00:01
So here we've got a question about the solo model, and we're told there's no change in population.
00:08
We're also told that there's no change in technology, right? no change in how efficient we are at converting output and labor to production.
00:24
Right? so our production function here is like y equals a, f of k and l.
00:31
L is fixed and a is fixed.
00:33
So the entire source of changes in y is going to come from k.
00:39
But of course, in the solo model, we know that y can't grow forever.
00:44
We have a savings function, right, representing diminishing returns to capital.
00:50
And then to balance that, we have a depreciation function, right? delta k.
00:55
So our steady state equilibrium will be where savings is balanced by depreciation, right? savings is equal to how much capital work.
01:05
Cumulating depreciation is how much capital we're losing.
01:09
So the savings versus depreciation pins down the amount of capital.
01:15
And then this f of k is the amount of consumption, right? that's the amount of consumption.
01:23
We are saving the height of the blue line and spending that money on capital investment, which means that all the other output left over is devoted to consumption, right? so, that gap between f of k and delta k is how much consumption we get.
01:39
It's all the income left over after we've spent our savings on building more capital.
01:44
So in general, the idea for optimality is we want to set the marginal benefit equals to the marginal cost...