## Office Hours: The Solow Model: Investments vs. Ideas

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

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.

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Practice Questions

## Contributed Content (0)

Let's focus on the first practice problem and put together what we know from the previous videos about steady state. We know that the steady state level of capital stock is that level of capital stock at which capital neither grows, nor shrinks, but stays the same. It would grow if the quantity taken away from GDP to be invested as new capital (call this "investment") was greater than the quantity of capital stock which is eroded or destroyed at that time (call this "depreciation"). And it would decrease, if depreciation was greater than investment. So the level of capital at which capital is constant is the level at which investment equals depreciation.
Now let's look at the graph to see that level. There is only one level of capital (on the horizontal axis) at which investment equals depreciation: the point of intersection between the investment line (function) and the depreciation line (function). To the left of that point, investment is greater than depreciation, so capital still grows. To the right of it, investment is lower than depreciation, so capital, on the net, erodes, or shrinks.
Let's see if that point is 100, the value of capital with which we start.
We are looking at country Inventive.
The video shows how to calculate GDP; investment, and depreciation.
GDP = 2 times square root of K = 2 times square root of 100 = 2 times 10 = 20
investment = investment rate times GDP at that point = .25 times 20 = 5
depreciation = depreciation rate times capital at that point = .03 times 100 = 3
So, can 100 be the steady state level of capital. No, because investment is greater than depreciation at that point. Capital is on the net growing. On the graph, this means we are still at the left of the intersection. So the steady state level of capital must be greater than 100.
Perhaps it is 111?
If we calculate we see that even when capital is 111, investment will still be greater than depreciation, so we shall still be at the left of the steady state level.
Can it be 278?
Yes! At that point, if we perform the calculations, we discover that investment is approximately equal to depreciation.
So it seems that what we know from the videos was enough to solve this problem.
If we search for youtube videos about "calculating the steady state level of capital in the Solow model" we see how to find the general solution, by equating the investment function with the depreciation function. But we did not need to do that here. We just tried possible values of capital to see whether, at any of these possible values, it so happened that investment was equal to depreciation.