Office Hours: The Solow Model: Investments vs. Ideas

This wk: Test yourself on Solow model and ideas with new Office Hours video!

Next wk: To spend or not to spend? That is, when it comes to government spending, which type of fiscal policy is best? You decide with next week’s Econ Duel video!

Ideas are a major factor in economic growth. But so are saving and investing. If you were given the choice between living in an inventive (more ideas) or a thrifty (more savings) country, which would you choose?

The Solow model of economic growth, which we recently covered in Principles of Macroeconomics, can help you make the choice. In this Office Hours video, Mary Clare Peate will use our simplified version of the Solow model to show you an easy way to work out each country’s economic prospects, and then compare them to see where you’d rather be.

Additional practice questions: http://bit.ly/1YcByds

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♪ (intro music) ♪

[Mary Clare] I've reviewed
the data online.

I've talked to a ton of college students.

Everyone is missing this one question.
It's time to make a video.

♪ (music) ♪

Today, we're going to take
a closer look at the Solow Model

by evaluating how different inputs
affect a country's economy.

Consider the following two Countries:
Inventive and Thrifty.

In Inventive, the country's economy grows

according to the following
production function:

gross domestic product equals
two times the square root of K,

and it devotes 25% of GDP
to making new investment goods.

Thrifty's production function is given
by GDP equals the square root of K,

and it devotes 50% of its GDP
to making new investment goods.

Both countries begin
with $100 worth of capital,

and both countries have
the same capital depreciation rates

and the same population.

If you had to choose, in which country
would you prefer to live?

As always, check out
our recent videos on the Solow Model,

and then try to solve
this problem by yourself.

If you're stuck, then come back
and we'll work through it together.

Ready?
I really like this question.

To get a better idea of what
this question is actually asking,

let's compare
the two countries side by side

to understand similarities
and differences.

First, we'll compare
the two countries' production functions,

and we see that they differ
by a multiple of two,

which loosely translates
to the country's ideas or productivity.

So Inventive, as its name suggests,
is more productive

with its factor of production, capital,
than Thrifty is.

So, what does Thrifty have going for it?

Not surprisingly, Thrifty has
that higher savings rate.

It's saving 50% of everything
it produces GDP-wise each year,

versus Inventive's 25%.

And everything else is the same:

capital stock, depreciation rates,
and population.

So what this question is really asking is,

is it more important for a country
to have a high savings rate like Thrifty,

or have more ideas and therefore
be more productive, like Inventive?

Where would you prefer to live?

The trickiest part here is translating
what an ordinary citizen cares about

into something
the Solow Model actually tracks.

Solow doesn't measure faster Wi-Fi,
even though we all care about that.

I mean, sure, we can and we will look
at how much GDP each country has,

how much it's investing
in its capital stock,

the usual Solow suspects.

But the real key here is
not so much GDP per se,

but rather the GDP that's left over
once we're done investing: consumption.

Consumption is that neglected variable
in the Solow Model,

but it's arguably what citizens
will care most about

given the Simple Solow Model framework.

So to outline our steps
for solving the problem,

we'll first track
Thrifty's economic prospects

on those three dimensions:
GDP, investment, and consumption.

We'll then do the exact same
thing for Inventive,

and finally we'll compare the two
to decide where we'd rather live.

The first step is to find
Thrifty's economic prospects.

Thrifty's production function is
GDP equals the square root of K.

Its initial capital stock is 100,
so the square root of 100 is 10.

This country is producing 10.

And, if this country is saving
50% of its GDP each year,

then the country is saving 5 of that 10.

More formally, we can graph
its investment function

as I equals 0.5 times
the square root of K.

If it's producing 10 and investing 5,
what's left over for consumption?

10 minus 5 is 5.

Now on to step two, which is
to do the exact same thing for Inventive.

Its production function is GDP
equals 2 times the square root of K.

And, given that it has the same
initial capital stock as Thrifty, 100,

its GDP this year is the square root
of 100 times 2, or 20.

If it's investing 25% of GDP
per year, 25% of 20 is 5.

More generally, its investment curve
is 0.5 times the square root of K.

And again, consumption
is just the leftover GDP after investment.

So 20 minus 5, or 15.

A quick aside here, notice
that the two countries' investment curves

are the same.

We'll revisit this later.

So we now move on to step three,
which is to compare the two.

Inventive seems like
the clear winner here.

Not only does it have
a much higher GDP than Thrifty,

but more importantly for the citizen,
the amount of GDP available

for consumption is much higher:
Inventive's 15 compared to Thrifty's 5.

Two things to note here.

First, you may think the difference
between consuming

something like 5 and 15 is really boring.

Like, who cares?
Those numbers are really small.

So let's try to put it
in real-world terms.

Inventive citizens consume three times
as much as Thrifty citizens.

This means that if
Thrifty citizens consumed, say,

$30,000 worth of stuff this year,

Inventive citizens would be consuming
$90,000 worth of stuff this year.

Suddenly, 5 versus 15 seems
like a much bigger deal.

And second, even though
population doesn't factor directly

into our Super Simple Solow Model,

it's important that the populations
of these two countries are equal,

as the problem originally states.

Given equal populations, we know
that GDP and consumption per person,

or per capita, will also be higher
in Inventive than in Thrifty.

Now, if we were in
a normal classroom right now,

this is probably the time
when you would raise your hand

and say something like,
"This looks great.

But, what about these two countries
in their steady states?

What if Thrifty, because
of all of their saving,

will be far better off
than Inventive in another,

I don't know, say 10 years?"

This is exactly the question
you should be asking.

It means that you understand
the whole point of the Solow Model.

It turns out that our answer
will hold in the steady state.

Inventive will produce and consume
more GDP in the long run.

If you want to better understand
why and how it holds,

check out our practice problems
at the end of the video.

In summary, Inventive citizens get
to consume more not only today,

but also tomorrow, making it
a more desirable country to live in.

What does this tell us?

It is incredibly important for
a country to have new ideas

and become more productive.

Saving is great, and will do a lot
to further a country's economic growth

and prosperity, but it can
only get us so far.

As always, please let us know
what you think.

And if you'd like more practice, please
check out our additional questions

at the end of this video.