00:01
Okay, so here we've got a production function, y equals 20 l to the half, k to the half, right? it didn't look like the functional form transcribed perfectly to the question here, but this is what it is, right? this is in particular called a cobb douglas production function, which is something that you'll see in a lot of places in macroeconomics, right? so the first thing we need to check is constant returns to cigail.
00:27
And constant returns means that if you double inputs or really increase them by any fraction, you get double outputs.
00:39
So i'm going to test this empirically by doubling both imports, right? so i'm going to replace l with xl and k with xk.
00:54
And so i'm going to increase l by a factor of x and increase k by a factor of x and see what happens to y.
01:01
So this gives us 20 xl to the 0 .5, xk to the 0 .5.
01:10
But then exponents distribute, so this is equal to 20 l to 0 .5, k to the 0 .5, x to the 0 .5, x to the 0 .5, x to the 0 .5 .5, x to the 0 .5 .5.
01:25
0 .5 equals 20 l to the 0 .5, k to the 0 .5, x equals y x.
01:34
So yes, this is the definition of constant returns to scale.
01:38
I increased both l and k by x, and then i got y x back...