Post on 13-Jul-2020
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EUAC , EUAB ......................................
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(TX) ..............................................................................................
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(f) ........................................................................................
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if ...............................................................................
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•
Capital
Labor
Land
Management
Technology
Goods
Services
•
•
•
Price Theory
•
•
•
Px
T
C
I
Pn
R
X
X= f (Px, T, C, I, Pn, R)
Px
T
C
I
Pn
R
Demand
Supply
Market Price
Demand Curve
X
X= f(px) ,
Px= g(x)
X
x
px
D
x
x
px
S
•
X= h(px)
Px= k(x)
X
P
Pe
P
X
Px
M
K
N
L
D S (Excess)
(Shortage)
x X’
O X’ Xe
Ox’ – Ox = x x = MN Pe
Ox – Ox’ = x’ x = KL Pe
Pe
x Px= g(x)= - x +
px = k(x)= x +
ep
χ
χχχ
χχ
xp
ppppe .
/
/
Δ
Δ=
Δ
Δ=
xy
x
y
y
x
y
yx
x
xy ⋅Δ
Δ=
Δ
Δ
=Ε
x
7=ΡΧ
Equilibrium Price
Elasticity
Price Elasticity of Demand
ep=
5.10200
2100)
100
7).(
57
400100()).(( −=−=
−
−=
Δ
Δ=
ΧΧΡX
P
P
xE
x
)).((x
p
dp
dxpE x
x
xx =
xx= ppx=
2006 =→= xp
3200
6100)).(( −=×−==
x
p
dp
dxE x
x
px
x
D
xx= px - px + px=
2=xp
93222 2 =+−×=X
14 −= x
x
pdp
dx
x
pp
x
p
dp
dxpE x
xx
x
xx ×−=×= )14(
)92( == xpx
56.19
14
9
2)124( ==×−×=xx pE
x52
+−
=x
px
n
Xn= apn+bpi+cy
Y =
Pn = n
Pi = i
C =
a= b=c=pi =y =
122
122)1001.0()45.0(2
+−=
+−=×+×+−=
nn
nnn
pX
ppX
pn
xn
o
5.14
32
431021022
10
−=×−=×=
=→=→+−=→+−=→+−
=
x
p
dp
dxpE
xppxxpx
p
x
x
xx
xxxx
(TR)
TR=Px.X
(AR)
x
x PX
XP
X
TRAR ===
Total Revenue
Average Revenue
(MR)TR
dX
dTRMR =
Px= x x
232
10
32
10
610100)25100(
250010250
25100.
25020050100
xxxxxdx
d
dx
dTRMR
TR
XPTR
P
x
x
xx
=−=+−×==
=×=
Χ+Χ−Χ==
=+−=
=
=
MR>
MR<
MR=
(TC)
TC = Cx .x
(AC)
AC = TC x
(MC)TC
MC = dTC/dx
)(
= TR- TC
Marginal Revenue
Total Cost
Average Cost
Marginal Cost
MC = MR
Px = x
TC = x
MC = MR
MC =dTC/dx=
TR = Px.x = x x
MR = dTR/dx= x
x= x= px=
Px= -x
TC = x + x +
a
b
c
= = TR – TC = Px.X- TC= ( -X)X- (X X ) = X + X-
d /dX= X = X=
Px= -X= =
x x = =
TR=P.X= ( )=
TC= + * =
Pure Competition
0→Δ
∞=×Δ
Δ=
x
x
xx
P
x
P
P
xPE
Perfect Competitio
Pl
x
P
•
px
x
D
x
•
•
•
•
Px
Px D
D
x
•
•
X= f(a,b,c)
X
a,b,c
•
A
A
Production Function
The Law of Diminishing Marginal Physical Product
MP = MPP = dx/d = f ( )
Marginal physical product
X
l
TP = x = f( )
AP = x/ = f( )/
A
A
C = K + f(x)
TC TFX TVC
C/X = K/X + f(x)/X
AC AFX AVC
= TR – TC = f(x) – g(x)
TC = Total Cost
TFX = Total Fixed Cost
TVX = Total Variable Cost
AC = Average Cost
AFX = Average Fixed Cost
AVX = Average Variable Cost
D / dx= f (x) –g (x) =
f (x) = g (x)
MR=MC
D / dx <
•
•
•
•
•
E = f (x , y)
E
X
Y
x
A
6%100100000
6000=∗
B
ROR
ROR
Rate of Return (ROR)
P
F
A
i
n
+
–
Present Worth
Future Worth
Uniform Annual Cost
Interest Rate
Number Of Interest Period
nn-
PF
)1(1 iPPiPF +=+=
iFFF 112 +=
( ) ( ) 2
12 )1(1)1(1 iPiiPiFF +=++=+= 2
2 )1( iPF +=
“ “ “
n
( ) n
nn iPiFF )1(11 +=+= −
P=
i=
A=
A= A= A=
n=
i=
F ?
F=?
niPF )1()1 +=
nI
FP)1(
1)2
+=
( i)n
/ ( i)n
PA
))1(
1)1((
n
n
ii
iAP
+
−+=
1)1(
)1((
−+
+=
n
n
I
IIPA
FA
)1)1(
(i
iAF
n−+
= )1)1(
(−+
=n
i
iFA
P=?
A
n n
A A A A
i=
P
F
n
n n
i=
(X / Y , i% , n)
(F/P, , ) =
(A/P, , ) =?
(A/P, , ) = =
(A/P, , ) = =
b a c
d
X=?
a / c = b / d a = – = c = ?
b = – = d = –
c = X = + = =
P=F(P/F ,i% ,n) (P/F , i% , n) F p
F=P(F/P ,i% ,n) (F/P , i% , n) P F
P=A(P/A ,i% ,n) (P/A , i% , n) A P
A=P(A/P ,i% ,n) (A/P , i% , n) P A
A=F(A/F ,i% ,n) (A/F , i% , n) F A
F=A(F/A ,i% ,n) (F/A , i% , n) A F
A= F(A/F, i%, n)
i=
A=
F=
F= A(F/A, i%, n) = (F/A, , ) = ( )=
PT =PA + PA
PA = PA' (P/F, , ) = PA (P/A, , ) (P/F, , )
= ( ) ( )=
PA = PA' (P/F, , ) = A (P/A, , ) (P/F, , )
= ( ) ( )=
PT= + =
PA' =?
A = A =
PT
i=
A =A =
PT=?
PA' =?
PA
PA
x
PT = P + P +P
= x(P/A, , ) + x(P/A, , )(P/F, , ) + x(P/A, , )(P/F, ,
)
= x ( ) X( )( ) X( )( )
X=
PT=
x x x
x x x
x x x
i=
P
P
P
x x x
x x x
x x x
GP
)%,,/(
)1()1(
1)1(
niGPGP
i
n
ii
i
i
GP
nn
n
=
+−
+
−+=
GA
)%,,(
1)1(
1
niGAGA
i
n
iGA
n
=
−++=
G=
PT = ?
A=
PA = ?
PT = PA + PG
PT = (P /A, , ) + (P/G , , )
PT = ( )+ ( )=
n- n
A
A
An-
An
A
PG = ?
G=
At = At ( + j) t = , , n
i
j
t
Att
A
jiji
ijAP
ntjAA
nn
t
t
≠−
++−=
=+=
−
−
)1()1(1
,...,1)1(
1
1
1
jii
nAP =
+=
)1(
)( 1
),,,(1 njiAPAP =
j > j = i # j
jijji
niFPnjPFAP ≠≥
−
−= 0
),,)(,,(11
A =
j = i = n =
P = A (P/A, , , )
P = ( ) =
73.2272721.1
50005
1
%10
1 =×
=+
=
==
i
nAP
ji
ie= ( + r/t)t –
= ie
= r
= t
r =
ie = ( + / ) – =
Effective Interest Rate
Nominal Interested Rate
Number Of Compounding Periods
F= ?
ie = ( + / ) - = =
F = (F/P, , ) + (F/P, , ) + (F/P, , )
=
11 −+=
t
et
ri
Continuous Compounding
n
F = P ( r/t)tn
r
t
n
F= P lim ( r/t)tn =Pe
r.n
t
F = Per.n
e =
F = P(F/P, r, n)
P = Fe –rn
P = F(P/F, r, n)
ie=er -
/ =
=
F = A(F/A, , ) = (F/A, , ) = ?
Ie = ( r/t)t – = ( + / )
– =
F = A(F/A, ie, )
=
F= P(F/P, , )
F= ( ) =
•
•
• NPW
NPW<
NPW>NPW=
PW
ABMARR
Present Worth Method
Equivalent Uniform Annual Cost (Benefit)
Benefit to Cost Method
BA
PWA = + (P/A, , ) – (P/F, , ) =
PWB = + (P/A, , ) (P/F, , ) =
A
BA
PWA= + (P/F, , ) – (P/F, , ) + (P/F, , ) –
(P/F, , ) – (P/F, , ) + (P/A, , ) =
B
A=
SV=
A=
SV=
A=
PWB= + (P/F, , ) – (P/F, , ) (P/F, , ) +
(P/A, , ) =
PWA<PWB A
P
A
1)1(
)1(
−+
+=
∞→
n
n
i
iiPA
n
iAPPiA
n
Pii
iiPA
n
n
=→=
∞→
=−+
+=
1)1(
)1(limlim
PWB
35000040000005.0
20000===
i
AP
EUAC , EUAB
•
•
•
•
P =
n =
SV =
EUAC= P(A/P, i%, n)-SV(A/F, i%, n) + …
EUAC= (A/P, , ) + – (A/F, , )=
(A/P,i%,n)
EUAC
BA
EUACA = (A/P, , ) – (A/F, , ) + + =
EEUACB = (A/P, , ) – (A/F, , ) + + =
BEUACB < EUACA
(i)
ROR= Rate Of Return
MARR= Minimum Attractive Rate of Return
ROR > = MARR
ROR < MARR
ROR
NPW=
PWB=PWC PWB – PWC = i = ROR
-P +A(P/A, i%,n) + SV(P/F,i%,n) +…=
+ (P/F,i%, ) + (P/F,i%, )=
i
=i
P=
N=
A=
F=
,i,P/F,i,P/A
F
n,i,P/F
n,i,P/F
i
a i b
c d
A=
P =
F=
%16.516.05
16.046.6919.355
%5%6
46.69
=+==
=→−−
−=
=
iROR
aa
d
c
b
a
NEUA=
NUAB=EUAC EUAB-EUAC=
-P(A/P,i%,n)+A+SV(A/F,i%,n) + =
i
MARR
ROR
ROR MARR
RORMARR
ROR
NPWNEUA
ROR(A)(B)
(A)(B)
= +
PWX PWY NPW
MARR
MARR
NPW
NPW
NEUA
NEUA
Extra Inuestment Analysis
PWBX
X
PWCX
PWBY
Y
PWCY
PWBZ
Z
PWCZ
PWBW
W
PWCW
MARR=a%
ROR MARR
ROR MARR
XYZ
W
X,YXYY
Z,YYZY
PWB
PWBZ
PWBY
PWBW
PWBX
PWC PWCW PWCZ PWCY PWCX
Z
Y
X
NPW=
MARR=a%
W
MARR
MARR
YX
X PWC= – (P/F, , )+ (P/F, , ) – (P/F, , )
=
PWB= (P/A, , )=
Y PWC= (P/F, , )=
PWB= (P/A, , )=
XYMARR=
PWB
PWC
NPW=
Y
X
PWB=
X
PWC=
PWB=
Y
PWC=
PWB=
Z
PWC=
PWB
PWC
= MARR
Y
X
Z
C’
B’
A’
NPW=
XY Y
YZY
n= , MARR=
E C A B D
PWC
PWB
PWB
PWC
MARR=
E C
A
B
D
NPW=
A
NPW= MARR
PWC=PWB NPW=
(MARR)
MARR=
EDC B A
EC A BD
DB
= (P/A, i%, ) ROR=
B
BA
ROR=
A
AC
ROR=
MARR=A
C
AE
ROR~ c
A
B / C = ( – ) /
(B/C)= ( PW / PW) = (PWB / PWC)
B/C= EUA / EUA = EUAB / EUAC
B/C > = B-C > =
B/C < B-C <
13135.150000)20%,10,(1000000
30000150000100000=
+
−+==
PAEUAC
EUAB
C
B
B / C = PWB / PWC
B / C = EUAB / EUAC
= ( B / C)
( B / C)
EDC B A
PWC
PWB
B/C
A B
PWC=
PWB= B / C = B
B C
PWC=
PWB= B / C = C
D C
PWC=
PWB= B / C = C
E C
PWC=
PWB= B / C = C
C
D = (P-SV) / n
D=
P =
SV=
Depreciation
Book Value
n=
m
BVm = P-m.D m= , , , … , n
45000)70005(800005
700010
1000080000
5 =×−=−=
→−
→−
=
DPBV
n
SVPD
m= BV = P =
m= n BVn = P- nD = SV
BVm= BVm – D
nM
SVPSYD
mnDm
,...,2,1
)(1
=
−+−
=
Dm=m
n=
m=
P=
SV=
Sum of the years Digits Method (SOYD)
2
)1(
1
+==
=
nnmSYD
n
m
(SOYD)
818.55)1000080000(55
)5.0)22(10(280000
)()5.0)2((
455.11)1000080000(55
1210
)(1
552
1110
2
)1(
10000
10
80000
2
2
=−+−−
=
−+−
=
=−+−
=
−+−
=
=×
=+
=
=
=
=
BV
SVPSYD
mnmBV
D
SVPSYD
mnD
nnSYD
SV
n
P
m
m
/n
Declining Balance Method (DB)
)()5.0)2((
SVPSYD
mnmPBVm −
+−−=
Dm = BVm (d)
BVm= P( -d)m
Dm = d.P( -d)m
d
SV= BVn = P( -d)n
SV/P = ( -d)n
d = - (SV/P)/n
P =
n =
Dm = d.P( -d)m
D = ( – ) =
BVm = P( -d)m
BV = ( – ) =
Dm = (P-SV) (A/F, i%, n) (F/P, i%, m )
BVm = P-(P-SV) (A/F, i%, n) (F/A,i%,m)
Sinking Fund Method
nA
(i%)(P-SV)
A = (P-SV) (A/F, i%, n)
D = ( – ) (A/F, , ) (F/P, , ) =
BV = – ( – ) (A/F, , ) (F/A, , ) =
Dm= (P-SV)Um / U
Um=m
U=
Dm = (P-SV) (Qm / Q)
Qm= m
Q=
n
PWD = Dm (P/F, i%, m)
m=
EUAD = PWD(A/P, i%, n)
PWDEUAD
(TX)
(GI)
(GFAT)
(OC)
(TR)
Cash Flow After Tax (CFAT)
(TX) TAX
Gross Income
Cash Flow After Tax
Operating Costs
Tax Rate
Cash Flow Before Tax
= –
CFBT = GI – OC
(TI)
= –
TI = CFBT – D
TI = GI – OC – D
(Tax)
=
TX = TI .TR
(CFAT)
=
CFAT = CFBT – TX
CFAT = CFBT – (CFBT – D) TR
CFAT = CFBT ( -TR) + D.TR
(NPW)
n
NPW = - P + CFATj (P/F, i%, j)
j=
NPW
(NEUA)
NEUA = NPW (A/P, i%, n)
NEUA
Taxable Income
NPW =
n
- P + CFATj (P/F, i%, j)= i=?
j=
i MARR
i<MARR
NEUA =
NPW(A/P, i%, n) = i=?
i MARR
i<MARR
P=
SV=
N=
K= , , , ,
(GI) = – K
(OC) = + K
CFAT
a
b
CFBT-TXTI.TR CFBT-D GI-OC
CFAT TX IT D CFBT OC GI
n
NPW = - P + CFATj (P/F, i%, j)
j=
NEUA=NPW(A/P, i%, n)
NPW= - + (P/F, , ) + (P/F, , ) + (P/F, ,
) + (P/F, , ) + (P/F, , )
NPW=
NEUA= (A/P, , )
NEUA=
CFAT TX TI D CFBT
+ (P/A, i%, ) + (P/F, i%, )=
ROR=
ROR<MARR
(TS)
CFAT=(GI-OC)-(GI-OC-D).TR
=(GI-OC)-(GI-OC)TR+D.TR
=(CFBT)( -TR)+D(TR)
TS=D(TR)
D
D(TR)
n
PWTS = Dm (P/F, i%, m) (TR)
m=
Tax Saving
(i)
PR
I
CFBT=GI-OC
TI=CFBT-D-I
TX=TI.TR
CFAT=CFBT-TX-I-PR
=TR
Principle
Interest
=MARR
PR=
I=
30005
015000=
−=D
Any year = GI-OC =
CFBT D TI TX CFAT
(P/A, i%, )= ROR=
NPW=
MARR=
I= ( )=
PR= ( ) / =
CFBT D I PR TI TX CFAT
CFAT =
NPW= + (P/A, i%, )=
i= ROR=
n
n
EUACEUAC
Replacement Analysis
Retirement
Defender
Replacement
Challenger
(SV)
,,F/A,,A/A
,,A/G
EUAC
EUAC (A/G, ,n) (A/P, ,n)
–SVt(A/F, ,n)
)n(
EDRV= = EUACD - EUACC
EDRV> EUACD>EUACC
EUACD = P(A/P, , ) – (A/F, , ) + = P +
EUACC = (A/P, , ) (A/F, , )+ =
P + – =
P=
•
•
•
•
•
•
Sensivity Analysis
PW= PW=PW=
PW= PW= PW=
PW= PW= PW=
PW
PW
Isoquant Curve
P= MARR=
= N=
SV=
=
,,A/F,,A/PNEUA
X ,,A/FY,,A/PNEUA
NEUA= + X- Y
NEUA>
NEUA=
NEUA<
NEUA=
X- Y+ =
X= Y= / =
Y= X= / =
X
Y
Y
X
NEUA>
NEUA<
NEUA=
- - - - -
(M)
(O)
(P)
P, O, M
Estimate
Most likely
Optimistic
Pessimistic
Mean
Variance
Beta Distribution
O M+P
O-P
O MP
O) = (P/A, i%, ) + (P/F, i%, ) RORO =
M) = (P/A, i%, ) RORM=
P) = (P/A, i%, ) RORP=
MARR
= ( ( )+ ) / =
= ( ( )+ ) / =
= ( ( )+ ) / =
= ( ( )+ ) / =
= (P/A, i , ) + (P/F, i%, ) ROR=
Point to point
X
X,,F/A,,A/PEUACO
X
XX
X,,A/PEUACD
X
xXxEUACD EUACO
B
X
XxX
•
•
•
•
•
Inflation
Price Inflation
Cost Inflation
APP
if = ((p – P ) / P )
if =
P(t) = t
P(t+ t)= t
t
P(t+ t)= P(t)( if)
P(t+n t)= P(t)( if)n
nt
K
ifkK
K = K ( ifk)
ifk = ( K . ) / (K . )
ifk = ( K . ) / (K . )
n
Inflation Rate
ififif
Pn
Pn= P ( if ) ( if ) ( if ) …. ( ifn)
Y(t)VP(t)
V= (Y(t)) / (P(t))
V= (Y(t )) / (P(t )) = (Y(t )) / (P(t )) = (Y(t )) / (P(t ))
tY'(t)
Y'(t)= (Y(t)) . (P(t )) / P(t)
P(t ) / P(t) = / ( if)n
= Dc / Da , n= t - t / t
D(t) = P(t ) / P(t) = Dc / Da
D(t)= / ( if)n = P(t ) / P(t) = Rc /Ra
Actual Dollar
Constant Dollar
Y'(t)= D(t) Y(t)
( / ) =
nM
In = ((Pn / PK ) + (Pn / PK ) + …. + (Pnm / PKm)) / M
K
n
M
Pnmmn
PKmm(K)
In = ((Pn W / PK ) + (Pn W / PK ) + …. + (PnmWm / PKm)) / (W + W +
… + Wm)
Wi
Price Index
WPI
CPI
WPI
IPI
If(t )= ((CPI(t ) – CPI(t)) / CPI(t))
CPI
= ( ) =
Wholesale Price Index
Consumer Price Index
Implicit Price Index
CPI
CPI CPICPI
.
( )=
- =
F= P(F/P, %, )
F= (f/p, %, )= ( + ) =
F= (F/P, , ) =
( +if = ) =
- =
(if= )
- ( / )=
CPI
=
= ( ) ( ) = ( ) ( ) =
= ( if)if
( - )
( if )( if ) … ( if )( if )= ( if)
A= (A/P, , ) =
K
/( )k = ( )
-k
( ) = ( )=
( ) =
( ) =
( ) =
( ) =
( ) =
( ) =
( ) =
( ) =
( ) =
( ) =
i
i'
i'
i=i'
(if)
i
i'
Market Interest Rate
Inflation- Free Rate
ii'if
ffCn
i=
( if)n
/ ( if)n
( i)n
( i')n
/ ( i)n
/ ( i')n
F
FC
n n-
n- n
P = A(P/A, , )
P = (P/A, , )
aC = / ( ) =
aC = / ( ) =
aC = / ( ) =
aC = / ( ) ( ) =
aC = / ( ) ( ) =
i=
aC = / ( ) ( ) =
aC = / ( ) ( ) =
aC = / ( ) ( ) =
(f)
f
a
abf
)( −=
a
b
08.0200
)200216(=
−=f
%1.7%71
176
2161216)1(176 3
3
=→=
=+→=+
ff
ff
if
if
PFtt
P= Ft / ( f)t ( i)
t
P= Ft / ( if)t ( i)
t ( f)
t = ( if)
t
if = i + f + if
If = + + =
098.14.195
)4.1951.214(1=
−+=CPI
= =
(Types of Inflation)
(Demand-Pull Inflation)
(Cost Push Inflation)
(Effects of Inflation)
(Inefficiency)
(Stagflation)
(Economic growth)
(Business Cycles)
•
•
•
•
Recession
Slump
Expansion
Boom
•
•
•
•
Gross National product (GNP)
Gross Domestic Product (GDP)
(GDP)
GNP=GDP+NA
. G. J. Thuesen, W. J. Fabrychy, Engineering Economy, (Prentice-Hall
international Series in Industrial and Systems Engineering), Prentice-
Hall College Div; ISBN: X; edition, .
. James L. Riggs, David D. Bedworch, Sabah U. Randhawa,
Engineering Economic, McGraw-Hill, Higher Education, ISBN;
, th edition, .
. Gerald W. Smit, Engineering Economy: Analysis of Capital
Expenditures, Iowa state university press, ISBN: ; th
edition, .
. Eugene Lodewick Grant, William B. Areson, William G. Ireson,
Principle of Engineering Economy, th edition, John Wiley & Sons;
ISBN: X; .
. Leland T. Blank, Anothony J. Tarquin, Engineering Economy,
McGraw-Hill, Series in Industrial Engineering and Management
science, McGraw-Hill Collage Div; ISBN; , th
edition,
.
. J. C. Sprague, J. D. Whittaker, Economic Analysis for Engineers and
Managers, Prentice-Hall, ISBN; , .
www.engclubs.net