00:01
So here we're given a production function, right? if k is equal to 2 and l is equal to 3, the quantity that we get by plugging those values in is equal to the minimum of 4 times 2 and 8 times 3, which is clearly equal to 8, right? b, we are now further told that the wage is equal to 60 and the rental rate on capital is equal to 20 and the q bar that we want to achieve is 8.
00:34
So the key thing to notice here is that normally you think of differentiating or something when you get these, but you can't differentiate minimum.
00:42
You see that this is 8 and that this is 24.
00:45
And you see here that the 16 units are wasted.
00:49
If this had been 24 or 400 or 9 or 8, we still got the same, right? for minimum of a, b implies that a equals b.
01:09
Otherwise, you're just wasting something, right? because if a is greater than b, you're wasting some a, and if b is greater than a, you're wasting some b.
01:16
Setting them equal to each other is the only place where there's no waste.
01:20
So if we need to get q bar equals 8, that implies that we need for k is equal to 8, and k is equal to 2, and we need 8l is equal to 8 and l is equal to 1...