Solutions to Homework Assignment 6 (Chapter 8).doc

SolutionstoHomeworkAssignment6(Chapter8). AVC=(1/Pb)xAPb. ForQ=100,APb=100/2=50,andAVC==(1/50)xAPb. Pb==20. TVC=bxPb=2x20=40. TFC=STC-TVC=240-40=200. SMC MPb OutputQ Inputb APb AVC STC - - 0 0 - - 200 50 100 2 50 240 75 250 4 280 50 350 6 320 425 8 360 25 475 10 400 500 12 . FirmshouldoperateatQ==475,MC=>MR=,and marginalprofitwillbenegative. AtQ=425,PROF=TR-STC=-360=-,aminimumloss. However,thefirmshouldoperateintheshortrun,sinceP>. AtMR-SMC=60-204+6Q-^2=-144+6Q-^2=0. Usingquadraticformula,Q1=40andQ2=60. ForQ=40,PROF=TR-STC=60x40-4,000-8,160+4,800-1,280=-6,240. ForQ=60,PROF=TR-STC=60x60-4,000-12,240+10,800-4,320=-6,160 AtQ=60,willhavealossof-6,160,andhenceshouldshutdown. 8. MR P Q TR STC AVC TVC MC - 110 10 1100 1400 60 600 - 90 100 20 2000 1500 35 700 10 70 90 30 2700 1700 30 900 20 50 80 40 3200 2000 30 1200 30 30 70 50 3500 2400 32 1600 40 10 60 60 3600 2900 35 2100 50 -10 50 70 3500 3500 2700 . Q=40,P==50profitdecreasessinceinthatrangeMC>. Profit=3,200-2,000=1,. Sincethefranchisefeeisafixedcost,, theprofit-maximizingquantityandpriceremainthesame,although . InversedemandfunctionP(Q)=80-=P(Q)xQ=80Q-^2. TomaximizeprofitMR-MC=8