00:01
So here we have a perfectly competitive situation, right? and in competition, price has to reflect marginal cost.
00:09
That's the key thing.
00:10
So we don't have a fixed price structure, right? we have to set things incorporating the uncertainty of the price.
00:24
Well, to do that, where does this come from? remember, this comes from profit maximization.
00:29
And we know that in the competitive situation, profit maximization needs to lead to a zero excess profit.
00:39
So for the first one, i'm going to set up a profit function.
00:43
Profit here depends on the price.
00:46
So with a 50 % chance, our revenue is going to be 10q.
00:53
And with a 50 % chance, our revenue is going to be 30q.
00:58
And then our costs are going to be q squared over 4.
01:03
Now i can simplify this, right, to 20q minus q squared over 4.
01:09
And then i can take the derivative with respect to q, which gives me 20 minus q over 2...