Question

The market demand curve for a pair of duopolists is given as P=38- Q where Q= Q4 + Q2 The constant per unit marginal cost is 14 for firm 1 and 17 for firm 2. Find the equilibrium price, quantity and profit for each firm in both the Cournot model and Bertrand model. (Round your answers to 2 decimal places (e.g., 32.16). Enter zero whenever required.) a) Cournot Equilibrium Price: Equilibrium Quantity for Firm 1: Equilibrium Quantity for Firm 2: Profit for Firm 1: Profit for Firm 2: a) Bertrand Equilibrium Price: Equilibrium Quantity for Firm 1: Equilibrium Quantity for Firm 2: Profit for Firm 1: Profit for Firm 2:

Answer 1

P=38-a Q= A, + Ora mc, = 14 ; MC₂ = 17. rofit for firme- 1 (..) = TR. - TC, = P. A. - TC, (38-a A, - TC. [Q-O + O2] = (38-Chi-Chala, - TC, x, = 386,-0, - chicz-TC, Differentiate west. A. - da 38 - 20. Orz-mc, o da, P Q = 38-02-14 Profit form form 2 (R2) = TR₂ - TC Ka = P. Ora - The = (38-4) - The = (38-0h D2) - TC,

K2 = 380-Q, Or- - TC2 Diff. w.rit. - daa - 38 - - 2012 - MC₂ - 0 daz I wil 20 = 38-O - 172 2 Ore = 21-2 1 O = 21-0. = 2 Solve for i) & (ii) - Qi = 34. Que 12 - 31-6x Di - 12 - 21-01 4 Ou - 48-21 - Que 4 Q = 27-O, 50 = 27 Ta = 5.4 7 Equilibrium Ou = 7.8 quantities

Equilibrium Price : P=38-0 P =38- o - a P = 38 - 5.4-7.8 P = 24.8 K = TR - TC TR = P. Q = 24.8 x 5.4 = 133.00 TC = mo.. dr = 14 x 5.4 = 75.6 a = 133.92 -75.6 5. = 58.32] Farm. I Prof au TR2 - The TR₂ = P. Oz = 24.8 x 7.8 = 193.4 TCa = MC.. Ora = 17 x 7.8 = 132.6 K = 193.44-132.6] A2 = 60.84 Firm-2 Profet

(b) Bertrand: P=38 - o a-On + O2 mc, 14 ; MC₂ = 17 Here, no different prices has been Charged by the firm's. Therefore, its omogensous goods case. (ie. Or, - Oul Equilibrium condition for irm's are - p=mc- For firm 1: P = mc, 38- a = 14 sext o = 24 For A or + Ora - Out Or = 20 - 20 =47 [or. =2805 - 10 =12 Firm - 2: P = Me, -38-a = 17) Q=21 Q = O tO2 = Ora + Ora = 2002 & 202 = 21 On = 10.5

Q = a + Ora = 12 + 10.5 Q = 22.5 P = 38 - or=38-22-5 P = 15.5 Profit of the firm's – firm 1 (A) = TR - TC, TR, - P. Ou = 15.5x 12 = 186 TC. = MC. O = 14 X2 = 168 = 186 - 168 a = 18 Form 2 (R2) = TR2 - TC2 R = P. Ca = 15.5 x 10.5 = 162.75 Tha & M. Ora = 17 x 10.5 = 178.5 K = 162.75-178.5 K2 = -15.75 [hoss because Mc > P