00:01
So here we're given a whole bunch of stuff about the solo model.
00:04
We're told that the rate of depreciation, the population growth is 2%, which is 0 .02.
00:10
We're told that the depreciation rate is 0 .1.
00:13
We're told that the savings rate is equal to 0 .1, and we're told that the production function per worker, right? we're given a per worker production function is 4 .8k to the 0 .5.
00:27
Right? so y is equal to y over l.
00:31
This is in per worker terms.
00:33
So what i need to do is since the output depends on capital, i need to find out k, right? if i'm going to tell you how much output is changing over time, i need to find out what's happening to capital because output is a function of capital.
00:51
We do that by invoking the law of motion, right my law of motion for the aggregate capital stock capital k is that cap the change in the capital is equal to the investment into new capital minus the depreciation oh sorry i tell the depreciation d right of the old capital right so this is the extra the new k from investment and this is the lost k from depreciation so and i want to set this is this is the equal to zero to see if there's a steady state, right? that's really what i'm doing.
01:30
So let me rewrite this just a little bit.
01:33
Kt, well, we know that the investment is equal to 0 .1 of yt, and that the depreciation rate is 10 .1 of kt.
01:45
Now if i wanted to divide all of these terms by lt, the population, lt, lt, right, what i would get here is that the change in kt over lt is equal to 0 .1.
02:05
Yt over lt is just the per worker production function.
02:09
So this is 4 .8k to the 0 .5 minus 0 .1k, right? pretty straightforward.
02:22
Now, what you can do here is set this equal to zero, and when you do this, you can solve for k, right? and you get a k star, which is equal to a steady state value, right, by solving this equation, right? you don't have to do it here.
02:41
There's no obligation to do it...