The Solow Model Animated!

eL-lettersModern Principles of Economics was the first principles textbook to make the Solow model of economic growth easily accessible to undergraduates. By focusing on simple mathematics that the students already know, like the square root function, we made the Solow model easy to understand without losing the power of the model to explain the world.

Modern Principles is the only textbook with the Super Simple Solow model! And now we’ve brought the model to life with a series of fun videos in our Principles of Macroeconomics class at MRUniversity. You’ve never seen the Solow model taught like this!

Introduction to the Solow Model introduces the questions and the “characters” that drive the story. Physical capital and diminishing returns explains the idea of a production function and diminishing returns. We then introduce capital depreciation and focus in on the most important idea for understanding the Solow model, the steady state:

I’ll cover some more videos in the Solow series later this week.


LOL you can do anything you want to the Solow model without hurting its ability to "explain the world" because it has almost no ability to explain the world!! Input accumulation differences explain precious little about income differences. Hall and Jones bruh.

China bruh! Why is it growing so fast? Capital accumulation!

More generally, however, of course your point is correct but you need the Solow model to know that it is correct! Before Solow there was no growth accounting.

But long term (steady state) in the Solow model is only through exogenous tech growth. Capital accumulation only affects growth up to the steady state limit.

And other than replacing Cobb's function with a square root function, what other simplification is there?

And why exclamation points? I've read no serious post uses exclamation points!

Hall & Jones >> China

I don't think it is ever sold as anything other than a simple model. There are literally hundreds of variants which are essentially Solow-esque in principle.

Among other things, economies may not adjust as fast as Solow-esque models may assume, and also, they tend to assume an absence of existing interests to rig the game to uphold their advantage (it would be economically irrational to assume otherwise).

Alex is quick to delete posts for making even the slightest unpleasant comment, such as simply pointing out that Greg Mankiw's book actually predates his own.

"Libertarianism" in action folks.

This blog being a thing of his creation and ownership, why should he be obliged to let others come dump on it? Do you imagine libertarians let drifters come soil their couches all day, because that's how they conceive libertarianism?

I say this as someone who gets deleted on occasion.

Sure. He's free to do so. I admire his tenacity for doing so 3 times in a row (and what I suspect will be a 4th time soon)

As I am free to point out false advertisement. The Solow model is taught in all undergraduate textbooks, way way before this one came along.

I vaguely recall that the second edition took out some stuff that was in the first edition. It could be that it was in the first edition. And if we go back forty years or so who knows. But the basic point that until recently, the last three or four years, other principles texts have been weak on growth is true.

People are free to do lots of stuff. They're still hypocrites when their freely-performed actions are inconsistent with their stated beliefs. Among the more open-minded, having such hypocrisy pointed out can be a means of getting them to reconcile their beliefs and actions.

Not that I actually know what is going on here with AIG and Alex, just stating this as a general point.

Mankiw's principles book predates our book by decades! No secret there! But it doesn't teach the Solow model, as I said.

Sure it does.

You are confusing his intermediate macro book which is much more advanced with his principles book.

No, quite sure its in his principles book. I learned it from his book in econ 101. Anyway, I can't find a copy of it right now.

Either way, it's also in Samuelson's book, even before that.

In Mankiw's book it's in Chapter 25 or 24, depending on the edition.

@AIG - There's a number of books that teach the Solow model, so what? AlexT is not claiming he's the first, just the first with this simplified framework that's probably a cartoon of the original.

And here's the Wikipedia page:

The secret to the Solow model is to know how to solve two differential equations, having the classic forms y'(t) = k*y(t) (exponential function) and y'(t) = y(t) -y^2(t) (Logistic function)

Then use a simplified Cobbs function, then assume constant coefficients and separation of variables at points. It's all very logical and easy to remember if you go through it a few times. I've since forgotten it but can with some practice relearn it. I bet even Solow forgot it at times (easy to do if you do models--once you step away from the model the details get fuzzy)

LOL, Ray, I appreciate your attempt at humor.

Page 533 has a very general discussion of diminishing returns and what Mankiw calls "catch up effect" (convergence). That's related to Solow but not quite Solow.

Most Principles books just show you a production function and are done with it when it comes to long run growth.

(On the other hand Mankiw does mention Malthus, which pretty much no other textbook does)

Mankiw discusses growth, does not have a model.

This comment definitely passes the bar of "slightest unpleasantry". Based on your general style of commentary, I don't think you are very socially aware of what most people would consider as "slightly unpleasant" as opposed to "outright assholish". But maybe I'm wrong and you are more aware than you let on.

1) Nice work on the video. 2) This seems to indicate that capital accumulation by the investing class would be a good thing, as opposed to redistribution to the consuming masses.

Perhaps we can redistribute members of the Investing and Consuming classes instead, with explicit instructions to behave like those in whichever class they are moved into typically behave.

I take your rhetoric to imply both would fail and wind up right back where they started, in which case I agree.

Capital accumulation can also be achieved via public sector spending. Namely, in various forms of infrastructure that increase the profitability of the marginal dollar invested in the private sector. Clearly, such argumentation should not be drawn to logical absurdity of a 100% command and control economy, but it is relevant.


But funny. I laughed hard at the ending of the last video. Poor K.

Can we look forward to Tyler and Alex being the first to bring the Aghion/Howitt Schumpeterian model to principles text ? Since it is richer and more interesting than Solow and with plenty of micro applications such as role of competition ?

Excellent video. Thanks.

This all just infotainment.

When you look at the data in Solows paper, you could just throw out Kapital of the equation and get a better fit.

The "marginal" in it is just introduced arbitrarily.

The moment you start asking, where is the tax in the distribution of the output the whole model goes up in smokes

You have no idea of what you're talking about, do you? There is no data in Solow's paper, it's a theoretical paper. I can't even make out the other parts of your comment.

Why is it assumed that capital which replaces depreciated capital has the same level of productivity? If productivity of capital is constantly increasing, a steady state of investment would imply constantly increasing physical output. I'm not an Economist, so I might be missing something.

The model is taught to beginners and is explicitly supposed to maximize mathematical simplicity and make it easier to learn and model the basic concepts involved. If you skim through some texts on growth theory, you will find a great number of extensions of the Solow model which do such things.

I think you are absolutely correct in what you implicitly suggest needs to be accounted for in a more complete application of such models.

The dynamic graph is nice, but giving little faces to economic variables like K? What age group are you teaching, 4 year olds? It sort of sends a signal to students: "I think of ya'll as a bunch of 4 year olds who need to be shown little anthropomorphic cartoons to pay attention and I don't really expect you to get this stuff". Oh well, at least that cutesy K is not doing a rap song or something.

An excellent video of complex concepts that are accessable to non-economisits.

We live in a world where the basis of ideas and innovation, is increasing exponentially as scientific knowledge increases. However, most of the innovation is limited to the "permissionless" sectors, where there are fewer bureaucrats between the knowledge, ideas and the implementation of those ideas. Silicon Valley is booming and "Joe Median" jobs are dying.

As a scientists operating in sectors of the economy with expotential rates of scientific progress and dramatic opportunities, the slow step in the "idea" process is regulatory bureaucrats. For example, with the new innovations in offshore aquacultue, So. California has the opportunity to create a 5 billion dollar industry with 50,000 Joe Median type jobs, without environmental impacts. However, this opportunity is blocked by activists, and regulatory bureaucrats who are all benefiting from delays and more study (if we knew all the answers, it wouldn't be innovative) and meaningless "concerns" and imaginary seraniros. Meanwhile, the technology, innovation and creativity is going elsewhere (some just south of the border in the same waters).

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