Office Hours: The Solow Model

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As I reviewed the data online

I talked to ton of college students

everyone is missing with this one question

it's time to make the video.

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today we are going to solve the following problems

from our video on the Solow models steady state.

country A produces GDP according to

the following equation:
GDP=5K .

and has a capital stock of 10,000

if the country devotes 25%of its GDP

to making investment goods,

how much is this country investing?

Additionally if 1% of all Capital depreciates
every years

is the country's GDP increasing,decreasing

or remaining constant- in that steady state?

As always, it's best to watch the video first.

and try to solve this problem by yourself.

if you have remaining questions,

you may always return, and we can
work out this question together.

Ready, this question has two parts

First finding how much this country 's investing

And second is determine whether or not
its GDP is growing.

Fortunately, that the first question is actually
a necessary step

for solving the second one

First things first,
the relevant information from that problem

is on the top of left hand corner of the board
for reference

As always, it's best way for identifying the steps
for solving the problem.

The first of two questions is very straight forward

simply derived investment (I)from
the GDP equation

and then solve for I given the current capital
stock for 10,000

To solve the second question

We'll need our answer from question one.

The amount of capital were accumulating
through the investment

Then find out how much the capital
were losing to the appreciation.

and finally we compare the two,
investment to the depreciation.

to determine wether the country's capital stock,

and therefore it's GDP is decreasing?
increasing or remain constant

in the study state.

let's look at this problem in depth by
looking at this graph

as you can see

GDP is measure on the y-axis

in previous Solow questions

You may have seen this labeled
total output Y instead of GDP

and K, Physical Capital
is measured on the X-axis

We know this country's GDP is 5K

and we actually already graphed it

this equation shows GDP is function of K

as K increases? GDP always increases.

although it by small amount.
because a lot diminished amounts

it's also worth noting
other variables could affect GDP constant

these like education, populations idea

so increase capital
is the only way this country's GDP grows

in our example,
this country has 10,000 GDP capital

if we plug that into equation

GDP is 500.

Now we know GDP is 500 time square root of K

and we also know the Investment is
25% of GDP

therefore, we substitute 5K in GDP

and that's it for step one.

To take a short cut, since we know GDP's
in this instance is 500

25%of 500 is 125

this country is investing 125 dollars into
capital accumulation

and that's the answer to step 2

a few quick things to know here

several variables actually measured along Y-axis
not just GDP

but we also measured investment

and eventually we are going to add depreciation

In general it looked very clever if we
added all these labels to the GDP

so we just leave it as GDP

and one other thing to know
if we investing for 125

and total GDP is 500,
Then what's happened to that remaining GDP?

It's been used for consumption.
You know, buying staff.

one of the following question
at the end of this video

actually testing understand this.

So while this country is accumulating 125
worth of capital

We don't yet know if the country's stock overall

is increasing decreasing or remain constantly.

because we don't know how much
the capital stock is wearing down,

or depreciating.

in a real world, machine's break, lap top dye

think physical capital in your life,

how many times you've dropped iPhone?

and have to get a new one.

or how often you displeased your phone,
even if it;s still worked.

So even though capital is been added
to stock 10,000 through investment,

some of these 10,000 is also lost to depreciation .

to those iPhone's dropping.

it helps graph the depreciation.
we know from the initial problem.

1% of all stock is depreciation

Graphically, 1% times K can be represent
roughly like this

If capital stock is 10,000,
So 1% of 10,000 is 100.

So 100 dollars worth of stock is wearing down

or depreciating each year

we now solved for step 3

We now have investment or depreciation
and compare the two,

if country invest 125 worth of capital,

and lose the 100 to depreciation

and investment is greater than depreciation,

and therefore the capital stock
will grow by 25 this year.

As represent by the difference
between these two curves.

We can now answer that final question.

The country's capital stock is increasing,

and therefore is so too, GDP.

And that's our answer.

because remember, according the equation

Increase in K, increase in GDP.

As long as investment is greater than depreciation

K and GDP will continue to increase.

Until Country's capital investment growth equals
depreciation.

At this point, it reaches steady state

Because capital gain through investment

is perfectly offset to capital lost from depreciation

and therefore,Neither the Capital stock
nor GDP changes at this point.

As always please let us know if you need

if you want to have additional practice,

we include some extra questions on Solow
and study guide in this video

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