00:01
In this video we have been given the inverse market demand for mineral water is here p and that is equal to 200 minus 10 q.
00:11
Now here we can say that q is the total market output and p is the market price.
00:18
So we can here say that in the first part of this very problem, since demand function for 2 is same and also the cost is 0, therefore to find the quantity of this problem.
00:29
Each we first need to multiply each side of the inverse demand function by q.
00:36
So it will be here pq and that is going to be here equals to 200 q minus 10 q square.
00:44
Now we need to take the derivative with respect to q to get the mr function.
00:50
So it will be here dtr and then it will be basically divided by dq and this is here going to be equals to mr and hence we can here say that as we can use the rule that for any linear demand curve p the rule we are writing now so rule is that for any linear demand curve p is equals to a minus b q the marginal revenue that is basically we can say mr can be written as it will be here equals to a minus 2bq so from this very information we can here say that tr is maximized when mr is equal to 0 therefore set the mr function equals to 0 and solve for q that is mr value is here going to be equals to 200 minus 20 q and that is here equals to 0.
01:53
So it means that the value of q will be here equals to 200 divided by 20 that is 10 and therefore q for each item is 10 units.
02:05
So we have find out the q for each items.
02:10
Now let us try to find out the second part of this very problem that is the answer for the second part of this very problem.
02:18
So to check whether this quantity will maximize the profits of both the forms or not, we need to set mr equals to mc and we need to solve for q.
02:28
So 200 minus 20 q will be here equals to 0 and thus q value is equal to 10 and we can say to find price, plug q is equal to 10 in the inverse demand function and solve for p.
02:44
So p is here going to be 200 minus 10 times q and q value is going to be 10.
02:50
So it will be here equals to 100...