00:01
So here we are optimizing, right? we have a demand function, which is q is equal to, sorry, 80 minus 0 .025p.
00:10
We have cost function, right, which is 100 plus 20 q.
00:15
So for a, in competition, the rule of thumb is to maximize profits, you said price is equal to marginal cost.
00:26
Well, what is marginal cost? marginal cost is the derivative of cost with respect to quantity, which is just 20.
00:34
What is price? well, to get price, we need to rearrange.
00:36
0 .025p is equal to 80 minus q.
00:43
If you divide by 0 .025 over 0 .025, that gives you, sorry, p is equal to 3 ,200 minus 40 q.
00:57
So now we set these things to be equal to each other.
01:01
And with that, i get 3200 minus 40q is equal to 20.
01:12
So i get 3 ,180 is equal to 40q, which implies that q is equal to 79 .5, right? that's how i would figure that one out...