A homogenous product is produced by two rival firms. The firms have the same costs. The demand faced by Firm 1 is: Q1 = 40 – P1 + ½P2 %3D The demand faced by Firm 2 is: Q2 = 40 – P2 + 2P1 The firms' total cost equations are: TC1 = 50Q1 TC2 = 50Q2 a. Show that if the firms collude to maximize joint profits, setting P1 = P2, then the outcome will be the monopoly solution. Each firm's output and profit will be half of the amounts found in question la. %3D

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A homogenous product is produced by two rival firms. The firms have the same costs.
The demand faced by Firm 1 is:
Q1 = 40 – P1 + ½P2
The demand faced by Firm 2 is:
Q2 = 40 – P2 + ½P1
The firms' total cost equations are:
TC1 =
50Q1
TC2 = 50Q2
a. Show that if the firms collude to maximize joint profits, setting P1 = P2, then the outcome
will be the monopoly solution. Each firm's output and profit will be half of the amounts
found in question la.
Qi* = Q2*
%3D
p* =
TR1 = TR2 =
Ni = N2 =
b. Suppose Firm 1 cheats on the collusive agreement. Firm 2 sets the price to which the firms
agreed in part A; Firm 1 takes Firm 2's price as given, and maximizes its own profits subject
to that assumption. Find the resulting prices and outputs.
Q1* =
P1* =
P2* =
14
Transcribed Image Text:A homogenous product is produced by two rival firms. The firms have the same costs. The demand faced by Firm 1 is: Q1 = 40 – P1 + ½P2 The demand faced by Firm 2 is: Q2 = 40 – P2 + ½P1 The firms' total cost equations are: TC1 = 50Q1 TC2 = 50Q2 a. Show that if the firms collude to maximize joint profits, setting P1 = P2, then the outcome will be the monopoly solution. Each firm's output and profit will be half of the amounts found in question la. Qi* = Q2* %3D p* = TR1 = TR2 = Ni = N2 = b. Suppose Firm 1 cheats on the collusive agreement. Firm 2 sets the price to which the firms agreed in part A; Firm 1 takes Firm 2's price as given, and maximizes its own profits subject to that assumption. Find the resulting prices and outputs. Q1* = P1* = P2* = 14
C. Find the two firms' revenues, costs, and profits when Firm 1 cheats.
TR1 =
TC =
TR2 =
TC2 =
12 =
Vin
d. Use your answers above to complete the payoff matrix.
FIRM 2 COLLUDES
FIRM 2 DEFECTS
FIRM 2 →
P2 =
P2 =
FIRM 1 Į
FIRM 1 COLLUDES
Ni =
P1 =
N2 =
FIRM 1 DEFECTS
P1 =
N2 =
N2 =
e. What is the Nash equilibrium (noncooperative) solution?
P2 =
P1 =
15
Transcribed Image Text:C. Find the two firms' revenues, costs, and profits when Firm 1 cheats. TR1 = TC = TR2 = TC2 = 12 = Vin d. Use your answers above to complete the payoff matrix. FIRM 2 COLLUDES FIRM 2 DEFECTS FIRM 2 → P2 = P2 = FIRM 1 Į FIRM 1 COLLUDES Ni = P1 = N2 = FIRM 1 DEFECTS P1 = N2 = N2 = e. What is the Nash equilibrium (noncooperative) solution? P2 = P1 = 15
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