Question

3. Coumot Competibion (26 points) Consider a Cournot model. The market demand is p-130-q-q Firm l's marginal cost is 10, and fim 2's marginal cost is also 10. There are no fixed costs. A. (10points) Derive the best response function for each firm B. (6 points) Find the Nash Equilibrium.

Answer 1

Soluben market damand function Is A)The P 130-a,-02 The prspt Lunchion tor eath fum lostunchion tor tum pav ctala (130-01,-9W c6) The m Chooses it output louel () to na X Inze ppd /30-29-2 i= 120-a/2 = 0 > bost n0spon se funcn 2 w्त 130-29/-4 120-9/ best esponue Luncten fum 2 The best sasponse furchon o eah Lim aue us he lovel autput that op tunuuu Hhe dutput leuel o un 2/1) The jum 112) best 9asponse function ane 120-V2 R2 191) 12 0- 2. csScanned with CamScanner

Nash equilib ILM S oo taned at dhe indessection best gesponso Lunction the 120-42 120-4 2 (2) (1) n Subs ti tute 120- 0/2 120 20 2 2 3V1 30 4 4b V = !20-V Auo The (Vi, V2)=/40, 40) Nas h =40 (C)The Markat P 130-40-40 130-Vi 50 P = 50 The propt of each n Is 40х40 50- 10) i T 1600 Pa/ 40Y 40 1600 л, Aus 50 x4D 10х40 5 0 6o0 D P 130 120 Here |On the we haue P en dhe Verntical axis heru z0 ntal axis Tue mauhet he aubrum auAnty is =, +% = &0

Consumey Surp lu he duerence be tuaon t actual maximum ling ness to pay and the euce paid dumes a/uantity 1TI IS quen bythe ara a truangle A area АBС (130-50)x8o AbC 3200 Answer lonsune Susplu 3 200 1S ICH Seanned ith CamScanner