Chapter#7 Cost Theory and Analysis Solution
Content
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
0
2
4
7
10
TOTAL COST
1000+80(0)=1000
1000+80(2)=1160
1000+80(4)=1320
1000+80(7)=1560
1000+80(10)=1800
MARGINAL COST
80
80
80
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
1
2
3
4
5
7-3
TC=200+5Q-0.04Q^2+0.001Q^3
MC=5-0.08Q+0.003Q^2
a) ATC , AVC , AFC , FC
FC=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
TOTAL COST
5000+1000(1)=6000
5000+1000(2)=7000
5000+1000(3)=8000
5000+1000(4)=9000
5000+1000(5)=10000
MARGINAL COST
1000
1000
1000
1000
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-AVC
10000+20000/50-30
Q=1500
7-5
TFC=20, P=10, PROFIT=2
A) BREAKEVEN OUTPUT=FC/P-VC
CM=P-VC
2=10-VC
VC=8
BREAKEVEN OUTPUT=20/10-8=10
B) PROFIT ELASTICITY=Q(P-VC)/Q(P-VC)-TFC
20(10-8)/20(10-8)-20
40/20
=2
7-6
A) BREAKEVEN OUTPUT=FC/P-VC
i)
500000/40-3=13513.5
ii)
510000/40-2=13421.0
iii)
380000/40-7=11515.1
iv)
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-VC
i)
200/20-15=40
ii)
500/20-10=50
iii)
1000/20-5=67
B) PROFIT ELASTICITY=Q(P-VC)/Q(P-VC)-TFC
i)
200(20-15)/ 200(20-15)-200=1.25
ii)
200(20-10)/ 200(20-10)-500=1.33
iii)
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=12000
ACCOUNT PROFIT 10000
SALARY 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 32000
SALARY FORGONE 20000
RATE OF INTEREST 12000
ECONOMIC PROFIT (0)
A)
B)
i)
ii)
iii)
C)
REVERSES CALCULATION
7-10
P=80, FC=200000, PROFIT=32
PROFIT ELASTICITY=Q(P-VC)/Q(P-VC)-TFC
i)
8000(80-48)/ 8000(80-48)-200000=4.57
ii)
10000(80-48)/ 10000(80-48)-200000=2.60
iii)
12000(80-48)/ 12000(80-48)-200000=2.08
FC=300000 VC=48-8=40 P=80
8000(80-40)/ 8000(80-40)-300000=16
8000(80-40)/ 8000(80-40)-300000=4
8000(80-40)/ 8000(80-40)-300000=2.66
Company increase risk and return by making investment in capital.
7-11
A) BREAKEVEN OUTPUT=FC/P-VC
10000/(900-700)=50
B) Assume Q=52
PROFIT ELASTICITY=Q(P-VC)/Q(P-VC)-TFC
52(900-700)/52(900-700)-10000
=26%
As Q increases profit elasticity declines
C) Q=60 , FC=11000 VC=700
60(900-700)/60(900-700)-11000
=12%
Q=60, FC=10000 VC=400
60(900-400)/60(900-400)-10000
=1.5%
PROVED
7-12
ADD FLIGHTS
7-13
A=TC=1000+0.03Q
B=TC=300+0.04Q
C=TC=100+0.05Q
B=C
300+0.04Q=100+0.05Q
Q=20000
If Q is less than 20000 than B is less than C
A=B
1000+0.03Q=300+0.04Q
700=0.01Q
Q=70000
If Q is less than 70000 than B is less than A
7-14
PROFIT+FIXED COST=100000
UNITS=10000
VARIABLE COST=4
VARIABLE COST=10000*4=40000
P=?
TR=140000
TR=P*Q
140000=P*10000
P=140000/10000
P=14
PROFIT+FIXED COST=100000
UNITS=11000
VARIABLE COST=4
VARIABLE COST=11000*4=44000
P=?
TR=144000
TR=P*Q
144000=P*10000
P=144000/10000
P=13.09
CHG IN PRICE=14-13.09
CHG PRICE=0.90
CHG IN PRICE= (14-13.09)*11000
CHG IN PROFIT=100001
7-15
a) TC=200Q-0.004Q^2
LONGRUN AVERAGE COST=TC/Q
LAC=200-0.004Q^2
7-16
TC=200-2Q+0.05Q^2
A) AC=TC/Q
AC=200Q^-1-2+0.05Q
AC’=-200Q^-2-2+0.05Q=0
=-200/Q^2+0.05Q=0
0.05Q=200/Q^2
SQ 4000=Q^2
Q=63.2
B) AC=200Q^-1-2+0.05Q
SO -1+1=0
DECREASING RETURN TO SCALE
C) MKT PRICE=4.32
AC=200/63.2-2+0.05 (63.24)
3.162-2+3.162
=4.32
7-17
TC=100Q-3Q^2+0.01Q^3
MC=100-6Q+0.03Q^2
AC=TC/Q
100-3Q+0.1Q^2
WE CAN SOLVE THIS BY 2 METHODS
i)
By taking AC’
ii)
AC=MC
WE WILL COLVE THIS BY AC’
-3+0.2Q=0
0.2Q=3
Q=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-TC
20Q-16+17Q-9Q^2+Q^3
ECONOMIC PROFIT=3Q-16-9Q^2+Q^3
B) MC=17-18Q+3Q^2
C) Q=8
AVC=17-9Q+Q^2
=17-9*8+8^2
=9
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
0
2
4
7
10
TOTAL COST
1000+80(0)=1000
1000+80(2)=1160
1000+80(4)=1320
1000+80(7)=1560
1000+80(10)=1800
MARGINAL COST
80
80
80
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
1
2
3
4
5
7-3
TC=200+5Q-0.04Q^2+0.001Q^3
MC=5-0.08Q+0.003Q^2
a) ATC , AVC , AFC , FC
FC=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
TOTAL COST
5000+1000(1)=6000
5000+1000(2)=7000
5000+1000(3)=8000
5000+1000(4)=9000
5000+1000(5)=10000
MARGINAL COST
1000
1000
1000
1000
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-AVC
10000+20000/50-30
Q=1500
7-5
TFC=20, P=10, PROFIT=2
A) BREAKEVEN OUTPUT=FC/P-VC
CM=P-VC
2=10-VC
VC=8
BREAKEVEN OUTPUT=20/10-8=10
B) PROFIT ELASTICITY=Q(P-VC)/Q(P-VC)-TFC
20(10-8)/20(10-8)-20
40/20
=2
7-6
A) BREAKEVEN OUTPUT=FC/P-VC
i)
500000/40-3=13513.5
ii)
510000/40-2=13421.0
iii)
380000/40-7=11515.1
iv)
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-VC
i)
200/20-15=40
ii)
500/20-10=50
iii)
1000/20-5=67
B) PROFIT ELASTICITY=Q(P-VC)/Q(P-VC)-TFC
i)
200(20-15)/ 200(20-15)-200=1.25
ii)
200(20-10)/ 200(20-10)-500=1.33
iii)
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=12000
ACCOUNT PROFIT 10000
SALARY 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 32000
SALARY FORGONE 20000
RATE OF INTEREST 12000
ECONOMIC PROFIT (0)
A)
B)
i)
ii)
iii)
C)
REVERSES CALCULATION
7-10
P=80, FC=200000, PROFIT=32
PROFIT ELASTICITY=Q(P-VC)/Q(P-VC)-TFC
i)
8000(80-48)/ 8000(80-48)-200000=4.57
ii)
10000(80-48)/ 10000(80-48)-200000=2.60
iii)
12000(80-48)/ 12000(80-48)-200000=2.08
FC=300000 VC=48-8=40 P=80
8000(80-40)/ 8000(80-40)-300000=16
8000(80-40)/ 8000(80-40)-300000=4
8000(80-40)/ 8000(80-40)-300000=2.66
Company increase risk and return by making investment in capital.
7-11
A) BREAKEVEN OUTPUT=FC/P-VC
10000/(900-700)=50
B) Assume Q=52
PROFIT ELASTICITY=Q(P-VC)/Q(P-VC)-TFC
52(900-700)/52(900-700)-10000
=26%
As Q increases profit elasticity declines
C) Q=60 , FC=11000 VC=700
60(900-700)/60(900-700)-11000
=12%
Q=60, FC=10000 VC=400
60(900-400)/60(900-400)-10000
=1.5%
PROVED
7-12
ADD FLIGHTS
7-13
A=TC=1000+0.03Q
B=TC=300+0.04Q
C=TC=100+0.05Q
B=C
300+0.04Q=100+0.05Q
Q=20000
If Q is less than 20000 than B is less than C
A=B
1000+0.03Q=300+0.04Q
700=0.01Q
Q=70000
If Q is less than 70000 than B is less than A
7-14
PROFIT+FIXED COST=100000
UNITS=10000
VARIABLE COST=4
VARIABLE COST=10000*4=40000
P=?
TR=140000
TR=P*Q
140000=P*10000
P=140000/10000
P=14
PROFIT+FIXED COST=100000
UNITS=11000
VARIABLE COST=4
VARIABLE COST=11000*4=44000
P=?
TR=144000
TR=P*Q
144000=P*10000
P=144000/10000
P=13.09
CHG IN PRICE=14-13.09
CHG PRICE=0.90
CHG IN PRICE= (14-13.09)*11000
CHG IN PROFIT=100001
7-15
a) TC=200Q-0.004Q^2
LONGRUN AVERAGE COST=TC/Q
LAC=200-0.004Q^2
7-16
TC=200-2Q+0.05Q^2
A) AC=TC/Q
AC=200Q^-1-2+0.05Q
AC’=-200Q^-2-2+0.05Q=0
=-200/Q^2+0.05Q=0
0.05Q=200/Q^2
SQ 4000=Q^2
Q=63.2
B) AC=200Q^-1-2+0.05Q
SO -1+1=0
DECREASING RETURN TO SCALE
C) MKT PRICE=4.32
AC=200/63.2-2+0.05 (63.24)
3.162-2+3.162
=4.32
7-17
TC=100Q-3Q^2+0.01Q^3
MC=100-6Q+0.03Q^2
AC=TC/Q
100-3Q+0.1Q^2
WE CAN SOLVE THIS BY 2 METHODS
i)
By taking AC’
ii)
AC=MC
WE WILL COLVE THIS BY AC’
-3+0.2Q=0
0.2Q=3
Q=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-TC
20Q-16+17Q-9Q^2+Q^3
ECONOMIC PROFIT=3Q-16-9Q^2+Q^3
B) MC=17-18Q+3Q^2
C) Q=8
AVC=17-9Q+Q^2
=17-9*8+8^2
=9
