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

The Solow model playlist: http://bit.ly/1sv2Pfa

Subscribe for new videos every Tuesday! http://bit.ly/1Rib5V8

Macroeconomics Course: http://bit.ly/1R1PL5x

-[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.

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 a 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. If you'd like more practice, please

check out our additional questions
at the end of this video.