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MANAGEIAL ECONOMICS (H.CRAIG PETERSEN, W.CRIS LEWIS) CHAPTER#9 PERFECT COMPETITION AND MONOPOLY SOLUTION PROBLEMS9-1 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=QD20000+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+200
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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=0Q=2000-50P50P=2000-QP=40-0.02QTR=P*QTR=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 increase9-8
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=25Deadweight loss =312.59-11
P=50-2Q
MC=10
A) Deadweight loss = (P-MC)*(QO-QM)/2TR=P*Q(50-2Q)QTR=502-2Q^2MR=50-4QMR=MC50-4Q=10
40=4QQ=10
P=50-2(10)
P=30
Deadweight loss = (30-10)*(20-10)/2
Deadweight loss =100
b) P=50-4QMR=50-8QMR=MC50-8Q=1040=8QQ=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 eliminatedb) 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