00:01
Okay, so to find the quantity at which the firm's total revenue is maximized, we want to determine the level of output that corresponds to the peak of the total revenue function.
00:11
So total revenue is calculated as the product of quantity and price.
00:16
So we have that total revenue is equal to quantity times price.
00:23
Now we're given the demand function 600 minus 3p.
00:26
We can find the corresponding price p, we're just solving for p.
00:29
So we get that, well we get 3p is going to be equal to 600 minus qd.
00:37
And then therefore we get p is equal to 600 minus qd.
00:47
Okay, so then just putting the price p back into the revenue function, total revenue is equal to q times p, so it's equal to q times the quantity 600 minus q.
01:01
And then to find the quantity at which the total revenue is maximized, we just take the derivative of the total revenue function, uh, with respect to q and then set it equal to zero...