Question

just #5

Assume that the pizza market consists of two firms, Conan's and Pizza Hut. The price of a Conan pizza is denoted by Pc and the price of a Pizza Hut Pizza is Ph. Both sellers have a marginal cost of $5 for another pizza. The demand curves facing the two firms are: Conan ("c"): Qc = 500-35Pc + 20Ph Pizza Hut ("h"): Qh = 625-41Ph+26Pc. 1. Calculate the equilibrium prices. Pl(c)=(Pc-5)(500-35Pc+20Ph) dPi(c)/dPc=675-70Pc+20Ph=0 70PC-20Ph=675 P c=13.78 Pi(h)=(Ph-5)(625-41 Ph+26Pc) dpi(h)/dPh=830-82Ph+26Pc=0 -26Pc+82Ph=830 Ph=14.49 lalu

Answer 1

#5. Poolit function of fim Conan. Freeze Te = TRc- Toc = Pc . Qc-mcc.gc. Tic = Pc (500- 35 Pc + 18 lnt & Pv J - 5 (500-356 + 18 Pn +8 kv) Partial Differentiate wit lc ITC - 500-70 Pc + 18 Pn + 8 Pu + 175 = 0. d pc 675+ 18 Ph + 8 kv = 70 Pc Best Responce funch of Conan SC = √ [675 + 18 Put 8 h 7 - i Now for firm- 1. TH= TRH- Tch = Pr. Qn- mcn. On Tin = ln (625-4P + 18 Pc + 10 Pv] - 05 [625-414 + 18 Pct loh Partial differentiate court Po ITH = 625-82 Pu + 8 Pc + 10 lv + 205 = 0 - 82 ln - 625+265 + 8 P + lopu » Pa = . 525 + 20 5 + 6 - low 1 In = - (830 + 8 let 10 to ] – 82 JPM

Foo from varsity TV = TRY - TCV = Pr. Qv- mcr. Qv TV = Pv (485-30 pv + 12 Pc + 9 in ) - 5 (485-30 pv + 12 Pet 9P4) Partial differentiation of Tv wrt Pr 485-60 pv + 12 Pc + 9 + 150 = 0 => 635 - Bolu + 12 Pc + 9 Pro = 60 pv = 635+ 12 ft 9 Por - Pr. = 1 [635 + 121 + 9 Ph] Best Res Ponce function of from varsity. Pvc Lo [635+ 12 + 9 PM ] ü) method to solve this (3) equation System. Substitute ii) in (i) (ن) n ( utt ( Pc = – (675 + 18 Pr + 8 P ] (li in i) - [675 + 18 ( 830 + 8 Pe + 10 kv ] + 8 h 1

75 + 18X830 + 18x8 80 82 82 S2 to los + 10 + 10 29 Be + 18 R +R] noke - (675 + 8x8 30 + 18xP Pc + 180 pv + 8 Pv] 675 + 18x830 + 18x P, 82 82 5740 Pc = 55350 + 14940 + 144 Pc + 180 Pv + 656 Po 2 5740 Pc - 144 Pc = 70290 +836 Pv 1 (5596) Pc = 70290 + 8 36 P l - (1) Now is in (ili REL (635 +12 %c + 9 PM] 60 Pu= 635+ 12 Pc + 9 1830 + 8 lc + 10 Pv] 60 L 4920 PV = 52070 +984 Pc + 7470 + 72 Pc + 90 Pv (4920-90) Py = 52070 +7470 + 1984 Pc +70pc) 4830 P = 59540 + 1054 PC 14830 PV = 59540+ 1054 Pc Solving C) and (2) Simcar teously

5596 Pc = 70290 + 836 [59540+ 1054 lc] 4830 5596 Pc = 70290 + 836×59540 + 836x1054 Pc 4830 4830 I 5596 Pc = 70290 + 10305.47417 182.4314 PC 6-182 80595.4741 = PC = 8059504741 5413.5696 = 14.8876 using equation (2) 4880 Py = 59540 + 1054 * 14.8876 = 59540 + 15691.5304 P = 752.31. 5.304 – 15.5758 4830 - thangat IP = 15.5758 Now using equation ( Pr = 1 [830 + 8 Pc + 10 lo7 82 Pn = 830+ 8 (14.8876 ) +10(15.5758)

82 /n = 830 + 119.1008 + 155.158. Ph = 1104.2588 82 I In= 13.4666 - Jo re & Nash equiliboium Prices PC = 14.8876 Py = 15.5758 Pr = 13.4666 Picking up upto Four dicimal hots digit gives This numbers. if we Pick Less or more you may get different ho's