Office Hours: The Solow Model
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0:00 - 0:03music
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0:03 - 0:04As I reviewed the data online
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0:04 - 0:06I talked to ton of college students
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0:06 - 0:09everyone is missing with this one question
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0:09 - 0:10it's time to make a video.
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0:10 - 0:15music
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0:15 - 0:18Today, we are going to solve
the following problems -
0:18 - 0:21from our video on the Solow Models steady state.
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0:21 - 0:23country A produces GDP according to
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0:23 - 0:28the following equation:
GDP=5√K -
0:28 - 0:30and has a capital stock of 10,000.
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0:30 - 0:35If the country devotes 25%of its GDP
to making investment goods, -
0:35 - 0:38how much is this country investing?
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0:38 - 0:42Additionally, if 1% of all Capital
depreciates every year, -
0:42 - 0:45is the country's GDP increasing,decreasing
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0:45 - 0:48or remaining constant
in that steady state? -
0:48 - 0:51As always,
it's best to watch the video first. -
0:51 - 0:54and try to solve this problem by yourself.
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0:54 - 0:56If you have remaining questions,
you can always return, -
0:56 - 0:59and we'll work through the problem together.
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0:59 - 1:02Ready? This question has two parts.
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1:02 - 1:05First, finding how much this country 's investing,
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1:05 - 1:08and second, to determine weather or not
its GDP is growing. -
1:08 - 1:10Fortunately,
that the first question -
1:10 - 1:14is actually a necessary step
for solving the second one. -
1:14 - 1:17First thing first.
The relevant information from that problem -
1:17 - 1:21is on the top of left hand corner
of the board for reference -
1:21 - 1:26As always, it's best way for identifying the steps
for solving the problem. -
1:26 - 1:29The first of two questions is very straight forward
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1:29 - 1:33simply derived investment (I) 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,
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1:40 - 1:42We'll need our answer from question one.
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1:42 - 1:46The amount of capital were accumulating
through investment -
1:46 - 1:50Then find out how much the capital
were losing to the appreciation. -
1:50 - 1:54and finally we compare the two,
investment to the depreciation. -
1:54 - 1:56to determine weather
the country's capital stock, -
1:56 - 2:00and therefore it's GDP is increasing,
decreasing, -
2:00 - 2:03or remaining constant
in the steady state? -
2:03 - 2:05Let's look a bit more in depth of
this problem by graphing it. -
2:05 - 2:09As you can see,
GDP is measured on the y-axis -
2:09 - 2:11In previous Solow questions
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2:11 - 2:15You may have seen this label does.
Total output 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 5√K
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2:23 - 2:26and we actually already graphed it.
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2:26 - 2:29This equation shows that GDP is function of K
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2:29 - 2:32As K increases? GDP also increases.
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2:32 - 2:35Although it by a small amount.
because a lot diminishing returns -
2:35 - 2:38It's also worth noting
that we are actually holding -
2:38 - 2:41other variables could affect GDP constantly.
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2:41 - 2:44Things like education, or population,
and ideas -
2:44 - 2:49So increase 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 5√K
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3:02 - 3:06and we also know the Investment is
25% of GDP, -
3:07 - 3:12therefore, we can substitute 5√K in for GDP.
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3:18 - 3:20And that's it, for step one.
To take a short cut, -
3:20 - 3:24since we know GDP's
in this instance is 500 -
3:24 - 3:2825%of 500 is 125.
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3:28 - 3:32This country is investing 125 dollars into
capital accumulation. -
3:32 - 3:36and that's the answer to step 2
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3:36 - 3:38A few quick things to know here
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3:38 - 3:41Several variables actually
measured along Y-axis. -
3:41 - 3:44Not just GDP,
but we're also measuring investment, -
3:44 - 3:47and eventually,
we are going to add depreciation. -
3:47 - 3:51In general, it looked pretty cluttered,
if we added all these labels up to the top. -
3:51 - 3:53so we just leave it as GDP
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3:53 - 3:57And one other thing to know,
if we investing 125, -
3:57 - 4:02and total GDP is 500,
what's happened to that remaining GDP? -
4:02 - 4:05It's been used for consumption.
You know, buying staff. -
4:05 - 4:07One of the following questions
at the end of this video -
4:07 - 4:10actually testing understanding this.
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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 stock overall -
4:17 - 4:20is increasing, decreasing,
or remaining constant. -
4:20 - 4:24because we don't know how much
the capital stock is wearing down, -
4:24 - 4:26or depreciating.
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4:26 - 4:30In a real world,
machine's break, laptops die. -
4:30 - 4:32Think physical capital in your own life,
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4:32 - 4:35how many times you've dropped iPhone?
and have to get a new one. -
4:35 - 4:39or how often you displeased your old phone,
even though it's still worked. -
4:39 - 4:44So even though Capital is been added
to stock of 10,000 through investment, -
4:44 - 4:47some of these 10,000
is also been lost to depreciation, -
4:47 - 4:49to those iPhone's dropping.
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4:49 - 4:52It helps to graph the depreciation.
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4:52 - 4:55We know from the initial problem,
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4:55 - 4:58that 1% of all Capital stock is depreciating.
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4:58 - 5:03Graphically, 1%K can be represented
roughly like this. -
5:03 - 5:07If capital stock is 10,000,
So 1% of 10,000 is 100. -
5:07 - 5:10So, 100 dollars worth of Capital stock
is wearing down, -
5:10 - 5:15or depreciating each year.
We 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 invest 125 worth of capital,
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5:22 - 5:25and loses 100 to depreciation,
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5:25 - 5:30and investment
is greater than depreciation, -
5:30 - 5:34and therefore, the capital stock
will grow by 25 this year. -
5:34 - 5:37As represented by the difference
between these two curves. -
5:37 - 5:41We can now answer that final question.
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5:41 - 5:43The country's capital stock is increasing,
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5:43 - 5:48and therefore, so too is GDP.
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5:48 - 5:53And that's our answer.
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5:53 - 5:56Because remember, according the equation
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5:56 - 5:58increase in K, increases GDP.
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5:58 - 6:01As long as investment
is greater than depreciation -
6:01 - 6:07K and GDP will continue to increase
until Country's capital investment -
6:07 - 6:09equals depreciation.
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6:09 - 6:11At this point, it reaches steady state
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6:11 - 6:14Because capital gain through investment
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6:14 - 6:18is perfectly offset
to capital lost from depreciation. -
6:18 - 6:23And therefore, neither the Capital stock
nor GDP changes at this point. -
6:23 - 6:26As always, please let us know everything
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6:26 - 6:28if you like to have additional practice,
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6:28 - 6:31We include some extra questions on Solow
and steady state in this video. -
6:31 - 6:38Music
- Title:
- Office Hours: The Solow Model
- Description:
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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
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