,
25% of 500 is 125. -
3:28 - 3:32This country is investing $125 dollars
into capital accumulation. -
3:32 - 3:36And that's the answer to step two.
-
3:36 - 3:38A few quick things to note here.
-
3:38 - 3:41Several variables are actually
measured along the y-axis. -
3:41 - 3:44Not just GDP,
but we're also measuring investment, -
3:44 - 3:46and eventually
we're going to add depreciation. -
3:46 - 3:48In general, it looks pretty cluttered
-
3:48 - 3:51if we were to add all of those labels
up to the top. -
3:51 - 3:53So we'll just leave it at GDP.
-
3:53 - 3:57And one other thing to note:
if we're investing 125, -
3:57 - 4:02and total GDP is 500,
what's happened to that remaining GDP? -
4:02 - 4:05It's being used for consumption,
you know, buying stuff. -
4:05 - 4:07One of the follow-up questions
at the end of this video -
4:07 - 4:10actually tests your understanding of this.
-
4:10 - 4:14So while this country is accumulating
125 worth of capital, -
4:14 - 4:17we don't yet know
if the country's capital stock overall -
4:17 - 4:20is increasing, decreasing,
or remaining constant, -
4:20 - 4:24because we don't know how much
of the capital stock is wearing down, -
4:24 - 4:26or depreciating.
-
4:26 - 4:30In the real world,
machines break, laptops die. -
4:30 - 4:32Think of physical capital
in your own life. -
4:32 - 4:35How many times have you dropped
your iPhone and had to get a new one? -
4:35 - 4:39Or how often have you replaced
an old phone, even though it still worked. -
4:39 - 4:44So even though capital is being added
to the stock of 10,000 through investment, -
4:44 - 4:48some of this 10,000
is also being lost to depreciation, -
4:48 - 4:49to those iPhones dropping.
-
4:49 - 4:52It helps to graph depreciation.
-
4:52 - 4:54We know from the initial problem
-
4:54 - 4:57that 1% of all capital stock
is depreciating. -
4:57 - 5:03Graphically, 1% times K
can be represented roughly like this: -
5:03 - 5:07If capital stock is 10,000,
1% of 10,000 is 100. -
5:07 - 5:10So, 100 dollars worth of capital stock
is wearing down, -
5:10 - 5:11or depreciating, each year.
-
5:11 - 5:15We've now solved for step 3.
-
5:15 - 5:19We now have investment and depreciation,
and can compare the two. -
5:19 - 5:22If the country invests
125 worth of capital, -
5:22 - 5:25and loses 100 to depreciation,
-
5:25 - 5:30then investment
is greater than depreciation, -
5:31 - 5:34and therefore, the capital stock
will grow by 25 this year, -
5:34 - 5:37as represented by the difference
between these two curves. -
5:38 - 5:41We can now answer that final question.
-
5:41 - 5:43The country's capital stock is increasing,
-
5:43 - 5:47and therefore, so too is GDP.
-
5:49 - 5:52And that's our answer.
-
5:53 - 5:55Because remember,
according to the equation -
5:55 - 5:58increases in K, increase GDP.
-
5:58 - 6:01As long as investment
is greater than depreciation -
6:01 - 6:04K and GDP will continue to increase
-
6:04 - 6:09until the country's capital investment
equals depreciation. -
6:09 - 6:13At this point, it reaches steady state
because capital gain through investment -
6:13 - 6:18is perfectly offset
to capital lost from depreciation. -
6:18 - 6:22And therefore, neither the capital stock
nor GDP changes at this point. -
6:23 - 6:25As always, please let us know
what you think. -
6:25 - 6:27And if you'd like to have
some additional practice, -
6:27 - 6:30we've included some extra questions
on Solow and steady state -
6:30 - 6:32at the end of this video.
-
6:32 - 6:34♪ (music) ♪
- Title:
- Office Hours: The Solow Model
- Description:
-
In last week’s Principles of Macroeconomics video, you learned about the steady state level of capital and the Solow model of economic growth. Here are two of the practice questions from that video:
Country A has K=10,000 and produces GDP according to the following equation: GDP=5√K.
1) If the country devotes 25% of its GDP to making investment goods, how much is the country investing?
2) If 1% of all machines become worthless every year (they depreciate, in other words) in Country A, GDP is...?These are tricky problems! If you're stumped, don’t worry. Mary Clare Peate from the Marginal Revolution University team is here to help.
Are you struggling with a different practice problem or concept from an MRU video? Let us know! Head on over to our feedback forums to suggest a topic for a future "Office Hours" video: http://bit.ly/1psatWs
Additional practice questions: http://bit.ly/1SvNoP8
The Solow Model and the Steady State: http://bit.ly/1YGYiA3
- Video Language:
- English
- Team:
- Marginal Revolution University
- Project:
- Office Hours
- Duration:
- 06:39
MRU_Admin edited English subtitles for Office Hours: The Solow Model | ||
MRU_Admin edited English subtitles for Office Hours: The Solow Model | ||
Marilia_PM approved English subtitles for Office Hours: The Solow Model | ||
Tanya Higgins accepted English subtitles for Office Hours: The Solow Model | ||
Tanya Higgins edited English subtitles for Office Hours: The Solow Model | ||
Yuanqing Edberg edited English subtitles for Office Hours: The Solow Model | ||
Yuanqing Edberg edited English subtitles for Office Hours: The Solow Model | ||
Yuanqing Edberg edited English subtitles for Office Hours: The Solow Model |