8. A.
i. When they cooperate then the cartel will be as good as monopoly. Thus, they will be producing up to MR = MC
P = 60 - Q
TR = 60Q - Q2
Differentiating TR wrt Q we get
MR = 60 - 2Q
Similarly differentiating TC wrt Q we get
TC = 24Q
MC = 24
Now equate MR = MC
60 - 2Q = 24
2Q = 60 - 24
2Q = 36
Q* = 18 units
P* = $ 42 per unit
Each firms output = 9 units
Profit of each firm = 42*9 -(24*9) = 378 - 216 = $ 162
ii. When they chose not to cooperate
P = 60 - Q1 - Q2
TR1 = 60Q1 - Q12 - Q1Q2
MR1 = 60 - 2Q1 - Q2
MC = 24
Therefore, 60 - 2Q1 - Q2 = 24
Similarly, solve for Q2
TR2 = 60Q2 -Q1 Q2 - Q22
MR2 = 60 - Q1 - 2Q2
Plug in Q1
Similarly, Q1 = 18 - 0.5*12 = 12 units
P = 60 - 12 - 12 = $ 36 per unit
Profit of both firms = 12*36 - 24*12 = $ 144
iii. When one firm cooperates and other don't
Let us assume firm 1 abides by the agreement thus as per agreement the firm will produce only 9 units(Refer part i).
Firm 2 cheat then the reaction function will be
Plug in Q1 and solve for Q2
Total output,Q = Q1 +Q2 = 9 + 13.5 = 22.5
P = 60 - Q
P = 60 - 22.5
P = $ 37.50 per unit
Profit of firm 1= 37.50*9 - 24*9 = $ 121.50
Profit of Firm 2 = 37.50*13.5 - 24*13.5 = $ 182.25
B. When the firms set the output level simultaneously then the output will be 12 each and price will be $36
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