Economics: Looking at the Solow Model 2

In my last economics post, we looked at three equations:

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

and turned the capital accumulation equation into this:

sY=dK_t

Now, we're going to plug it into the production function so we can determine the optimal amount of K.

To do so,


sY=dK_t ---------> Y=dK/s

From now on, I'm going to remove the t subscript, mainly because it's a hassle to type. So,

dK/s=AK^αL^1-α

K = sAK^αL^1-α/d

K^1-α = sAL^1-α/d

K = (sAL^1-α/d)^1/(1-α)

We can now simplify the equation further:

K=L* (sA/d)^1/(1-α)

So now, what does this tell us? It tells us the steady state.

I currently don't have a graph nor the time to make one online, so I will provide this:
Simple Solow Model at Wolfram

In the next batch of notes, I will go over the basic assumptions of Solow Model, as I have neglected to do so in the first set. I will also look at the per capita equations, and transition dynamics.