Thursday’s (1/31) Class

Today we talked very briefly about the components of GDP, in an identity that you will be seeing frequently throughout this course.

Y = C + I + G + NX

Y is, of course, GDP, C is consumption, I is investment, G is government expenditures and NX is net exports. The sum total of these four items is the total GDP of our macroeconomy.

Now that we fully understand what GDP is (and isn’t), and how important it is from an economic stand-point, as the measure of economic well-being, we want to know what makes it tick. And by tick, I mean grow. Specifically, we want to know:

  • What causes growth?
  • What makes some countries richer than others?
  • What are the factors for sustainable growth?

For this we turn to the theory of economic growth, and specifically the Solow Growth model. This rests on two fundamental points:

  1. Savings and investment drive capital intensity
  2. Technology and organization drive labor efficiency

To examine the relationship of these two factors (capital intensity and labor efficiency) we turn to the production function. In particular, we look at the Cobb-Douglas production function which relates the two and looks something like this:

Cobb Douglas Production Function

Y/L is the output per worker and K/L is the capital stock per worker. E is the level of efficiency or technology in the Solow economy. The parameter alpha controls the point at which marginal diminishing returns set into the production function. Take a look at a production function with varying levels of alpha.

Cobb Douglas Production Function for Varying Levels of Alpha

As you can see, for alpha = 0, the production function is flat (which means diminishing marginal returns are already set into the function), and for alpha = 1, the production function is a straight line increasing at a constant rate. This means that for each $1 increase in K/L, Y/L increases correspondingly by $1.

Now, in each model we have to consider the equilibrium conditions. To make life easier for us, we assume that the labor force never increases, and efficiency is always the same. The conditions for which equilibrium holds in this case, is when capital never grow either. This is because the equilibrium condition (or the steady-state rule) is that:

  1. K/L
  2. Y/L
  3. E

Must all three be growing at the same proportional rate. If the rate for #2, and #3 is 0 (as we assume), then so it must be for #1. And, the only time when K/L does not grow is when the total savings (or total investment, since they are assumed equal) equals total depreciation. This can be written in mathematical form as:

Equilibrium 1

But this is mathematically equivalent to saying the following:

Equilibrium 2

And this is the equilibrium condition when we have no growth in the labor force, and no growth in the efficiency. Here’s how it figures in to the Cobb-Douglas production function. Note that we didn’t talk about it in class, I’m just throwing it in here to give you some food for thought before the next class.

Equilibrium 3

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