Office Hours: The Solow Model: Investments vs. Ideas

Summary

This educational video explores the Solow Model, comparing two hypothetical countries, Inventive and Thrifty, with different production functions and savings rates. It highlights the importance of productivity and ideas over high savings rates for long-term economic growth and prosperity. The video challenges viewers to consider which country they'd prefer to live in, ultimately revealing that Inventive's higher GDP and consumption make it a more desirable place, both now and in the steady state.

Takeaways

• 📚 The video discusses the Solow Model, a tool for evaluating economic growth through different inputs.
• 🌟 The script introduces two hypothetical countries, Inventive and Thrifty, with different production functions and investment rates.
• 💡 Inventive has a production function that suggests higher productivity, with GDP being twice the square root of capital (K).
• 🏦 Thrifty, on the other hand, has a simpler production function with GDP equal to the square root of K and a higher investment rate of 50% of GDP.
• 💰 Both countries start with the same amount of capital and face the same depreciation rates and population sizes.
• 🤔 The central question posed is whether a high savings rate (like Thrifty's) or high productivity (like Inventive's) is more beneficial for a country's economy.
• 📉 The script emphasizes the importance of consumption, which is often overlooked in the Solow Model but is crucial for the well-being of citizens.
• 📊 By comparing GDP, investment, and consumption, the script outlines a method to evaluate the economic prospects of both countries.
• 📈 In the initial comparison, Inventive has a higher GDP and more consumption after investment than Thrifty.
• 🔄 Despite having the same investment curves, Inventive's higher productivity leads to greater consumption for its citizens.
• 🔮 The video also addresses the steady state of both countries, suggesting that Inventive will maintain its advantage in the long run.
• 🌐 The conclusion is that new ideas and productivity are more critical for a country's prosperity than just saving and investment.

Q & A

What is the Solow Model discussed in the video?

The Solow Model is an economic growth model that evaluates how different inputs, such as capital and productivity, affect a country's economy over time.

What are the two countries featured in the video script?

The two countries featured are 'Inventive' and 'Thrifty', which are used to illustrate different economic growth strategies.

How does the production function differ between Inventive and Thrifty?

Inventive's production function is GDP = 2 times the square root of K, while Thrifty's is GDP = the square root of K. This indicates Inventive is more productive.

What percentage of GDP does each country invest according to the script?

Inventive invests 25% of its GDP, while Thrifty invests 50%, showing a higher savings rate in Thrifty.

What is the initial capital stock for both countries?

Both countries start with an initial capital stock of $100.

What is the significance of the investment curve being the same for both countries?

The investment curves being the same (I = 0.5 * the square root of K) indicates that both countries invest a proportionate amount of their GDP, despite different total GDPs.

What is the main economic indicator that citizens care about according to the video?

Consumption is the main economic indicator that citizens care about, as it represents the GDP left over after investment.

How does the video script suggest comparing the two countries' economic prospects?

The script suggests comparing GDP, investment, and consumption for both countries to evaluate their economic prospects.

What is the consumption difference between Inventive and Thrifty in the initial year?

In the initial year, Inventive consumes 15 units of GDP, while Thrifty consumes 5 units, showing a significant difference.

Why is productivity more important than savings according to the video?

Productivity is more important because it leads to higher GDP and consumption levels, both in the short and long term, making a country more desirable to live in.

How does the video script address the concern about the countries' steady states?

The script reassures that Inventive will continue to produce and consume more GDP in the long run, even in the steady state, due to its higher productivity.

Outlines

00:00

📊 Economic Growth Comparison: Inventive vs. Thrifty

This paragraph introduces a comparative analysis of two hypothetical countries, Inventive and Thrifty, using the Solow Model. It sets the stage for a discussion on the impact of different economic inputs on a nation's growth. The focus is on the countries' production functions, investment rates, and the initial capital stock. The paragraph invites viewers to consider which country they would prefer to live in, based on productivity and savings rates. It emphasizes the importance of consumption, which is often overlooked in the Solow Model but is a key determinant of citizens' well-being. The summary also outlines the steps to evaluate the economic prospects of both countries, starting with GDP, investment, and consumption calculations for Thrifty.

05:05

💡 The Role of Productivity and Savings in Long-Term Prosperity

The second paragraph delves into the implications of the countries' economic strategies on their citizens' consumption and long-term prosperity. It highlights the significant difference in consumption levels between Inventive and Thrifty, translating the model's output into real-world terms to illustrate the impact on citizens' lifestyles. The paragraph also addresses the importance of equal population sizes in assessing per capita GDP and consumption. Furthermore, it anticipates a common question regarding the steady state of the economies, confirming that Inventive will maintain its advantage over Thrifty in the long run. The summary concludes by emphasizing the value of innovation and productivity over savings alone in driving a country's economic growth and prosperity, and it invites viewers to engage with additional resources for a deeper understanding.

Keywords

💡Solow Model

The Solow Model, named after Robert Solow, is a growth model in economics that explains long-term economic growth in terms of the accumulation of capital and technological progress. In the video, the Solow Model is used to evaluate how different inputs, such as the savings rate and productivity, affect the economies of two hypothetical countries, Inventive and Thrifty.

💡Gross Domestic Product (GDP)

Gross Domestic Product is the total monetary or market value of all finished goods and services made within a country during a specific period. The script uses GDP to illustrate the economic output of the two countries, showing how different production functions and investment rates affect the GDP of Inventive and Thrifty.

💡Investment Goods

Investment goods are items produced with the intention of being used in the future to create additional output. In the context of the video, both countries allocate a percentage of their GDP to create new investment goods, which is a key factor in their economic growth and the Solow Model analysis.

💡Productivity

Productivity refers to the efficiency of production, often measured as the ratio of output to inputs. The script highlights the difference in productivity between Inventive and Thrifty, with Inventive being more productive due to its higher production function multiplier.

💡Savings Rate

The savings rate is the proportion of income not consumed and set aside for future use. The video script contrasts the savings rates of the two countries, with Thrifty having a higher savings rate, which is a critical factor in evaluating their long-term economic prospects.

💡Capital Depreciation

Capital depreciation refers to the loss in value of capital assets due to wear and tear, obsolescence, or other factors. The script mentions that both countries have the same capital depreciation rates, which is an important economic parameter in the Solow Model.

💡Consumption

Consumption is the use of goods and services to satisfy human wants or needs. In the video, consumption is identified as the key variable that citizens care about, as it represents the GDP left over after investment, and is a measure of economic well-being.

💡Steady State

In economics, a steady state is a situation in which the economy's key variables are growing at a constant rate. The script discusses the long-term steady state of the two countries, emphasizing that Inventive will continue to produce and consume more GDP in the long run.

💡Economic Growth

Economic growth is the increase in the production capacity of an economy. The video uses the Solow Model to analyze how different factors contribute to the economic growth of the two countries, focusing on the role of investment, savings, and productivity.

💡Technological Progress

Technological progress refers to the advancements in technology that can increase productivity and economic growth. Although not explicitly mentioned in the script, the difference in production functions between Inventive and Thrifty can be interpreted as a proxy for varying levels of technological progress.

💡Per Capita

Per capita refers to a measure of an economic value per person in a given area, often used to compare economic well-being between populations of different sizes. The script concludes that, given equal populations, Inventive's higher GDP and consumption translate to higher per capita figures, making it a more desirable place to live.

Highlights

The Solow Model is evaluated to understand how different inputs affect a country's economy.

Two hypothetical countries, Inventive and Thrifty, are compared using the Solow Model.

Inventive has a more productive production function, doubling the square root of capital (K), compared to Thrifty's single square root of K.

Thrifty has a higher savings rate at 50% of GDP compared to Inventive's 25%.

Both countries start with $100 of capital and have the same depreciation rates and population.

The question posed is whether a high savings rate or productivity is more important for a country's economy.

Consumption, the leftover GDP after investment, is the key variable for citizens' well-being in the Solow Model.

Thrifty's initial GDP is $10, with $5 saved and $5 left for consumption.

Inventive's initial GDP is $20, with $5 invested and $15 available for consumption.

Inventive citizens consume three times more than Thrifty citizens in the initial comparison.

Population equality ensures that per capita GDP and consumption are higher in Inventive.

The steady state analysis confirms Inventive's long-term advantage in GDP production and consumption.

The importance of new ideas and productivity for a country's economic growth is emphasized.

Saving contributes to economic growth but has limitations compared to productivity gains.

Inventive is deemed a more desirable country to live in due to higher consumption today and in the future.

The video includes practice problems for further understanding of the Solow Model.

Additional questions are provided at the end of the video for more practice.

Transcripts

♪ (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.