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