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music
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As I reviewed the data online
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I talked to ton of college students
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everyone is missing with this one question
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it's time to make the video.
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today we are going to solve the following problems
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from our video on the Solow models steady state.
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country A produces GDP according to
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the following equation:
GDP=5K .
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and has a capital stock of 10,000
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if the country devotes 25%of its GDP
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to making investment goods,
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how much is this country investing?
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Additionally if 1% of all Capital depreciates
every years
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is the country's GDP increasing,decreasing
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or remaining constant- in that steady state?
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As always, it's best to watch the video first.
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and try to solve this problem by yourself.
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if you have remaining questions,
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you may always return, and we can
work out this question together.
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Ready, this question has two parts
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First finding how much this country 's investing
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And second is determine whether or not
its GDP is growing.
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Fortunately, that the first question is actually
a necessary step
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for solving the second one
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First things first,
the relevant information from that problem
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is on the top of left hand corner of the board
for reference
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As always, it's best way for identifying the steps
for solving the problem.
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The first of two questions is very straight forward
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simply derived investment (I)from
the GDP equation
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and then solve for I given the current capital
stock for 10,000
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To solve the second question
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We'll need our answer from question one.
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The amount of capital were accumulating
through the investment
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Then find out how much the capital
were losing to the appreciation.
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and finally we compare the two,
investment to the depreciation.
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to determine wether the country's capital stock,
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and therefore it's GDP is increasing,
decreasing, or remain constant
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In the steady state?
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let's look a bit more in depth at this problem
by graphing it.
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As you can see,
GDP is measured on the y-axis
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In previous Solow questions
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You may have seen this label does.
Total output Y instead of GDP
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and K, Physical Capital
is measured on the X-axis
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We know this country's GDP is 5K
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and we actually already graphed it
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this equation shows GDP is function of K
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as K increases? GDP always increases.
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although it by small amount.
because a lot diminished amounts
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it's also worth noting
other variables could affect GDP constant
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these like education, populations idea
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so increase capital
is the only way this country's GDP grows
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in our example,
this country has 10,000 GDP capital
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if we plug that into equation
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GDP is 500.
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Now we know GDP is 500 time square root of K
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and we also know the Investment is
25% of GDP
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therefore, we substitute 5K in GDP
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and that's it for step one.
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To take a short cut, since we know GDP's
in this instance is 500
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25%of 500 is 125
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this country is investing 125 dollars into
capital accumulation
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and that's the answer to step 2
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a few quick things to know here
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several variables actually measured along Y-axis
not just GDP
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but we also measured investment
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and eventually we are going to add depreciation
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In general it looked very clever if we
added all these labels to the GDP
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so we just leave it as GDP
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and one other thing to know
if we investing for 125
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and total GDP is 500,
Then what's happened to that remaining GDP?
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It's been used for consumption.
You know, buying staff.
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one of the following question
at the end of this video
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actually testing understand this.
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So while this country is accumulating 125
worth of capital
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We don't yet know if the country's stock overall
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is increasing decreasing or remain constantly.
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because we don't know how much
the capital stock is wearing down,
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or depreciating.
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in a real world, machine's break, lap top dye
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think physical capital in your life,
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how many times you've dropped iPhone?
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and have to get a new one.
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or how often you displeased your phone,
even if it;s still worked.
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So even though capital is been added
to stock 10,000 through investment,
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some of these 10,000 is also lost to depreciation .
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to those iPhone's dropping.
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it helps graph the depreciation.
we know from the initial problem.
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1% of all stock is depreciation
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Graphically, 1% times K can be represent
roughly like this
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If capital stock is 10,000,
So 1% of 10,000 is 100.
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So 100 dollars worth of stock is wearing down
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or depreciating each year
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we now solved for step 3
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We now have investment or depreciation
and compare the two,
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if country invest 125 worth of capital,
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and lose the 100 to depreciation
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and investment is greater than depreciation,
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and therefore the capital stock
will grow by 25 this year.
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As represent by the difference
between these two curves.
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We can now answer that final question.
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The country's capital stock is increasing,
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and therefore is so too, GDP.
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And that's our answer.
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because remember, according the equation
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Increase in K, increase in GDP.
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As long as investment is greater than depreciation
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K and GDP will continue to increase.
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Until Country's capital investment growth equals
depreciation.
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At this point, it reaches steady state
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Because capital gain through investment
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is perfectly offset to capital lost from depreciation
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and therefore,Neither the Capital stock
nor GDP changes at this point.
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As always please let us know if you need
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if you want to have additional practice,
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we include some extra questions on Solow
and study guide in this video
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