Economics: Looking at the Solow Model 1

Since I seem to be on a roll with posting class notes, I'd figured I might as well post what I went over in my macroeconomics class. Today, we continued our journey with the Solow Growth Model. Unlike a simple production function, the Solow Growth Model takes into account Capital Accumulation.

To calculate the Solow Model, we require a few equations:

Y= AK^αL^1-α
Y= C + I
K_t+1=K_t + I - dK_t

The first equation refers to the production formula. A certain output Y is equal to A, the technology factor, K, some amount of capital, and L, labor. The production formula follows the basic Cobb Douglas form where we have K, L and some form of alpha. Alpha is less than one.

The second equation basically states that the general output is equal to consumption and investment. What does not get consumed is saved and therefore invested. This formula leads to another formula where I= sY. s stands for a savings rate. We assume in this equation that the savings rate is equal throughout the country.

The last equation is the capital accumulation function. If we simplify the function, it will look something like this:

ΔK = I - dK_t

All the formulas are related to each other. Now, how can we calculate the optimal value for our country?

We utilize all the formulas to create one super amazing formula. In the Solow Model, all economies move to a steady state. The steady state is where the amount of K is optimal. Now several things can actually shift the K, but we'll discuss that later.

To calculate the steady state, we first take the last equation.

ΔK = I - dK_t ----------> 0 = I - dK_t

Now, why do we do that? Basically, the best point is where Investment is equal to depreciation. The idea is similar to Marginal Product or Maximization Problems.

So, after playing with that equation, we get something like this:

I = dK_t ----------> sY=dK_t

Now, let's plug that into the production function!