https://www.nicovideo.jp/watch/sm34569425 https://www.youtube.com/watch?v=i2iCYz2ouzg

2. “Wit beyond measure is man’s greatest treasure.”
— Luna Lovegood —

6.
Q = 100 − P
π(qi) = Pqi − C(qi)
dπ(qi)
dqi
= P −
dC(qi)
dqi
= 0
C(qi) = 20qi
dC(qi)
dqi
= 20
Q = 100 − P
P = 20

7.
Q = 100 − P
Q = 40
π(Q) = P(Q)Q − C(Q)
dπ(Q)
dQ
=
d(P(Q)Q)
dQ
−
dC(Q)
dQ
= 0
dP(Q)Q
dQ
=
d
dQ
(100 − Q)Q = 100 − 2Q
P(Q)
Q = 100 − P
dC(qi)
dqi
= 20
P = 20

8.
Q = 100 − P
qA, qB
πi(qi) = P(Q)qi − C(qi)
Q = qA + qB
dπi(qi)
dqi
= 0
P(Q) = 100 − Q = 100 − (qA + qB)

9.
Q = 100 − P
πi(Q) = P(Q)qi − C(qi)
Q = qA + qB
dπA(Q)
dqA
= 0 ⟺ qA(qB) = 40 −
1
2
qB
P(Q) = 100 − Q = 100 − (qA + qB)
⟺ πi(Q) = (100 − qA − qB)qi − 20qi

10.
Q = 100 − P
qA(qB) = 40 −
1
2
qB
qB(qA) = 40 −
1
2
qA
qA
qB
(
80
3
,
80
3
)

11.
Q = 100 − P
Q = qA + qB =
160
3
qA
qB
(
80
3
,
80
3
)
Q = 100 − P
P = 20
160
3
140
3

12. 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

15. See you next time