Q6 . (20 Marks ) Two firms serve a market with demand given by Q = 200 - P. There are no other suppliers . Firm One constant marginal costs of 19 dollars per unit it produces while has firm two constant marginal costs of 17 dollars per unit produced A) Assuming the firms operate as Cournot Duopolists calculate profit maximizing quantities , price and profits COURNOT Firm 1 wants to pick q , to MAX & , = (P, - AC, )q, GIVEN q2 1 = ((200 - q2) - 91 )91 - 19q1 X X q1 = (200 - q2) - 291 - 19 = 0 MR1 = MC1 q1 = (181 /2) - 1/2q2 Firm 1's Reaction Function Firm 2 wants to pick q2 to MAX & 2 = (P2 - AC2)92 GIVEN q1 2 = ( (200 - q1) - 92 )92 - 1792 8, /X q2 = (200 - q1) - 292 - 17 = 0 MR2 = MC2 q2 = (183 /2) - 1/2q1 Firm 2's Reaction Function Substituting the 2" reaction function into the 1st gives: q1 = (181 /2) - 1/2 (183 /2) + (1/4)q, = (362 - 183 )/4 + (1/4)q, = (179 /4) + (1/4)q1 (3/4)q1 = (179 /4) q1* = (179 /4)(4/3) = (179/3) = 59.67 12* = (183 /2) - 1/2q,* = (183/2) - 1/2(179/3) = (549 - 179)/6 = 370 /6 = 61.67 Q* = q * + q2* = 59.67 + 61.67 = 121.34 P* = 200 - Q* = 200 - 121.34 = $ 78.66 * = (P* - AC )q, * = (78.66 - 19 ) (59.67 ) = (59.66 ) (59.67 ) = $ 3,559.12 (per period ) 8, * = (P* - AC2)q2* = (78.66 - 17 ) (61.67 ) = (59.66 ) (61.67 ) = $ 3,802.57 (per period )