## The Solow Model and the Steady State

Instructor: Alex Tabarrok, George Mason University

Remember our simplified Solow model? One end of it is input, and on the other end, we get output. What do we do with that output? Either we can consume it, or we

Remember our simplified Solow model? One end of it is input, and on the other end, we get output.

What do we do with that output?

Either we can consume it, or we can save it. This saved output can then be re-invested as physical capital, which grows the total capital stock of the economy.

There's a problem with that, though: physical capital rusts.

Think about it. Yes, new roads can be nice and smooth, but then they get rough, as more cars travel over them. Before you know it, there are potholes that make your car jiggle each time you pass. Another example: remember the farmer from our last video? Well, unless he's got some amazing maintenance powers, in the end, his tractors will break down.

Like we said: capital rusts. More formally, it depreciates.

And if it depreciates, then you have two choices. You either repair existing capital (i.e. road re-paving), or you just replace old capital with new. For example, you may buy a new tractor.

You pay for these repairs and replacements with an even greater investment of capital.

We call the point where investment = depreciation the steady state level of capital.

At the steady state level, there is zero economic growth. There's just enough new capital to offset depreciation, meaning we get no additions to the overall capital stock.

A further examination of the steady state can help explain the growth tracks of Germany and Japan at the close of World War II.

In the beginning, their first few units of capital were extremely productive, creating massive output, and therefore, equally high amounts available to be saved and re-invested. As time passed, the growing capital stock created less and less output, as per the logic of diminishing returns.

Now, if economic growth really were just a function of capital, then the losers of World War II ought to have stopped growing once their capital levels returned to steady state.

But no, although their growth did slow, it didn't stop. Why is this the case?

Remember, capital isn't the only variable that affects growth. Recall that there are still other variables to tinker with. And in the next video, we'll show two of those variables: education (e) and labor (L).

Together, they make up our next topic: human capital.

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## Contributed Content (0)

They do not denote the same phenomenon, but you are right that the principle is the same.
Steady state output is the level of output (production) at which the rate of capital investment is equal to the rate of capital depreciation.
Malthusian equilibrium is the level of output which equals the amount of output needed to barely feed the existing population, no more, no less.
To understand the dynamics that makes Malthusian equilibrium an equilibrium, plot the output as a function with decreasing returns, and the population as a function with increasing returns or perhaps simply linear. You only need these two curves(functions). When population is too low to consume existing output, they do not invest in capital, they make children until there are enough peole to eat (consume) the surplus output. If they make too many children, going past the subsistence level for the existing population, mortality increases, decreasing the value of the population.

Hi Rodrigo,
We're releasing new videos in this course every Tuesday, with some exceptions. This video will be live today.
Cheers,
Meg