Chapter#9 Perfect Competition and Monopoly Solution

MANAGEIAL ECONOMICS (H.CRAIG PETERSEN, W.CRIS LEWIS) CHAPTER#9 PERFECT COMPETITION AND MONOPOLY SOLUTION PROBLEMS 9-1 QS=20000+30P QD=40000-20P B) QS=QD 20000+30P=40000-20P 50P=20000 P=400 Q=20000+30(400) Q=32000 C) QS=20000+30P QD=50000-20P QS=QD 20000+30P=50000-20P 50P = 30000 P=600 Q=20000+30(600) Q=38000 9-2 A) QS=20000+30p QD=40000-20P QS=QD

20000+30p=40000-20p 50p=20000 P=400 P=MC 400=200+4Q 200/4=Q Q=50 b) AC=1000/50+200+2(50) =320 AC=1000/Q+200+2Q TC=AC (Q) (1000/Q+200+2Q)Q TC=1000+200Q+Q^2 ECONOMIC PROFIT=TR-TC TR=P*Q 400*50-(1000+20050+50^2) 20000-1000-10000-5000 ECONOMIC PROFIT=4000 9-3 TC=500Q-20Q^2+Q^3 MC=500-40Q+3Q^2 A) AC=MC AC=TC/Q= (500Q-20Q^2+Q^3)/Q AC=500-20Q+Q^2 500-20Q+Q^2=500-40Q+3Q^2

20Q-2Q^2=0 Q (20-2Q) =0 20-2Q=0 ,

Q=0

20=2Q Q=10 b) TR=TC P10=500(10)-20(10)^2+910)^3 P10=4000 P=400 9-4 MC=4+0.2Q P=10 P=MC 10=4+0.2Q Q=30 reduced output 9-5 QS=3000+200P QD=13500-500P QS=QD 3000+200P=13500-500P 10500=700P P=10500/700 P=15 P=MC 15=15-4Q+3Q^2/10

-4Q+3Q^2/10=0 -40Q+3Q^2=0*10 -40Q+3Q^2=0 Q (-40+3Q)=0 3Q=40 Q=40/3 B) ECONOMIC PROFIT=TR-TC TR=P*Q We can derive TC from MC as fixed cost is given 150 in question MC=15-4Q+3Q^2/10 TC=150-15Q-4Q^2+3Q^3/10 15(40/3)-(150-15(40/3)-4Q^ (40/3) +3(40/3) ^3/10) 200-150-200+355.5-237.03 ECONOMIC PROFIT= -31.53 9-6 P=200-4Q MC=4Q MR=MC TR=P*Q TR= (200-4Q) Q TR=200Q-4Q^2 MR=chg TR/Q MR=200-8Q MR=MC 4Q=200-8Q

12Q=200 Q=200/12 Q=16.7 P=200-4(16.7) P=133.2 b) NO, ECONOMIC PROFIT CAN NOT BE CALCULATED BECAUSE TC AND FOXED COST IS NOT GIVEN. 9-7 A) Revenue maximization MR=0 Q=2000-50P 50P=2000-Q P=40-0.02Q TR=P*Q TR=40Q-0.02Q^2 MR=chg TR/Q MR=40Q-0.04Q=0 40=0.04Q Q=1000 P=40-0.02(1000) P=20 b) If revenue is greater profit will also increase 9-8 Q=50-5P 0=50-5P 5P=50 P=10 CONSUMER SURPLUS PRICE-PE 10-5

=5 9-9 P=110-4Q MC=10 TR=P*Q (110-4Q)Q TR=110Q-4Q^2 MR=chg TR/Q MR=110-8Q MC=MR 10=110-8Q 8Q=100 Q=12.5 P=110-4(12.5) P=60 B) Deadweight loss = (P-MC)*(QO-QM)/2 (60-10)*(25-12.5)/2----when there will be no QO given we will derive it by doubling QM 12.5+12.5=25 Deadweight loss =312.5 9-11 P=50-2Q MC=10 A) Deadweight loss = (P-MC)*(QO-QM)/2 TR=P*Q (50-2Q)Q TR=502-2Q^2 MR=50-4Q MR=MC 50-4Q=10

40=4Q Q=10 P=50-2(10) P=30 Deadweight loss = (30-10)*(20-10)/2 Deadweight loss =100 b) P=50-4Q MR=50-8Q MR=MC 50-8Q=10 40=8Q Q=5 P=50-4(5) P=30 Deadweight loss = (30-10)*(10-5)/2 Deadweight loss =50 9-12 P=50 MC=10+2Q A) P=MC 50=10+2Q 40=2Q 40/2=Q 20=Q B) P=51 P=MC 51=10+2Q

41=2Q 41/2=Q 20.5=Q c) If MC increase by 1 and the price remain same so output will decline b/c cost is increasing and we have no changes in price. 9-13 TR=300Q-Q^2/2 TC=5000+60Q+Q^2 A) MR=MC 300-2Q/2=60+2Q 300-60=2Q+2Q/2 240=4Q+2Q/2 480=6Q Q=80 ECONOMIC PROFIT=TR-TC 300(80) - (80) ^2/2-5000-60(80) + (80) ^2 24000-3200-5000-4800-6400 ECONOMIC PROFIT=4600 B) AC=MC AC=TC/Q= (5000+60Q+Q^2)/Q AC=5000/Q+60+Q AC=MC 5000/Q+60+Q=60+2Q 5000/Q=1Q 5000=Q^2

Q= 70.7 ECONOMIC PROFIT=TR-TC 300(70.7) - (70.7) ^2/2-5000-60(70.7) + (70.7) ^2 ECONOMIC PROFIT=4470 9-14 p=16 TC=Q^3/3-5Q^2+40Q P=MC 16=3Q^2/3-10Q+40 Q^2-10Q+24=0 For ax2 + bx + c = 0, the value of x is given by:

x = [ 10 ± √(102-4×1×24) ] / (2×1) Solve:

x = [ 10 ± √(100-96) ]/2 x = [ 10± √(4) ]/2 x = ( 10 ± 2 )/2 x = 6 or 4

9-15 P=12Q^-1/3 Mc=2 FIRST WE WILL CALCULATE Q2-q1/p2-p1 (P/12)^-3=Q^-1/3*-3 Q=12^3P^-3 Q=1728P^-3

Q2-q1/p2-p1=1728(-3)P^-3-1 =-5184P^-4 SECONDLY Mc=P=2 THIRDLY P=12Q^-1/3 (2/12)^-3=Q^-1/3*-3 6^3=Q Q=216 Q2-q1/p2-p1*P/Q -5184P^-4*2/216 -24/P^4*2 AS P=2 -24/2^4*2 =-3 B) MC=MR 2=8Q^-1/3 8/2=Q^0.33 (4)=Q1/3*3 Q=64 P=12/64^0.33 P=3 9-16 AC=10-0.2Q+0.005Q^2 Ac’=-0.2+0.01q=0

Q=0.2/0.01 Q=20

9-17 TR=1000Q-Q^2 TC=-200Q-Q^2+Q^3 MR=MC 1000-2Q=200-2Q+3Q^2 1200=3Q^2 400=Q^2 Q=20 TR=P*Q TR=PQ P=1000Q/Q-Q^2/Q P=1000-20 P=980 9-18 AC=50-6Q+0.2Q^2 P=5 a) In the long run profit is eliminated b) AC=MC 50-6Q+0.2Q^2=50-12Q+0.6Q^c 6Q=0.4Q^2 Q=15

c) AC=50-6Q+0.2Q^2 AC=50-6(15)+0.2(15)^2 AC=5 9-19 P=80-4Q TC=10Q+Q^2 A) MC=MR TR=P*Q TR= (80-4Q) Q TR=80Q-4Q^2 MR=80-8Q TC=10Q+Q^2 MC=10+2Q MC=MR 10+2Q=80-8Q 10Q=70 Q=7 B) ECONOMIC PROFIT=TR-TC 80(7)-4(7) ^2-10(7)-(7) ^2 ECONOMIC PROFIT=245 9-20 TC=1000Q-30Q^2+Q^3 SHUTDOWN=MC=AC

1000-60Q+3Q^2=1000-30Q+Q^2 2Q^2=30Q Q=15 P=MC P=1000-60(15) +3(15) ^2 P=775 BELOW 775 FORM SHOULD SHUTDOWN ITS OPERATION 9-21 TR=480Q-8Q^2 TC=400+8Q^2 A) MC=MR 16Q=480-16Q 480=32Q Q=15 B) P=MC P=TR/Q P=480-8Q P=MC 480-8Q=16Q 480=24Q Q=20 P=480-8(20) P=320