4. Two firms with differentiated products are competing in prices with the following demand curves QA = 80 - 2PA + PB and QB = 100 - 2PB + PA Assume production is costless. a. Give equations for and graph each firm's reaction curve. b. If both firms set their prices at the same time, what is the Nash equilibrium price, quantity, and profit for each firm? c. Suppose A sets its price first and then B responds. What price does each firm set now? What are their demands and profits? d. Compare the profits from part b and c. Is there first mover advantage in price competition? Why or why not? 13r 2 QA= 50-2DA +PB A BDI 25 213=105-2 PB+ PA 20 PA B A: (80 - 2 PA + PB) PA 13 ( 100 - 2 PB+PA) PB = 80 PA - 2 PA + PAPB 100 PB - 2 P13 + PAPB MR: 80- 4DA +PB =0 MR = 100- 4PB + PAZO (60-2 Pat ( 25+2 PAI ) PA 80+PB = 4PA 100 + PA = 4PB Bra 20 + 2 PB = PA Brb 25 +GPA=PB J - ( 105 - 7PA ) PA 105 PA-7 DA 20 + 4 ( 2 7 + 4 PA ) = PA 25 + 4 ( 20 + 4 PB ) = PB 2 20 + 6 .25 + 76 PA = PA 25 + 5 + To PB = PB MR = 105 - 3,5 PA=0 PB= 25+4.30=32.5 26:25 = 16 PA 105= 3.5PD 30 = 10 Pb PA = 30 = 65 PA= 28 PR= 32 RA= 80-60+32.5 Profit b: 2/12.5 QA= 80- 2(28)+32 QB= 100-2-32 252.5 +28 1STAA= 1575 = 56 - 64 ProfitA = 28x 56 profitb D these is a sligt first mover advantage = 1560 - - 2048