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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