Question

= Consider an industry consisting of two firms which produce a homogeneous commodity. The industry demand function is Q = 100 – P, where Q is the quantity demanded and P is its price. The total cost functions are given as C1 = 50q1 for firm 1, and C2 = 60qz for firm 2, where Q 91 +92. a. (6 points) Suppose both firms are Cournot duopolists. Find and graph each firm's reaction function. What would be the equilibrium price, quantity supplied by each firm and their profits? b. (5 points) Now suppose the firms start acting as Stackelberg duopolists. Suppose in particular that firm 1 acts as the leader, whereas firm 2 acts as the follower. Find the new equilibrium price, quantity produced by each firm and the profits. Comment on equilibrium price, total output and total surplus in comparison to the Cournot equilibrium. c. (5 points) Suppose the two firms merge into one firm. Compare the profits in this case with those under the Cournot conditions assumed in (a) above. d. (4 points) If the firms got into a Bertrand competition, what is likely to happen? You do not need to solve the problem; just explain verbally.

Answer 1

= 100-P 50 q1 (баилома и гол) 609 G Q qi+92 P= 100 - Q P = 100 - 91-92 Poolit of fiyat Total lost To fal Revenue 50q Pig 50 qr n = (100-9, -92) 91 Dift wit to 16 we ( get ive - - 100-aq-q2 50 og Tue put og 50 - q2 = sql que 50-92 {BR, Xunchan (92) 4

Profit of fim a ta - 60 q 2 (100-91-92) q. 6042 100 - q - 2q2 - 60 Ona 092 z put saz 292 40 - 992 - 9 2 40 q = 892 40-91 92 BRath (q) = 40-q 2 subsitut the value of qi q2, we get since 92 4o-q 2 0 2 242 - 40 - ( 50-22) » 292 80 50 +92 9 D 4q2 = 30 +92

S 392 3 30 6 ใน 10 Subsitute ใน M ++ น- 56 - 10 2 ¥ E 10 40 . 1 น. 3 0 9- 50X4. ++ 4) BR2 t 0 10 40 30 15 ++ P = 100 ใน = 2 P= P= 160 10 - 10 100 - 30 p* - 10 ๐ ๐ - 40 ( 20) 50 C80) = 400-

in ournot to 5 in stackleberg Profit of from I has increased to 450 from uoo in cournot and from fallen to in cournot үхри لوا 25 100

comparison to courneet (400 HOO = 500). 80 will in edy In case into Bertrand competition, then a price game they play in Contrast to quantity game cournot model. they will equate there Best response Junction in terms of price and the firm newing price takel all the market here as there products are homogenous will