00:01
Let c of x and r of x be the total cost and revenue at a production level of x units.
00:06
Suppose c prime of x is greater than 0 and r prime of x is less than 0.
00:11
Now, our p of x is equal to the difference between the revenue and the cost, that is r of x minus c of x.
00:23
So if we take the derivative of p, we get p prime of x equal to r prime of x.
00:31
Minus c prime of x.
00:34
If c prime of x is greater than zero and r prime of x is less than zero then our p prime of x equals a negative number minus a positive number this gives us a negative number so this has to be less than zero so the marginal profit will be negative and this statement is true.
01:03
Now for the second problem we have, if the marginal profit is positive for some x, then the company must be earning a profit at that production level.
01:14
Now when we say marginal profit, it refers to the profit earned by a business.
01:21
If p prime of x is greater than zero, then r prime of x must be, or r prime of x minus c prime of x must be, must be greater than zero.
01:34
That means our prime of x will be greater than c prime of x...