MANAGEIAL ECONOMICS (H.CRAIG PETERSEN, W.CRIS LEWIS)

CHAPTER#7 COST THEORY AND ANALYSIS

SOLUTION

PROBLEMS

7-1

Y=A+BX

We can calculate total cost by the method of linear regression with the help of financial calculator.

TC=1000+80Q

TFC=1000

TVC=80Q

AVERAGE TOTAL COST=TC/Q

TC= (1000+80Q)/Q

ATC=1000/Q+80

AVERAGE FIXED COST=TFC/Q

AFC=1000/Q

AVERAGE VARIABLE COST=TVC/Q

80Q/Q=80

MC=CHG TC/CHG Q

RATE OF OUTPUT TOTAL COST MARGINAL COST0 1000+80(0)=1000 -2 1000+80(2)=1160 804 1000+80(4)=1320 807 1000+80(7)=1560 8010 1000+80(10)=1800 80

7-2

Y=A+BX

FC=5000

We can calculate total variable cost by the method of linear regression with the help of financial calculator.

TC=5000+1000Q

AVERAGE TOTAL COST=TC/Q

TC= (5000+1000Q)/Q

ATC=5000/Q+1000

AVERAGE VARIABLE COST=TVC/Q

1000Q/Q=1000

MC=CHG TC/CHG Q

RATE OF OUTPUT TOTAL COST MARGINAL COST1 5000+1000(1)=6000 -2 5000+1000(2)=7000 10003 5000+1000(3)=8000 10004 5000+1000(4)=9000 10005 5000+1000(5)=10000 1000

7-3

TC=200+5Q-0.04Q^2+0.001Q^3

MC=5-0.08Q+0.003Q^2

a) ATC , AVC , AFC , FCFC=200

AVERAGE TOTAL COST=TC/Q

(200+5Q-0.04Q^2+0.001Q^3)/Q

ATC=200Q^-1+5-0.04+0.001Q^2

AFC=200Q^-1

AVERAGE VARIABLE COST=TVC/Q

(5Q-0.04Q^2+0.001Q^3)/Q

AVC=5-0.04Q+0.001Q^2

b) AVC=MC

5-0.04Q+0.001Q^2=5-0.08Q+0.003Q^2

0.04Q-0.002Q^2=0

Q(0.04-0.002Q)=0

0.04=0.002Q

Q=20

C) IF FC=500 THE RESULT WOULD BE SAME

7-4

TR=50Q

TC=10000+30Q

A) TR=TC

50Q=10000+30Q

Q=500

B) Q=FC+PROFIT/P-AVC10000+20000/50-30Q=1500

7-5TFC=20, P=10, PROFIT=2A) BREAKEVEN OUTPUT=FC/P-VC

CM=P-VC2=10-VCVC=8BREAKEVEN OUTPUT=20/10-8=10

B) PROFIT ELASTICITY=Q(P-VC)/Q(P-VC)-TFC20(10-8)/20(10-8)-2040/20

=27-6

A) BREAKEVEN OUTPUT=FC/P-VCi) 500000/40-3=13513.5ii) 510000/40-2=13421.0iii) 380000/40-7=11515.1iv) 200000/40-3=5405.4

B) TO INCREASE THE SIZE OF BUDJET,STUDENT MUST INCREASE AND FIXED COST CAN BE CONTROL BY INCREASING THE WORKING HOURS OF FACULTY.

C) ADV: EDUCATION COST WILL INCREASE SO THERE WILL BE MORE PROFIT.

7-7

P=20

A) BREAKEVEN OUTPUT=FC/P-VCi) 200/20-15=40ii) 500/20-10=50iii) 1000/20-5=67

B) PROFIT ELASTICITY=Q(P-VC)/Q(P-VC)-TFCi) 200(20-15)/ 200(20-15)-200=1.25ii) 200(20-10)/ 200(20-10)-500=1.33iii) 200(20-5)/ 200(20-5)-1000=1.5

C) Highly leveraged is (ii) and least leveraged is (i)

7-8

TR=2000000

TC=400000+1010000

ECONOMIC PROFIT=TR-TC

2000000-400000-1010000

ECONOMIC PROFIT=590000

Office should be opened.

7-9

A) ACCOUNT PROFIT=10000 , SALARY=20000 , RATE OF INTEREST=15%of 80000=12000ACCOUNT PROFIT 10000SALARY FORGONE (20000)RATE OF INTEREST (12000)ECONOMIC PROFIT (32000)

B) TO have economic profit at breakeven point so we will assume it 0 and we have to do reverse calculation to calculate account profit.

ACCOUNT PROFIT 32000SALARY FORGONE 20000RATE OF INTEREST 12000ECONOMIC PROFIT (0) REVERSES CALCULATION

7-10P=80, FC=200000, PROFIT=32

A) PROFIT ELASTICITY=Q(P-VC)/Q(P-VC)-TFCi) 8000(80-48)/ 8000(80-48)-200000=4.57ii) 10000(80-48)/ 10000(80-48)-200000=2.60iii) 12000(80-48)/ 12000(80-48)-200000=2.08

B) FC=300000 VC=48-8=40 P=80i) 8000(80-40)/ 8000(80-40)-300000=16ii) 8000(80-40)/ 8000(80-40)-300000=4iii) 8000(80-40)/ 8000(80-40)-300000=2.66C) Company increase risk and return by making investment in capital.

7-11A) BREAKEVEN OUTPUT=FC/P-VC

10000/(900-700)=50B) Assume Q=52

PROFIT ELASTICITY=Q(P-VC)/Q(P-VC)-TFC52(900-700)/52(900-700)-10000=26%As Q increases profit elasticity declines

C) Q=60 , FC=11000 VC=70060(900-700)/60(900-700)-11000=12%Q=60, FC=10000 VC=40060(900-400)/60(900-400)-10000=1.5%

PROVED7-12ADD FLIGHTS7-13A=TC=1000+0.03QB=TC=300+0.04QC=TC=100+0.05QB=C300+0.04Q=100+0.05QQ=20000If Q is less than 20000 than B is less than CA=B1000+0.03Q=300+0.04Q700=0.01QQ=70000If Q is less than 70000 than B is less than A7-14PROFIT+FIXED COST=100000UNITS=10000VARIABLE COST=4VARIABLE COST=10000*4=40000P=?TR=140000TR=P*Q140000=P*10000P=140000/10000P=14PROFIT+FIXED COST=100000UNITS=11000VARIABLE COST=4VARIABLE COST=11000*4=44000P=?TR=144000TR=P*Q144000=P*10000P=144000/10000P=13.09CHG IN PRICE=14-13.09CHG PRICE=0.90CHG IN PRICE= (14-13.09)*11000CHG IN PROFIT=100001

7-15a) TC=200Q-0.004Q^2LONGRUN AVERAGE COST=TC/QLAC=200-0.004Q^27-16TC=200-2Q+0.05Q^2A) AC=TC/Q

AC=200Q^-1-2+0.05QAC’=-200Q^-2-2+0.05Q=0=-200/Q^2+0.05Q=00.05Q=200/Q^2SQ 4000=Q^2Q=63.2

B) AC=200Q^-1-2+0.05QSO -1+1=0DECREASING RETURN TO SCALE

C) MKT PRICE=4.32AC=200/63.2-2+0.05 (63.24)3.162-2+3.162=4.327-17TC=100Q-3Q^2+0.01Q^3MC=100-6Q+0.03Q^2AC=TC/Q100-3Q+0.1Q^2WE CAN SOLVE THIS BY 2 METHODS i) By taking AC’ii) AC=MC

WE WILL COLVE THIS BY AC’-3+0.2Q=00.2Q=3Q=15

7-18

FC=25000

TVC=0.15Q+0.1Q^2

ATC=TC/Q

TC=25000+0.15Q+0.1Q^2

ATC=25000Q-1+0.15+0.1Q

-25000/Q^2+0.1=0

25000/Q^2=0.1

25000/0.1=Q^2

Q=500

7-19

TR=TC

P*Q=1000+200Q-9Q^2+0.25Q^3

P= (1000+200Q-9Q^2+0.25Q^3)/Q

P=1000/Q+200-9Q+0.25Q^2

VC=200Q-9Q^2+0.25Q^3

AVC=200-9Q+0.25Q^2

AVC’=-9+0.5Q=0

0.5Q=9

Q=18

P=1000/18+200-9(18)+0.25(18)^2

P=174.5

7-20

A) ECONOMIC PROFIT=TR-TC20Q-16+17Q-9Q^2+Q^3ECONOMIC PROFIT=3Q-16-9Q^2+Q^3

B) MC=17-18Q+3Q^2C) Q=8

AVC=17-9Q+Q^2=17-9*8+8^2=9