Question

Problem 2. Cournot Competition with Three Firms Suppose there are three identical firms engaged in quantity competition. The demand is P=1-Q where Q = 91 +92 +93. To simplify, assume that the marginal cost of production is zero. Compute the Cournot equilibrium (i.e., quantities, price, and profits).

Answer 1

۳ - م و -۱ + 1 = ده + 2 = 9 - ۳۷ د = = 0 - 2 (و- - ي (ع) ز% (2f23 - ره ر4 - 3 42 - 9123 227, = 1- 24 - 22 - 23 زن put ot, DIT 37 o - ر%8 - 1 - 2 2 0= (= دو + 42 پرو و 2 = 242 - 22 = ه (ي - 6- و - ۶ (23 + 42 - (۶) 43 42 - 2 - ر2 42 - دو - 02 = = % - 242 - 22 02 put t 2712 22 042 =0 4 - 1 ع و = 23 - 342 - 3و 4 a + 1 = | - = 3 ۱۱ = % 3م 23 - ہ ۔ 23 (8 - و = 3 - %3 4) + 2 + 23) - 2 % 23 - - 23 - 2ع 3

DIT 3 = 19,- 22 - 223 093 put op zo - 1A a 93 -qi-q2- 223 aut 92 +223 = 6 =) From , & cilig 1-1-8 221 + 22 +23 = 1 at 292 +93 = 1 927 92 +993 1 2 1 1 22 / 3 93 i A1 = 2(4-1) - 1 (2-1) it (1-2)

Lucия (та т му "s_nulo TAI = 1 1 2 1 1 2 1 = 114-1)-1(2-1) + 1 (1-2) = 3-101 A2) = = 2(2-1)-1(2-1) + (1-1) 2-1 to =1 A3) = 1 2 - - 2(2-1)-1(1-1) +1(1-2) = 2 -0-1 =] q) = Al TAI 423_192) JAL TAI

= 2+ 22 + 23 __= + ५ + + = 3 ५ p = - 6 =- 34 [1] = ११) - TC) | 44 - - 12 = 22 - 12 _ = ११, - To -० =