00:01
So we have 50 firms, they behave in a competitive manner and we have the identical cost function for each of the firms.
00:15
That is c is equal to y squared over 2 and then there is monopolist.
00:36
Marginal cost for the monopolist is zero.
00:41
The demand curve for the product is a thousand minus 5p.
00:53
So we want the monopolist profit maximizing output and price.
01:06
So what we need to do is solve for p in terms of q.
01:18
So we can't use the demand function that's given because that's demand for the product.
01:23
We need the demand for the monopolist.
01:34
So let's do the previous parts that are not shown in the question.
01:44
We need to find the supply curve of one of the competitive firms.
01:51
So we're given the cost function.
01:59
From this we can get the marginal cost.
02:02
So that's going to be the derivative.
02:06
So using the power rule we get marginal cost is equal to y.
02:15
There are 50 firms and we can get this supply function for all 50 firms.
02:25
So we just multiply marginal cost for one firm by 50.
02:34
So that's for the entire fringe.
02:43
So this is perfectly competitive.
02:58
The price is equal to marginal cost and we can see marginal cost is equal to y.
03:04
Quantity supply is therefore equal to 50 times the price.
03:13
And then the supply function for one firm is q is equal to y.
03:45
So then we need to find demand faced by the monopolist.
03:53
So this is equal to the residual demand.
03:56
So when we have a firm we have to take the market demand and then subtract the demand from the fringe or the supply from the fringe.
04:19
So this should be supply.
04:21
So that's why we found the supply from the fringe overall.
04:27
So whenever you see a problem with monopoly and fringe you're going to find the supply for the fringe overall when you're trying to get the demand for the monopoly.
04:39
So then we have market demand as 1000 minus 5p.
04:48
And then we found supply for the fringe overall was 50p.
04:52
Or actually that should have been 50p...