00:01
So here we have a monopoly situation, which means we have a demand curve, right? i'm going to go ahead, though, and calculate a revenue curve.
00:09
A revenue curve is price times quantity, and if i sub in, that's 1 ,000 minus 10 k times q.
00:16
That means marginal revenue, which is the derivative of revenue with respect to quantity, is going to be 1 ,000 minus 20 q, as opposed to marginal cost, which is 100 plus 10 q.
00:30
We should always diagram these things.
00:32
It never hurts to sketch a picture.
00:35
The demand starts at 1 ,000 and slopes down.
00:39
The marginal revenue also slopes down like this, and marginal cost starts at 100 and slopes up.
00:49
So the optimal point for monopoly is where marginal cost is equal to marginal revenue, right? so if we set marginal revenue equals to marginal cost, we get a thousand minus 20 q is equal to oh sorry this was not a thousand this is a hundred which i did draw it correctly just getting carried away um is equal to a hundred plus 10 q so this tells us that 900 is equal to 30 q q is equal to 30 and that makes the price um the price would be equal to 700 so of 30 and 700.
01:33
There's my monopoly price and quantity.
01:35
Now for the competitive market, i need to figure out this intersection, right? in competition, you set price equal to marginal cost.
01:43
So in competition, instead, price is equal to marginal cost.
01:46
So we got 1 ,000 minus 10 q is equal to 100 plus 10 q...