Furthermore, I tried testing this out with real numbers and it didn't work.
I set Qh = 12 - 0.5P and Ql = 8 - 2P
Therefore MRh = 12 - P and MRl = 8 - 4P
I then set MC = 2
If the firm can price discriminate:
Firm maxes profits re H where MRh = MC
12 - P = 2
P = 10
Qh = 12 - 0.5(10) = 7
Firm maxes profits re L where MRl = MC
8 - 4P = 2
P = 1.5
Ql = 8 - 2(1.5) = 5
If the firm can't price discriminate:
Q*= Qh + Ql (P =< 4 because we can't have Ql < 0)
= (12 - 0.5P) + (8 - 2P) = 20 - 2.5P
=> MR* = 20 - 5P
Firm maxes profits where MR* = MC
20 - 5P = 2
P = 3.6
Q* = 20 - 2.5(3.6) = 11
But Qh + Ql = 12
12 <> 11 ???
Last edited by a moderator: Jun 18, 2017