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Cournot vs. Stackelberg Oligopoly Suppose the inverse demand function and the cost functions for two duopolists...

Cournot vs. Stackelberg Oligopoly Suppose the inverse demand function and the cost functions for two duopolists are given by:

P = 100 – (Q1 + Q2)             C1(Q1) = 2Q1             C2(Q2) = 2Q2

a. Cournot: Assume two Cournot duopolists.

i. What is firm 1’s Quantity and Profit?

R1 = (100-Q1-Q2) * Q1

R1 = 100Q1 - Q12 - Q2Q1

MR1 = 100 - 2Q1 - Q2

C1(Q1) = 2Q1

MC1 = 2

MR1 = MC1

ii. What is firm 2’s Quantity and Profit?

R2 = (100-Q1-Q2) * Q2

R2 = 100Q2 - Q1Q2 -Q22

MR2 = 100 - Q1 - 2Q2

iii. What is the market Price?

b. Stackelberg: Assume two firms in a homogeneous-product Stackelberg oligopoly, where firm 1 is the leader and firm 2 is the follower.

i. What is firm 1’s Quantity and Profit?

ii. What is firm 2’s Quantity and Profit?

iii. What is the market Price?

c. Which (of the four) firms makes the highest profit? The lowest profit?

d. Which market has the lowest market price (Cournot or Stackelberg)?

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Answer #1

P= 100-(ait Q2) Ci (61) = 2 Q1, C2(Q2 ) = 2 Q2 (a) Cournet cluo folists Profit function of firm- T = TRI- TI - P. Q 1-20 - (Pfrom Bra 201= 98- (98-09) =) 201 = 2/98) - 98 tai 2 = 401 = 98 tai = 301 = 98 98 32.67 from Bra Q2 = 98-ai 2 => 202 = 98-98 3=) P = 300-196 3 - 104 & 34.67 T = (P2301 (1942) 98 98 2 (98 TI= (P-2) a = 9604 1067011 o By Symmetry Ti = T2 960 9604 ? 106(b) Stackelbergi from-2 as Firm-i as Leader and forower using Profit function of from-1 and Bra T,= (98-01-22 lai 98-01- (287P= 100- 73.5 = 26.5 Answer: (i) from is quantity Q1 = 49 T= (P-219,= (26.5-2) 49 = (24.5)49 Profit T, 120005 of firm- (1) firfrom 2 makes Laucest Profit T2 = 600:25 (2) market Poice with Cournot (P) 34067 Highest Profit markest Price with Stackelberg

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