https://www.nicovideo.jp/watch/sm34645513 https://www.youtube.com/watch?v=1WT77eYBpN4

2. “Happiness can be found, even in the darkest of times,
if one only remembers to turn on the light.”
— Albus Dumbledore —

4.
Q = 100 − P
Q = qA + qB =
160
3
qA
qB
(
80
3
,
80
3
)
Q = 100 − P
P = 20
160
3
140
3

5. Q = 100 − P
Q = P
Q = 100 − P
P = 20
200
3 Q = 100 − P
Q = P
100
3
200
3
Q = 100 − P
P = 20
160
3
140
3
Q = 100 − P
Q = P
100
3
200
3
Q = 100 − P
P = 20

6.
Q = 100 − P
qi
πi(qi) = P(Q)qi − Ci(qi)
Q = q1 + q2 + … + qn
dπi(qi)
dqi
= 0
P(Q) = 100 − Q
Ci(qi) = C(qi)

7.
Q = 100 − P
πi(Q) = P(Q)qi − C(qi)
dπi(Q)
dqi
= 0 ⟺ qi(q−i) = 40 −
1
2
q−i
P(Q) = 100 − Q = 100 − (q1 + q2 + … + qn)
⟺ πi(Q) = (100 − (q1 + q2 + … + qi + ⋯ + qn))qi − 20qi
q−i = q1 + q2 + … + qi−1 + qi+1 + ⋯ + qn

8.
Q = 100 − P
qi(q−i) = 40 −
1
2
q−i
Q =
n
∑
i=1
qi(q−i) =
n
∑
i=1
{40 −
1
2
q−i} = 40n −
1
2
(n − 1)Q
4
∑
i=1
q−i = q2 + q3 + q4
+q1 + q3 + q4
+q1 + q3 + q4
+q1 + q2 + q3
q−1
q−2
= Q − q1 + Q − q2 + Q − q3 + Q − q4 = 4Q − Q = (4 − 1)Q
⇒ Q(n) =
80n
n + 1
q*i
=
1
n
Q =
80
n + 1 Q(2) =
2 * 80
2 + 1
=
160
3

9.
Q = 100 − P
Q(n) =
80n
n + 1 Q = 100 − P
P = 20
80n
n + 1
100 + 20n
n + 1
Q(n) =
80n
n + 1
→ 80

10. Q = 100 − P
Q = P
Q = 100 − P
P = 20
200
3 Q = 100 − P
Q = P
100
3
200
3
Q = 100 − P
P = 20
160
3
140
3
Q = 100 − P
Q = P
100
3
200
3
Q = 100 − P
P = 20

13. See you next time