00:01
So here we're talking about monopoly.
00:02
And we start off with the demand curve, actually an inverse demand curve of 220 minus 3q.
00:09
We have marginal cost of 40.
00:12
And we know that a monopolist in equilibrium desires to set marginal revenue equals to marginal cost.
00:18
That's how they maximize profits.
00:20
Keep producing units until the increase in revenues generated by more production is just balanced by the increase in cost.
00:30
So we need to find the marginal revenue.
00:33
Well, let's think about what revenue is.
00:36
Revenue is equal to price times quantity, but we have an expression for price, 220 minus 3q.
00:43
So we can see that marginal revenue or the derivative of revenue with respect to quantity is 220 minus 6 q, right? that's our normal rule of thumb for linear demand.
00:55
It's the same intercept, but double the slope.
00:57
So we start off at 220.
00:59
We have a demand curve.
01:01
We have a marginal revenue curve, and we have a marginal cost curve, right? actually, i'll put the 40 over there.
01:10
Right.
01:11
So the monopolist wants to set marginal revenue equal to marginal cost, so we can do exactly that.
01:16
Marginal revenue is equal to marginal cost.
01:19
We get 220 minus 6q is equal to 40.
01:25
I'm going to group like terms...