00:01
Okay, so we have the monopolist.
00:03
We have the demand curve q equals 11 minus p.
00:09
We need to find the equilibrium quantity and price.
00:14
So let's express the demand curve with p as an independent variable.
00:19
So p will be 11 minus q.
00:23
Total revenue, we need the marginal revenue curve for the monopolist.
00:27
So since total revenue is price times quantity, we can write it as 11q minus q squared, just multiplying price up here times quantity.
00:41
Okay, but i don't want to confuse myself when i come back to look at the demand curve, so i'm going to take that back off.
00:49
And so marginal revenue is going to be the derivative of this respect to q.
00:55
Marginal revenue is equal to 11 minus 2q.
00:58
So we can find, well, let's draw it out as well.
01:04
So we have a demand curve that looks like this and a marginal revenue curve that looks like this.
01:14
So those are the same points.
01:16
And it intersects here at 5 .5.
01:21
And we have a marginal cost curve equal to 6.
01:27
So let's just find all these points where the marginal revenue curve is equal to 6.
01:34
So a price of 6 on the marginal revenue will give us a quantity of 2 .5.
01:46
And let's go ahead and figure out where the marginal cost intersects the demand curve.
01:52
So the demand curve when price is 6 is 11 minus 6 or 5.
01:59
So actually i haven't draw i haven't drawn this to scale properly but nonetheless this point here is five and and i'm sorry this is six here for the price okay so we want to first of all calculate the lerner index which is price minus marginal cost over price so here we oh i'm sorry we have to figure out what the price is at a quantity of two and a half that's a kind of our equilibrium price so if we we plug two and a half in for price, we'll see that quantity is going to be 8 .5 just by using the demand curve...