# The Solow Model and Ideas

Instructor: Alex Tabarrok, George Mason University

According to our previous videos in this section, the Solow model seems to predict that we’ll always end up in a steady state with no economic growth . But, the

According to our previous videos in this section, the Solow model seems to predict that we’ll always end up in a steady state with no economic growth.

But, the Solow model still has one variable unaccounted for: ideas.

So, can ideas keep us growing?

Ideas do one thing really well: they give us more bang for our buck.

This means we get more output for the same inputs of capital and labor. Ideas are a way of upping our productivity, increasing output per worker across different industries.

Just how much extra output are we talking about?

Well, imagine changing the A variable of the Solow model from 1 to 2. This means a doubling of our productivity.

This shifts the entire output curve upward. When output doubles, so does investment. Once investment comes in faster than depreciation, we end up accumulating capital once again.Thus, the economy keeps growing, which further boosts output.

Now, think of what would happen, if ideas continually improved. With each improvement, ideas would keep shifting the output curve upward, which will continually increase investment as well, and allow us to keep to the left of the steady state.

And when we stay to the left, that means we keep growing.

What all this means is, growth at the cutting edge is determined by two things.

First, it's determined by how fast new ideas are formed, and second, by how much those ideas increase productivity.

You now have a complete picture of our simple Solow model. It's a model that accounts for catching up growth, due to capital accumulation, and cutting edge growth, due to the buildup of ideas.

Now, since ideas foster growth at the cutting edge, we're left with the question that naturally follows: what factors help spur the accumulation of ideas?

That's what we'll discuss in the next video, so hang tight!

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## Transcript

We've covered a lot of the Super Simple Solow Model. We've looked at the dynamics of capital accumulation, how changes in savings rates influence growth, and we've looked look at some of the predictions of the Solow Model. One thing we've learned is that the model seems to inevitably predict that we end up in a steady state with no growth. Now, however, we're going to turn to the last of our variables: Ideas.

Can ideas keep us growing? Better ideas mean that we get more bang for our buck, more output from the same inputs of capital and labor. Alternatively, we can think about this as increasing our productivity. Henry Ford, for example, took ideas from lots of other industries, like meatpacking, bicycle making, and brewing, and he combined them in a way that had never before been used in the manufacturing of automobiles. This novel combination of ideas sparked a dramatic increase in productivity that transformed the world. The same types of processes - they're continuing today, and in all industries, increasing output per worker across the economies.

So, let's go back to our previous graph of capital and output. We can now add ideas as a multiplier. Better ideas multiply the output from the same capital stock. So, if A increases from 1 to 2, that's a doubling of our productivity. And that shifts the output curve up. When output doubles, so does investment. Now, once again, investment is greater than depreciation. So, we begin accumulating capital once again. And that further boosts our output. So better ideas spur more output, which creates more investment, which leads to capital accumulation. So better ideas lead to growth in two ways: The increased productivity of a given capital stock, and the increased investment, which increases capital accumulation.

Now imagine that ideas are constantly improving. You'd have continual shifts upward of the output curve. And that means continual shifts upward of the investment curve. We'd always stay to the left of the steady state, and there, we'd continually grow. So, growth at the cutting edge - it's determined by how fast new ideas are formed, and how much those new ideas increase our productivity. So that's our Super Simple Solow Model. It combines a model of catching up growth due to capital accumulation, with a model of cutting edge growth due to idea accumulation.

If you want to dive further into the Solow Model, check out our textbook, "Modern Principles." We also have more material in our Development Economics course. In that course, we'll add population growth to the model. and dive deeper into the data to see how well the model predicts. We'll find some things it predicts really well, and other things not so much. Finally, since ideas drive growth on the cutting edge, we'd like to know what factors help to spur the creation of new ideas. This topic is a personal favorite of mine, and it's up next.